TSTP Solution File: SWW306+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW306+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:07:00 EDT 2024
% Result : Theorem 157.60s 157.50s
% Output : CNFRefutation 157.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWW306+1 : TPTP v8.2.0. Released v5.2.0.
% 0.05/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Wed Jun 19 06:25:24 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.14/0.47 start to proof:theBenchmark
% 157.26/157.35 %-------------------------------------------
% 157.26/157.35 % File :CSE---1.7
% 157.26/157.35 % Problem :theBenchmark
% 157.26/157.35 % Transform :cnf
% 157.26/157.35 % Format :tptp:raw
% 157.26/157.35 % Command :java -jar mcs_scs.jar %d %s
% 157.26/157.35
% 157.26/157.35 % Result :Theorem 143.320000s
% 157.26/157.35 % Output :CNFRefutation 143.320000s
% 157.26/157.35 %-------------------------------------------
% 157.34/157.36 %------------------------------------------------------------------------------
% 157.34/157.36 % File : SWW306+1 : TPTP v8.2.0. Released v5.2.0.
% 157.34/157.36 % Domain : Software Verification
% 157.34/157.36 % Problem : Hoare's Logic with Procedures 434896, 5000 axioms selected
% 157.34/157.36 % Version : Especial.
% 157.34/157.36 % English :
% 157.34/157.36
% 157.34/157.36 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 157.34/157.36 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 157.34/157.36 % Source : [Bla11]
% 157.34/157.36 % Names : hoare_434896.5000.p [Bla11]
% 157.34/157.36
% 157.34/157.36 % Status : ContradictoryAxioms
% 157.34/157.36 % Rating : 0.72 v7.5.0, 0.75 v7.4.0, 0.87 v7.3.0, 0.86 v7.1.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0
% 157.34/157.36 % Syntax : Number of formulae : 5230 (1698 unt; 0 def)
% 157.34/157.36 % Number of atoms : 12686 (4462 equ)
% 157.34/157.36 % Maximal formula atoms : 13 ( 2 avg)
% 157.34/157.36 % Number of connectives : 8446 ( 990 ~; 148 |; 704 &)
% 157.34/157.36 % ( 891 <=>;5713 =>; 0 <=; 0 <~>)
% 157.34/157.36 % Maximal formula depth : 22 ( 6 avg)
% 157.34/157.36 % Maximal term depth : 19 ( 2 avg)
% 157.34/157.36 % Number of predicates : 151 ( 150 usr; 0 prp; 1-6 aty)
% 157.34/157.36 % Number of functors : 394 ( 394 usr; 51 con; 0-7 aty)
% 157.34/157.36 % Number of variables : 16681 (16523 !; 158 ?)
% 157.34/157.36 % SPC : FOF_CAX_RFO_SEQ
% 157.34/157.36
% 157.34/157.36 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 157.34/157.36 % 2011-03-01 11:36:31
% 157.34/157.36 %------------------------------------------------------------------------------
% 157.34/157.36 %----Relevant facts (4985)
% 157.34/157.36 fof(fact_ext,axiom,
% 157.34/157.36 ! [V_g_2,V_f_2] :
% 157.34/157.36 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 157.34/157.36 => V_f_2 = V_g_2 ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_empty,axiom,
% 157.34/157.36 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 157.34/157.36 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_triple_Oinject,axiom,
% 157.34/157.36 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 157.34/157.36 ( c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2) = c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_H_2,V_com_H_2,V_fun2_H_2)
% 157.34/157.36 <=> ( V_fun1_2 = V_fun1_H_2
% 157.34/157.36 & V_com_2 = V_com_H_2
% 157.34/157.36 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_cut,axiom,
% 157.34/157.36 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 157.34/157.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 157.34/157.36 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 157.34/157.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_hoare__derivs_Oinsert,axiom,
% 157.34/157.36 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 157.34/157.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.36 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 157.34/157.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_bot__fun__def,axiom,
% 157.34/157.36 ! [V_x_2,T_c,T_b] :
% 157.34/157.36 ( class_Orderings_Obot(T_b)
% 157.34/157.36 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_triple_Orecs,axiom,
% 157.34/157.36 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_triple_Osimps_I2_J,axiom,
% 157.34/157.36 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_empty__not__insert,axiom,
% 157.34/157.36 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_insert__not__empty,axiom,
% 157.34/157.36 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_doubleton__eq__iff,axiom,
% 157.34/157.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.34/157.36 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.34/157.36 <=> ( ( V_a_2 = V_ca_2
% 157.34/157.36 & V_b_2 = V_d_2 )
% 157.34/157.36 | ( V_a_2 = V_d_2
% 157.34/157.36 & V_b_2 = V_ca_2 ) ) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_singleton__inject,axiom,
% 157.34/157.36 ! [V_b_2,V_a_2,T_b] :
% 157.34/157.36 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 157.34/157.36 => V_a_2 = V_b_2 ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_bot__apply,axiom,
% 157.34/157.36 ! [V_x_2,T_c,T_b] :
% 157.34/157.36 ( class_Orderings_Obot(T_b)
% 157.34/157.36 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_hoare__derivs_OSkip,axiom,
% 157.34/157.36 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSKIP,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 157.34/157.36 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_a2_2,c_Com_Ocom_OSKIP,V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_conseq2,axiom,
% 157.34/157.36 ! [V_Qa_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 157.34/157.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.36 => ( ! [B_Z,B_s] :
% 157.34/157.36 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 157.34/157.36 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
% 157.34/157.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 157.34/157.36
% 157.34/157.36 fof(fact_conseq1,axiom,
% 157.34/157.36 ! [V_Pa_2,V_Qa_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 157.34/157.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_H_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.36 => ( ! [B_Z,B_s] :
% 157.34/157.36 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 157.34/157.36 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 157.34/157.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_insert__code,axiom,
% 157.34/157.37 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 157.34/157.37 <=> ( V_y_2 = V_x_2
% 157.34/157.37 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_insert__commute,axiom,
% 157.34/157.37 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_insert__absorb2,axiom,
% 157.34/157.37 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_the__elem__eq,axiom,
% 157.34/157.37 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Comp,axiom,
% 157.34/157.37 ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 157.34/157.37 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.37 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Qa_2,V_d_2,V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.37 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSemi(V_ca_2,V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_conseq12,axiom,
% 157.34/157.37 ! [V_Qa_2,V_Pa_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 157.34/157.37 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_H_2,V_ca_2,V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.34/157.37 => ( ! [B_Z,B_s] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 157.34/157.37 => ! [B_s_H] :
% 157.34/157.37 ( ! [B_Z_H] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 157.34/157.37 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) )
% 157.34/157.37 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) )
% 157.34/157.37 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 157.34/157.37 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2)),c_Com_Ocom_OAss(V_a3_2,V_a4_2),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Ass,axiom,
% 157.34/157.37 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2)),c_Com_Ocom_OAss(V_X_2,V_a_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_the__elem__def,axiom,
% 157.34/157.37 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Collect__conv__if,axiom,
% 157.34/157.37 ! [T_b,V_a_2,V_Pa_2] :
% 157.34/157.37 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.34/157.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 157.34/157.37 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.34/157.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Collect__conv__if2,axiom,
% 157.34/157.37 ! [T_b,V_a_2,V_Pa_2] :
% 157.34/157.37 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.34/157.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 157.34/157.37 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.34/157.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_singleton__conv,axiom,
% 157.34/157.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_singleton__conv2,axiom,
% 157.34/157.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__constant__conv,axiom,
% 157.34/157.37 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.34/157.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.34/157.37 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.34/157.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.34/157.37 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__singletonD,axiom,
% 157.34/157.37 ! [V_x_2,V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 157.34/157.37 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.34/157.37 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__refl,axiom,
% 157.34/157.37 ! [V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Opreorder(T_a)
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_equalityI,axiom,
% 157.34/157.37 ! [V_B_2,V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.34/157.37 => V_A_2 = V_B_2 ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_empty__subsetI,axiom,
% 157.34/157.37 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__refl,axiom,
% 157.34/157.37 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Collect__def,axiom,
% 157.34/157.37 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 157.34/157.37
% 157.34/157.37 fof(fact_le__fun__def,axiom,
% 157.34/157.37 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.34/157.37 ( class_Orderings_Oord(T_c)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.34/157.37 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_linorder__linear,axiom,
% 157.34/157.37 ! [V_y,V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Olinorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.34/157.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_set__eq__subset,axiom,
% 157.34/157.37 ! [T_b,V_B_2,V_A_2] :
% 157.34/157.37 ( V_A_2 = V_B_2
% 157.34/157.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__eq__iff,axiom,
% 157.34/157.37 ! [V_y_2,V_x_2,T_b] :
% 157.34/157.37 ( class_Orderings_Oorder(T_b)
% 157.34/157.37 => ( V_x_2 = V_y_2
% 157.34/157.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.34/157.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__image__iff,axiom,
% 157.34/157.37 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.34/157.37 <=> ? [B_AA] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 157.34/157.37 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_equalityD1,axiom,
% 157.34/157.37 ! [T_b,V_B_2,V_A_2] :
% 157.34/157.37 ( V_A_2 = V_B_2
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_equalityD2,axiom,
% 157.34/157.37 ! [T_b,V_B_2,V_A_2] :
% 157.34/157.37 ( V_A_2 = V_B_2
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__eq__refl,axiom,
% 157.34/157.37 ! [V_y,V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Opreorder(T_a)
% 157.34/157.37 => ( V_x = V_y
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_le__funD,axiom,
% 157.34/157.37 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 157.34/157.37 ( class_Orderings_Oord(T_c)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__mono,axiom,
% 157.34/157.37 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__antisym__conv,axiom,
% 157.34/157.37 ! [V_x_2,V_y_2,T_b] :
% 157.34/157.37 ( class_Orderings_Oorder(T_b)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.34/157.37 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_ord__eq__le__trans,axiom,
% 157.34/157.37 ! [V_c,V_b,V_a,T_a] :
% 157.34/157.37 ( class_Orderings_Oord(T_a)
% 157.34/157.37 => ( V_a = V_b
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_xt1_I3_J,axiom,
% 157.34/157.37 ! [V_c,V_b,V_a,T_a] :
% 157.34/157.37 ( class_Orderings_Oorder(T_a)
% 157.34/157.37 => ( V_a = V_b
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__trans,axiom,
% 157.34/157.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_ord__le__eq__trans,axiom,
% 157.34/157.37 ! [V_c,V_b,V_a,T_a] :
% 157.34/157.37 ( class_Orderings_Oord(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.34/157.37 => ( V_b = V_c
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_xt1_I4_J,axiom,
% 157.34/157.37 ! [V_c,V_a,V_b,T_a] :
% 157.34/157.37 ( class_Orderings_Oorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.34/157.37 => ( V_b = V_c
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__antisym,axiom,
% 157.34/157.37 ! [V_y,V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Oorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.34/157.37 => V_x = V_y ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_order__trans,axiom,
% 157.34/157.37 ! [V_z,V_y,V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Opreorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_xt1_I5_J,axiom,
% 157.34/157.37 ! [V_x,V_y,T_a] :
% 157.34/157.37 ( class_Orderings_Oorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.34/157.37 => V_x = V_y ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_xt1_I6_J,axiom,
% 157.34/157.37 ! [V_z,V_x,V_y,T_a] :
% 157.34/157.37 ( class_Orderings_Oorder(T_a)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_equalityE,axiom,
% 157.34/157.37 ! [T_b,V_B_2,V_A_2] :
% 157.34/157.37 ( V_A_2 = V_B_2
% 157.34/157.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_le__funE,axiom,
% 157.34/157.37 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 157.34/157.37 ( class_Orderings_Oord(T_c)
% 157.34/157.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_linorder__le__cases,axiom,
% 157.34/157.37 ! [V_y,V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Olinorder(T_a)
% 157.34/157.37 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__image,axiom,
% 157.34/157.37 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_empty__is__image,axiom,
% 157.34/157.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.34/157.37 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
% 157.34/157.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__empty,axiom,
% 157.34/157.37 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__is__empty,axiom,
% 157.34/157.37 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.34/157.37 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.34/157.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_image__insert,axiom,
% 157.34/157.37 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_empty__Collect__eq,axiom,
% 157.34/157.37 ! [V_Pa_2,T_b] :
% 157.34/157.37 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 157.34/157.37 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_Collect__empty__eq,axiom,
% 157.34/157.37 ! [V_Pa_2,T_b] :
% 157.34/157.37 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.34/157.37 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_bot__least,axiom,
% 157.34/157.37 ! [V_x,T_a] :
% 157.34/157.37 ( class_Orderings_Obot(T_a)
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__empty,axiom,
% 157.34/157.37 ! [V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.34/157.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__insertI,axiom,
% 157.34/157.37 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_subset__insertI2,axiom,
% 157.34/157.37 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_insert__mono,axiom,
% 157.34/157.37 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 157.34/157.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 157.34/157.37
% 157.34/157.37 fof(fact_asm,axiom,
% 157.34/157.37 ! [V_Ga_2,V_ts_2,T_b] :
% 157.34/157.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 157.34/157.37 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 157.34/157.37
% 157.34/157.38 fof(fact_weaken,axiom,
% 157.34/157.38 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 157.34/157.38 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 157.34/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 157.34/157.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_empty__def,axiom,
% 157.34/157.38 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_insert__Collect,axiom,
% 157.34/157.38 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I13_J,axiom,
% 157.34/157.38 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I12_J,axiom,
% 157.34/157.38 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I9_J,axiom,
% 157.34/157.38 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I8_J,axiom,
% 157.34/157.38 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I25_J,axiom,
% 157.34/157.38 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_com_Osimps_I24_J,axiom,
% 157.34/157.38 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 157.34/157.38
% 157.34/157.38 fof(fact_the__eq__trivial,axiom,
% 157.34/157.38 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_the__sym__eq__trivial,axiom,
% 157.36/157.38 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__ident,axiom,
% 157.36/157.38 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_com_Osimps_I3_J,axiom,
% 157.36/157.38 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 157.36/157.38 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 157.36/157.38 <=> ( V_com1_2 = V_com1_H_2
% 157.36/157.38 & V_com2_2 = V_com2_H_2 ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_com_Osimps_I1_J,axiom,
% 157.36/157.38 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 157.36/157.38 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 157.36/157.38 <=> ( V_vname_2 = V_vname_H_2
% 157.36/157.38 & V_fun_2 = V_fun_H_2 ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__constant,axiom,
% 157.36/157.38 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_equalityCE,axiom,
% 157.36/157.38 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 157.36/157.38 ( V_A_2 = V_B_2
% 157.36/157.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 157.36/157.38 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_emptyE,axiom,
% 157.36/157.38 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insertCI,axiom,
% 157.36/157.38 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 157.36/157.38 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 157.36/157.38 => V_a_2 = V_b_2 )
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insertE,axiom,
% 157.36/157.38 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 157.36/157.38 => ( V_a_2 != V_b_2
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_subsetD,axiom,
% 157.36/157.38 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__eqI,axiom,
% 157.36/157.38 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 157.36/157.38 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_CollectI,axiom,
% 157.36/157.38 ! [T_b,V_a_2,V_Pa_2] :
% 157.36/157.38 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_eq__mem__trans,axiom,
% 157.36/157.38 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 157.36/157.38 ( V_a_2 = V_b_2
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_eqelem__imp__iff,axiom,
% 157.36/157.38 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 157.36/157.38 ( V_x_2 = V_y_2
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_eqset__imp__iff,axiom,
% 157.36/157.38 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 157.36/157.38 ( V_A_2 = V_B_2
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_mem__def,axiom,
% 157.36/157.38 ! [V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_equals0D,axiom,
% 157.36/157.38 ! [V_a_2,T_b,V_A_2] :
% 157.36/157.38 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_empty__iff,axiom,
% 157.36/157.38 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_ex__in__conv,axiom,
% 157.36/157.38 ! [V_A_2,T_b] :
% 157.36/157.38 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.38 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_all__not__in__conv,axiom,
% 157.36/157.38 ! [V_A_2,T_b] :
% 157.36/157.38 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__absorb,axiom,
% 157.36/157.38 ! [V_A_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insertI2,axiom,
% 157.36/157.38 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__ident,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
% 157.36/157.38 <=> V_A_2 = V_B_2 ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__iff,axiom,
% 157.36/157.38 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 157.36/157.38 <=> ( V_a_2 = V_b_2
% 157.36/157.38 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insertI1,axiom,
% 157.36/157.38 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_set__mp,axiom,
% 157.36/157.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_set__rev__mp,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_in__mono,axiom,
% 157.36/157.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_rev__image__eqI,axiom,
% 157.36/157.38 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_imageI,axiom,
% 157.36/157.38 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__iff,axiom,
% 157.36/157.38 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.38 <=> ? [B_x] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.38 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_CollectE,axiom,
% 157.36/157.38 ! [V_Pa_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.38 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_CollectD,axiom,
% 157.36/157.38 ! [V_Pa_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.38 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_mem__Collect__eq,axiom,
% 157.36/157.38 ! [V_Pa_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.38 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Collect__mem__eq,axiom,
% 157.36/157.38 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_singletonE,axiom,
% 157.36/157.38 ! [V_a_2,V_b_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.38 => V_b_2 = V_a_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_singleton__iff,axiom,
% 157.36/157.38 ! [V_a_2,V_b_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.38 <=> V_b_2 = V_a_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__subset,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 157.36/157.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_subset__insert,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__image,axiom,
% 157.36/157.38 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__compr__raw,axiom,
% 157.36/157.38 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__compr,axiom,
% 157.36/157.38 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_pred__subset__eq,axiom,
% 157.36/157.38 ! [V_S_2,V_R_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_bot__empty__eq,axiom,
% 157.36/157.38 ! [V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_pred__equals__eq,axiom,
% 157.36/157.38 ! [V_S_2,V_R_2,T_b] :
% 157.36/157.38 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 157.36/157.38 <=> V_R_2 = V_S_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_the__inv__into__def,axiom,
% 157.36/157.38 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_override__on__def,axiom,
% 157.36/157.38 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 157.36/157.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_diff__single__insert,axiom,
% 157.36/157.38 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_subset__insert__iff,axiom,
% 157.36/157.38 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 157.36/157.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_imageE,axiom,
% 157.36/157.38 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.38 => ~ ! [B_x] :
% 157.36/157.38 ( V_b_2 = hAPP(V_f_2,B_x)
% 157.36/157.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__subsetI,axiom,
% 157.36/157.38 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.38 ( ! [B_x] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) )
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_rev__predicate1D,axiom,
% 157.36/157.38 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 157.36/157.38 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 157.36/157.38 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_predicate1D,axiom,
% 157.36/157.38 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 157.36/157.38 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.36/157.38 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_subsetI,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( ! [B_x] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_DiffI,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_DiffE,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__idemp,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__iff,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.38 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_DiffD1,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_DiffD2,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_empty__Diff,axiom,
% 157.36/157.38 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__empty,axiom,
% 157.36/157.38 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__cancel,axiom,
% 157.36/157.38 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__subset,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__mono,axiom,
% 157.36/157.38 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_double__diff,axiom,
% 157.36/157.38 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__Diff1,axiom,
% 157.36/157.38 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__Diff__if,axiom,
% 157.36/157.38 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 157.36/157.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__insert,axiom,
% 157.36/157.38 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__insert2,axiom,
% 157.36/157.38 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__Diff__single,axiom,
% 157.36/157.38 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_image__diff__subset,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_set__diff__eq,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Diff__insert__absorb,axiom,
% 157.36/157.38 ! [V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_insert__Diff,axiom,
% 157.36/157.38 ! [V_A_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_override__on__apply__in,axiom,
% 157.36/157.38 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_override__on__apply__notin,axiom,
% 157.36/157.38 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 157.36/157.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.38 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_override__on__emptyset,axiom,
% 157.36/157.38 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_eq__mem,axiom,
% 157.36/157.38 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 157.36/157.38 <=> V_x_2 = V_y_2 ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__diff__def,axiom,
% 157.36/157.38 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.36/157.38 ( class_Groups_Ominus(T_b)
% 157.36/157.38 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_flat__lub__def,axiom,
% 157.36/157.38 ! [V_b_2,V_A_2,T_b] :
% 157.36/157.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.38 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.38 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_minus__apply,axiom,
% 157.36/157.38 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.36/157.38 ( class_Groups_Ominus(T_b)
% 157.36/157.38 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_diff__eq__diff__less__eq,axiom,
% 157.36/157.38 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.36/157.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.36/157.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.36/157.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__upd__image,axiom,
% 157.36/157.38 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_psubset__insert__iff,axiom,
% 157.36/157.38 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 157.36/157.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 157.36/157.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 157.36/157.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 157.36/157.38 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.38 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
% 157.36/157.38 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_inj__on__insert,axiom,
% 157.36/157.38 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 157.36/157.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 157.36/157.38 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.38 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_the__inv__into__into,axiom,
% 157.36/157.38 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__left__comm__idem__remove,axiom,
% 157.36/157.38 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_Powp__mono,axiom,
% 157.36/157.38 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__upd__triv,axiom,
% 157.36/157.38 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 157.36/157.38
% 157.36/157.38 fof(fact_inj__on__empty,axiom,
% 157.36/157.38 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 157.36/157.38 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.36/157.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.36/157.38 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 157.36/157.38 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.36/157.38 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_linorder__cases,axiom,
% 157.36/157.38 ! [V_y,V_x,T_a] :
% 157.36/157.38 ( class_Orderings_Olinorder(T_a)
% 157.36/157.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.38 => ( V_x != V_y
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_order__less__asym,axiom,
% 157.36/157.38 ! [V_y,V_x,T_a] :
% 157.36/157.38 ( class_Orderings_Opreorder(T_a)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_xt1_I10_J,axiom,
% 157.36/157.38 ! [V_z,V_x,V_y,T_a] :
% 157.36/157.38 ( class_Orderings_Oorder(T_a)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_order__less__trans,axiom,
% 157.36/157.38 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.38 ( class_Orderings_Opreorder(T_a)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_xt1_I2_J,axiom,
% 157.36/157.38 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.38 ( class_Orderings_Oorder(T_a)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.36/157.38 => ( V_b = V_c
% 157.36/157.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 157.36/157.38
% 157.36/157.38 fof(fact_ord__less__eq__trans,axiom,
% 157.36/157.38 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.38 ( class_Orderings_Oord(T_a)
% 157.36/157.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.39 => ( V_b = V_c
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubset__trans,axiom,
% 157.36/157.39 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I1_J,axiom,
% 157.36/157.39 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( V_a = V_b
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_ord__eq__less__trans,axiom,
% 157.36/157.39 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Oord(T_a)
% 157.36/157.39 => ( V_a = V_b
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I9_J,axiom,
% 157.36/157.39 ! [V_a,V_b,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__asym_H,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__imp__not__eq2,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => V_y != V_x ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__imp__not__eq,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => V_x != V_y ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__imp__not__less,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__not__sym,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_less__imp__neq,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => V_x != V_y ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__neqE,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( V_x != V_y
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__antisym__conv3,axiom,
% 157.36/157.39 ! [V_x_2,V_y_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__less__linear,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 | V_x = V_y
% 157.36/157.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_not__less__iff__gr__or__eq,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 157.36/157.39 | V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__neq__iff,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( V_x_2 != V_y_2
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__irrefl,axiom,
% 157.36/157.39 ! [V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__idem,axiom,
% 157.36/157.39 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 157.36/157.39 ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.36/157.39 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__other,axiom,
% 157.36/157.39 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 157.36/157.39 ( V_z_2 != V_x_2
% 157.36/157.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__twist,axiom,
% 157.36/157.39 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 157.36/157.39 ( V_a_2 != V_ca_2
% 157.36/157.39 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__apply,axiom,
% 157.36/157.39 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 157.36/157.39 ( ( V_z_2 = V_x_2
% 157.36/157.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 157.36/157.39 & ( V_z_2 != V_x_2
% 157.36/157.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__same,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__upd,axiom,
% 157.36/157.39 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__idem__iff,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 157.36/157.39 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__def,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 <=> ! [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.39 => ! [B_xa] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.36/157.39 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 157.36/157.39 => B_x = B_xa ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__strict__subset,axiom,
% 157.36/157.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__id2,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_diff__eq__diff__less,axiom,
% 157.36/157.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.36/157.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.36/157.39 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.36/157.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__def,axiom,
% 157.36/157.39 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 157.36/157.39 ( ( V_x_2 = V_a_2
% 157.36/157.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 157.36/157.39 & ( V_x_2 != V_a_2
% 157.36/157.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__left__comm__idem__insert,axiom,
% 157.36/157.39 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__contraD,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( V_x_2 != V_y_2
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.36/157.39 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__iff,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.36/157.39 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.36/157.39 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__onD,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.36/157.39 => V_x_2 = V_y_2 ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_subset__inj__on,axiom,
% 157.36/157.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__fun__updI,axiom,
% 157.36/157.39 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__diff,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 157.36/157.39 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 157.36/157.39 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_less__fun__def,axiom,
% 157.36/157.39 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.36/157.39 ( class_Orderings_Oord(T_c)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.36/157.39 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I8_J,axiom,
% 157.36/157.39 ! [V_z,V_x,V_y,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__le__less__trans,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I7_J,axiom,
% 157.36/157.39 ! [V_z,V_x,V_y,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__le__trans,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I11_J,axiom,
% 157.36/157.39 ! [V_a,V_b,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.36/157.39 => ( V_a != V_b
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__le__neq__trans,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.39 => ( V_a != V_b
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__le__imp__less__or__eq,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 | V_x = V_y ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__antisym__conv2,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__imp__le,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_leD,axiom,
% 157.36/157.39 ! [V_x,V_y,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_xt1_I12_J,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( V_a != V_b
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__neq__le__trans,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Orderings_Oorder(T_a)
% 157.36/157.39 => ( V_a != V_b
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__antisym__conv1,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_not__leE,axiom,
% 157.36/157.39 ! [V_x,V_y,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_leI,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__le__less,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Oorder(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 | V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_less__le__not__le,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Opreorder(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_order__less__le,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Oorder(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 & V_x_2 != V_y_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__le__less__linear,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.36/157.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__not__le,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_linorder__not__less,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Orderings_Olinorder(T_b)
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubsetD,axiom,
% 157.36/157.39 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_not__psubset__empty,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_subset__psubset__trans,axiom,
% 157.36/157.39 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubset__subset__trans,axiom,
% 157.36/157.39 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubset__imp__subset,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_subset__iff__psubset__eq,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 | V_A_2 = V_B_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubset__eq,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 & V_A_2 != V_B_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_the__inv__into__f__f,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_the__inv__into__f__eq,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_the__inv__into__onto,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__the__inv__into,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__image__set__diff,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.39 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_f__the__inv__into__f,axiom,
% 157.36/157.39 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.39 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_diff__eq__diff__eq,axiom,
% 157.36/157.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.36/157.39 ( class_Groups_Oab__group__add(T_b)
% 157.36/157.39 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 157.36/157.39 => ( V_a_2 = V_b_2
% 157.36/157.39 <=> V_ca_2 = V_d_2 ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__iff__surj,axiom,
% 157.36/157.39 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 157.36/157.39 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => ( ? [B_f] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 157.36/157.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 157.36/157.39 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 157.36/157.39 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 157.36/157.39 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 157.36/157.39 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 157.36/157.39 | ? [B_x,B_y] :
% 157.36/157.39 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 157.36/157.39 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 157.36/157.39 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Diff1__fold__graph,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_mk__less__def,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 157.36/157.39 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.36/157.39 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_psubset__imp__ex__mem,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => ? [B_b] : hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_image__Pow__mono,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_the__inv__into__comp,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 157.36/157.39 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 157.36/157.39 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_folding__one_Osingleton,axiom,
% 157.36/157.39 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 157.36/157.39 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.39 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold1Set__sing,axiom,
% 157.36/157.39 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 157.36/157.39 <=> V_a_2 = V_b_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_nonempty__iff,axiom,
% 157.36/157.39 ! [T_b,V_A_2] :
% 157.36/157.39 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 <=> ? [B_x,B_B] :
% 157.36/157.39 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B)
% 157.36/157.39 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_quotient__diff1,axiom,
% 157.36/157.39 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.39 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_PowI,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold1Set_Ointros,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Cantors__paradox,axiom,
% 157.36/157.39 ! [V_A_2,T_b] :
% 157.36/157.39 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_o__assoc,axiom,
% 157.36/157.39 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_o__apply,axiom,
% 157.36/157.39 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_o__eq__dest,axiom,
% 157.36/157.39 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.36/157.39 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 157.36/157.39 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_o__eq__elim,axiom,
% 157.36/157.39 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.36/157.39 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 157.36/157.39 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__top,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__not__empty,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_o__def,axiom,
% 157.36/157.39 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_quotient__empty,axiom,
% 157.36/157.39 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_quotient__is__empty2,axiom,
% 157.36/157.39 ! [V_r_2,V_A_2,T_b] :
% 157.36/157.39 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
% 157.36/157.39 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_quotient__is__empty,axiom,
% 157.36/157.39 ! [V_r_2,V_A_2,T_b] :
% 157.36/157.39 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 157.36/157.39 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_image__compose,axiom,
% 157.36/157.39 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__imageI2,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__upd__comp,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 157.36/157.39 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.36/157.39 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__empty,axiom,
% 157.36/157.39 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__bottom,axiom,
% 157.36/157.39 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 157.36/157.39 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_OemptyI,axiom,
% 157.36/157.39 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_empty__fold__graphE,axiom,
% 157.36/157.39 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 157.36/157.39 => V_x_2 = V_z_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__iff,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 157.36/157.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_PowD,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_image__Pow__surj,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 157.36/157.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 157.36/157.39 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__def,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_comp__inj__on__iff,axiom,
% 157.36/157.39 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 157.36/157.39 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_comp__inj__on,axiom,
% 157.36/157.39 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.39 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__on__imageI,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
% 157.36/157.39 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_empty__fold1SetE,axiom,
% 157.36/157.39 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold1Set__nonempty,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 157.36/157.39 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph_OinsertI,axiom,
% 157.36/157.39 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.36/157.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__mono,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Powp__Pow__eq,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 157.36/157.39 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_folding__one_Oremove,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.39 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 157.36/157.39 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold1Set_Oequations,axiom,
% 157.36/157.39 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 157.36/157.39 <=> ? [B_a,B_A] :
% 157.36/157.39 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 157.36/157.39 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 157.36/157.39 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_insert__fold1SetE,axiom,
% 157.36/157.39 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 157.36/157.39 => ~ ! [B_a,B_A] :
% 157.36/157.39 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_fold__graph__permute__diff,axiom,
% 157.36/157.39 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 157.36/157.39 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_K__record__comp,axiom,
% 157.36/157.39 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ).
% 157.36/157.39
% 157.36/157.39 fof(fact_folding__one_Oinsert__remove,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.39 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.36/157.39 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_folding__one_Oinsert,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.39 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inv__into__comp,axiom,
% 157.36/157.39 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 157.36/157.39 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 157.36/157.39 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_quotientI,axiom,
% 157.36/157.39 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inj__singleton,axiom,
% 157.36/157.39 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__insert,axiom,
% 157.36/157.39 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_top1I,axiom,
% 157.36/157.39 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup1CI,axiom,
% 157.36/157.39 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 157.36/157.39 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 157.36/157.39 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 157.36/157.39 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup1E,axiom,
% 157.36/157.39 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 157.36/157.39 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 157.36/157.39 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_UNIV__I,axiom,
% 157.36/157.39 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite_OemptyI,axiom,
% 157.36/157.39 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_UnCI,axiom,
% 157.36/157.39 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 157.36/157.39 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_UnE,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite_OinsertI,axiom,
% 157.36/157.39 ! [V_a_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__imageI,axiom,
% 157.36/157.39 ! [V_h_2,T_c,V_F_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Diff,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Collect__conjI,axiom,
% 157.36/157.39 ! [V_Qa_2,V_Pa_2,T_b] :
% 157.36/157.39 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.39 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Collect__subsets,axiom,
% 157.36/157.39 ! [V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup1I2,axiom,
% 157.36/157.39 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 157.36/157.39 ( hBOOL(hAPP(V_B_2,V_x_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup1I1,axiom,
% 157.36/157.39 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 157.36/157.39 ( hBOOL(hAPP(V_A_2,V_x_2))
% 157.36/157.39 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_ball__Un,axiom,
% 157.36/157.39 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( ! [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.36/157.39 <=> ( ! [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.36/157.39 & ! [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 157.36/157.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_bex__Un,axiom,
% 157.36/157.39 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 157.36/157.39 ( ? [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.36/157.39 <=> ( ? [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.36/157.39 | ? [B_x] :
% 157.36/157.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 157.36/157.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__assoc,axiom,
% 157.36/157.39 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__left__commute,axiom,
% 157.36/157.39 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__left__absorb,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__commute,axiom,
% 157.36/157.39 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__absorb,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__UNIV__right,axiom,
% 157.36/157.39 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Un__UNIV__left,axiom,
% 157.36/157.39 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_top__apply,axiom,
% 157.36/157.39 ! [V_x_2,T_c,T_b] :
% 157.36/157.39 ( class_Orderings_Otop(T_b)
% 157.36/157.39 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__UnI,axiom,
% 157.36/157.39 ! [V_Ga_2,V_F_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Prod__UNIV,axiom,
% 157.36/157.39 ! [T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__fun__UNIVD2,axiom,
% 157.36/157.39 ! [T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__apply,axiom,
% 157.36/157.39 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( class_Lattices_Olattice(T_b)
% 157.36/157.39 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__assoc,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__aci_I6_J,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup_Oassoc,axiom,
% 157.36/157.39 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 157.36/157.39 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.39 ( class_Groups_Oab__semigroup__mult(T_a)
% 157.36/157.39 => 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)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__left__commute,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__aci_I7_J,axiom,
% 157.36/157.39 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup_Oleft__commute,axiom,
% 157.36/157.39 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__left__idem,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__aci_I8_J,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup_Oleft__idem,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_mult__left__idem,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__commute,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__aci_I5_J,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup_Ocommute,axiom,
% 157.36/157.39 ! [V_b,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__fun__def,axiom,
% 157.36/157.39 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( class_Lattices_Olattice(T_b)
% 157.36/157.39 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__idem,axiom,
% 157.36/157.39 ! [V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup_Oidem,axiom,
% 157.36/157.39 ! [V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_mult__idem,axiom,
% 157.36/157.39 ! [V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_times_Oidem,axiom,
% 157.36/157.39 ! [V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__top__right,axiom,
% 157.36/157.39 ! [V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__top__left,axiom,
% 157.36/157.39 ! [V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Un,axiom,
% 157.36/157.39 ! [V_Ga_2,V_F_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
% 157.36/157.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.36/157.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__code,axiom,
% 157.36/157.39 ! [V_A_2,T_b] :
% 157.36/157.39 ( class_Finite__Set_Ofinite(T_b)
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Plus__UNIV__iff,axiom,
% 157.36/157.39 ! [T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 157.36/157.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__option__UNIV,axiom,
% 157.36/157.39 ! [T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 157.36/157.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite,axiom,
% 157.36/157.39 ! [V_A_2,T_b] :
% 157.36/157.39 ( class_Finite__Set_Ofinite(T_b)
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__UNIV,axiom,
% 157.36/157.39 ! [T_b] :
% 157.36/157.39 ( class_Finite__Set_Ofinite(T_b)
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_image__surj__f__inv__f,axiom,
% 157.36/157.39 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.36/157.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_surj__f__inv__f,axiom,
% 157.36/157.39 ! [V_y_2,V_f_2,T_b,T_c] :
% 157.36/157.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_surj__iff__all,axiom,
% 157.36/157.39 ! [V_f_2,T_b,T_c] :
% 157.36/157.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inv__f__eq,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.39 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.36/157.39 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inv__f__f,axiom,
% 157.36/157.39 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.39 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_iso__tuple__UNIV__I,axiom,
% 157.36/157.39 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_Pow__UNIV,axiom,
% 157.36/157.39 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_nat__seg__image__imp__finite,axiom,
% 157.36/157.39 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 157.36/157.39 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Pow__iff,axiom,
% 157.36/157.39 ! [V_A_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 157.36/157.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__Collect__not,axiom,
% 157.36/157.39 ! [V_Pa_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 157.36/157.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__range__imageI,axiom,
% 157.36/157.39 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 157.36/157.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__ord_I3_J,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__ge1,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_inf__sup__ord_I4_J,axiom,
% 157.36/157.39 ! [V_x,V_y,T_a] :
% 157.36/157.39 ( class_Lattices_Olattice(T_a)
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__ge2,axiom,
% 157.36/157.39 ! [V_x,V_y,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__iff__sup,axiom,
% 157.36/157.39 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.36/157.39 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__sup__iff,axiom,
% 157.36/157.39 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_b)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
% 157.36/157.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 157.36/157.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__supI1,axiom,
% 157.36/157.39 ! [V_b,V_a,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__supI2,axiom,
% 157.36/157.39 ! [V_a,V_b,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__absorb2,axiom,
% 157.36/157.39 ! [V_y,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__absorb1,axiom,
% 157.36/157.39 ! [V_x,V_y,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.36/157.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__supI,axiom,
% 157.36/157.39 ! [V_b,V_x,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__least,axiom,
% 157.36/157.39 ! [V_z,V_x,V_y,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_sup__mono,axiom,
% 157.36/157.39 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_le__supE,axiom,
% 157.36/157.39 ! [V_x,V_b,V_a,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
% 157.36/157.39 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.36/157.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_less__supI1,axiom,
% 157.36/157.39 ! [V_b,V_a,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_less__supI2,axiom,
% 157.36/157.39 ! [V_a,V_b,V_x,T_a] :
% 157.36/157.39 ( class_Lattices_Osemilattice__sup(T_a)
% 157.36/157.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 157.36/157.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__UNIV__surj__inj,axiom,
% 157.36/157.39 ! [V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.39 => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.39 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 157.36/157.39
% 157.36/157.39 fof(fact_finite__UNIV__inj__surj,axiom,
% 157.36/157.39 ! [V_f_2,T_b] :
% 157.36/157.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_surj__imp__inj__inv,axiom,
% 157.36/157.40 ! [V_f_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__image__comp,axiom,
% 157.36/157.40 ! [V_X_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__inv__f__f,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__imp__surj__inv,axiom,
% 157.36/157.40 ! [V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_o__inv__o__cancel,axiom,
% 157.36/157.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_sup__eq__bot__iff,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.40 ( class_Lattices_Obounded__lattice__bot(T_b)
% 157.36/157.40 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 157.36/157.40 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 157.36/157.40 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_sup__bot__right,axiom,
% 157.36/157.40 ! [V_x,T_a] :
% 157.36/157.40 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_sup__bot__left,axiom,
% 157.36/157.40 ! [V_x,T_a] :
% 157.36/157.40 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UnI2,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UnI1,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.40 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__empty,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__empty__right,axiom,
% 157.36/157.40 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__empty__left,axiom,
% 157.36/157.40 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__insert__left,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__insert__right,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__mono,axiom,
% 157.36/157.40 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__least,axiom,
% 157.36/157.40 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__absorb2,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__absorb1,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_subset__Un__eq,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__upper2,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__upper1,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__Un,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__Diff,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__Diff__cancel2,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__Diff__cancel,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UNIV__not__empty,axiom,
% 157.36/157.40 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__Pow__subset,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_subset__UNIV,axiom,
% 157.36/157.40 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite_Oequations_I1_J,axiom,
% 157.36/157.40 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__insert,axiom,
% 157.36/157.40 ! [V_A_2,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 157.36/157.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_injD,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.36/157.40 => V_x_2 = V_y_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__eq,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.36/157.40 <=> V_x_2 = V_y_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_rev__finite__subset,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__subset,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__Diff2,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fun__left__comm__idem__sup,axiom,
% 157.36/157.40 ! [T_b] :
% 157.36/157.40 ( class_Lattices_Osemilattice__sup(T_b)
% 157.36/157.40 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold__graph__imp__finite,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_sup__Un__eq,axiom,
% 157.36/157.40 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fun__left__comm__idem,axiom,
% 157.36/157.40 ! [T_b] :
% 157.36/157.40 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.36/157.40 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Collect__disj__eq,axiom,
% 157.36/157.40 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UNIV__def,axiom,
% 157.36/157.40 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_range__composition,axiom,
% 157.36/157.40 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__Collect__disjI,axiom,
% 157.36/157.40 ! [V_Qa_2,V_Pa_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2))))
% 157.36/157.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.36/157.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_top__greatest,axiom,
% 157.36/157.40 ! [V_x,T_a] :
% 157.36/157.40 ( class_Orderings_Otop(T_a)
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_insert__is__Un,axiom,
% 157.36/157.40 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Diff__partition,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Diff__subset__conv,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 157.36/157.40 <=> V_A_2 = V_B_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_range__eqI,axiom,
% 157.36/157.40 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 157.36/157.40 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_rangeI,axiom,
% 157.36/157.40 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Diff__UNIV,axiom,
% 157.36/157.40 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_comp__surj,axiom,
% 157.36/157.40 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__into__injective,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 157.36/157.40 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 => V_x_2 = V_y_2 ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__into__into,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_f__inv__into__f,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.40 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__image__eq__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 157.36/157.40 <=> V_A_2 = V_B_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__comp,axiom,
% 157.36/157.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 157.36/157.40 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__surj,axiom,
% 157.36/157.40 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__into__f__eq,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.36/157.40 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__into__f__f,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__Diff__insert,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
% 157.36/157.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__inv__into__cancel,axiom,
% 157.36/157.40 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__imageD,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__def,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_insert__def,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_the__inv__f__f,axiom,
% 157.36/157.40 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__fun,axiom,
% 157.36/157.40 ! [T_d,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__image__mem__iff,axiom,
% 157.36/157.40 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_range__ex1__eq,axiom,
% 157.36/157.40 ! [V_b_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.40 <=> ? [B_x] :
% 157.36/157.40 ( V_b_2 = hAPP(V_f_2,B_x)
% 157.36/157.40 & ! [B_y] :
% 157.36/157.40 ( V_b_2 = hAPP(V_f_2,B_y)
% 157.36/157.40 => B_y = B_x ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold__graph__insert__swap,axiom,
% 157.36/157.40 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 157.36/157.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__image__subset__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__set__diff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_singleton__quotient,axiom,
% 157.36/157.40 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__surj__inj,axiom,
% 157.36/157.40 ! [V_f_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
% 157.36/157.40 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_endo__inj__surj,axiom,
% 157.36/157.40 ! [V_f_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 157.36/157.40 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inv__into__image__cancel,axiom,
% 157.36/157.40 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__on__inv__into,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.36/157.40 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_o__eq__dest__lhs,axiom,
% 157.36/157.40 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.36/157.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 157.36/157.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Oremove,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image__simple_Oremove,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image_Oreindex,axiom,
% 157.36/157.40 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 157.36/157.40 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_quotientE,axiom,
% 157.36/157.40 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.36/157.40 => ~ ! [B_x] :
% 157.36/157.40 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Oinsert__remove,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Image__Un,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Un__Image,axiom,
% 157.36/157.40 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Image__mono,axiom,
% 157.36/157.40 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Image__empty,axiom,
% 157.36/157.40 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__Collect__le__nat,axiom,
% 157.36/157.40 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__Collect__less__nat,axiom,
% 157.36/157.40 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 157.36/157.40 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__comp,axiom,
% 157.36/157.40 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__left__comp,axiom,
% 157.36/157.40 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image__simple_Oempty,axiom,
% 157.36/157.40 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.36/157.40 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image_Odistrib,axiom,
% 157.36/157.40 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.40 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__comp_H,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 157.36/157.40 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 157.36/157.40 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__image__simple_Oinsert,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding_Oinsert,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__M__bounded__by__nat,axiom,
% 157.36/157.40 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Ounion__idem,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Oinsert__idem,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one_Oclosed,axiom,
% 157.36/157.40 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_quotient__def,axiom,
% 157.36/157.40 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__vimage__singleton,axiom,
% 157.36/157.40 ! [V_a_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__transfer,axiom,
% 157.36/157.40 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( ! [B_y] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__empty__induct,axiom,
% 157.36/157.40 ! [V_Pa_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 157.36/157.40 => ( ! [B_a,B_A] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 157.36/157.40 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimageI,axiom,
% 157.36/157.40 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 157.36/157.40 ( hAPP(V_f_2,V_a_2) = V_b_2
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP1__I,axiom,
% 157.36/157.40 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 157.36/157.40 ! [V_N_2] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 157.36/157.40 <=> ? [B_m] :
% 157.36/157.40 ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_infinite__UNIV__nat,axiom,
% 157.36/157.40 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP1__iff,axiom,
% 157.36/157.40 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 157.36/157.40 <=> ? [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__code,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 157.36/157.40 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__ident,axiom,
% 157.36/157.40 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__UN,axiom,
% 157.36/157.40 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__o,axiom,
% 157.36/157.40 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimageI2,axiom,
% 157.36/157.40 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimageD,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__eq,axiom,
% 157.36/157.40 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__empty,axiom,
% 157.36/157.40 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__mono,axiom,
% 157.36/157.40 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__UNIV,axiom,
% 157.36/157.40 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__Un,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__compose,axiom,
% 157.36/157.40 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__Diff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Image__UN,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__Collect__eq,axiom,
% 157.36/157.40 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__vimage__subset,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_surj__image__vimage__eq,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP__UN__eq,axiom,
% 157.36/157.40 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__def,axiom,
% 157.36/157.40 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 157.36/157.40 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__idem_Oidem__comp,axiom,
% 157.36/157.40 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.36/157.40 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__singleton__eq,axiom,
% 157.36/157.40 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 157.36/157.40 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__insert,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__vimageD,axiom,
% 157.36/157.40 ! [V_F_2,V_h_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 157.36/157.40 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__subsetD,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__vimageI,axiom,
% 157.36/157.40 ! [V_h_2,T_c,V_F_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.36/157.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__vimage__image__eq,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Image__eq__UN,axiom,
% 157.36/157.40 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__const,axiom,
% 157.36/157.40 ! [T_c,V_A_2,V_ca_2,T_b] :
% 157.36/157.40 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.40 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.36/157.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.36/157.40 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__nat__set__iff__bounded,axiom,
% 157.36/157.40 ! [V_N_2] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 157.36/157.40 <=> ? [B_m] :
% 157.36/157.40 ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__subsetI,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__I,axiom,
% 157.36/157.40 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__Pow__subset,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__eq__UN,axiom,
% 157.36/157.40 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__eq__UN,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__insert,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I3_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I2_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I3_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I2_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ball__UN,axiom,
% 157.36/157.40 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 157.36/157.40 ( ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 => ! [B_xa] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP__commute,axiom,
% 157.36/157.40 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__UN__flatten,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I9_J,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I9_J,axiom,
% 157.36/157.40 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP__le__iff,axiom,
% 157.36/157.40 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__SUP__iff,axiom,
% 157.36/157.40 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 157.36/157.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.36/157.40 & class_Orderings_Olinorder(T_b) )
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
% 157.36/157.40 <=> ? [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.36/157.40 <=> ? [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP__const,axiom,
% 157.36/157.40 ! [V_M_2,T_b,V_A_2,T_c] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UNION__empty__conv_I1_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.36/157.40 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__empty2,axiom,
% 157.36/157.40 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__constant,axiom,
% 157.36/157.40 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.36/157.40 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.36/157.40 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UNION__empty__conv_I2_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b,T_c] :
% 157.36/157.40 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.36/157.40 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__subset__iff,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 157.36/157.40 <=> ! [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I10_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_image__UN,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I10_J,axiom,
% 157.36/157.40 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__Un,axiom,
% 157.36/157.40 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__Un__distrib,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUPR__apply,axiom,
% 157.36/157.40 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.36/157.40 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I6_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I6_J,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_vimage__UN,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP__subset,axiom,
% 157.36/157.40 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__SUPI,axiom,
% 157.36/157.40 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 157.36/157.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__insert__distrib,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__upper,axiom,
% 157.36/157.40 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__absorb,axiom,
% 157.36/157.40 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 157.36/157.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__simps_I1_J,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__singleton,axiom,
% 157.36/157.40 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ).
% 157.36/157.40
% 157.36/157.40 fof(fact_UN__extend__simps_I1_J,axiom,
% 157.36/157.40 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 157.36/157.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
% 157.36/157.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 157.36/157.40 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 157.36/157.40 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 157.36/157.40 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 157.36/157.40 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OgreaterThan__iff,axiom,
% 157.36/157.40 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OlessThan__iff,axiom,
% 157.36/157.40 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OatLeast__iff,axiom,
% 157.36/157.40 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_ord_OatMost__iff,axiom,
% 157.36/157.40 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__or__eq__imp__le,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 | V_m = V_n )
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP2__I,axiom,
% 157.36/157.40 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__less__mono2,axiom,
% 157.36/157.40 ! [V_l,V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__imp__diff__less,axiom,
% 157.36/157.40 ! [V_n,V_k,V_j] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__not__refl,axiom,
% 157.36/157.40 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__neq__iff,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2] :
% 157.36/157.40 ( V_m_2 != V_n_2
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_linorder__neqE__nat,axiom,
% 157.36/157.40 ! [V_y,V_x] :
% 157.36/157.40 ( V_x != V_y
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__irrefl__nat,axiom,
% 157.36/157.40 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__not__refl2,axiom,
% 157.36/157.40 ! [V_m,V_n] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 157.36/157.40 => V_m != V_n ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__not__refl3,axiom,
% 157.36/157.40 ! [V_t,V_s] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 157.36/157.40 => V_s != V_t ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__less__cases,axiom,
% 157.36/157.40 ! [V_Pa_2,V_n_2,V_m_2] :
% 157.36/157.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.36/157.40 => ( ( V_m_2 = V_n_2
% 157.36/157.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.36/157.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.36/157.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_mult__le__mono,axiom,
% 157.36/157.40 ! [V_l,V_k,V_j,V_i] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_mult__le__mono2,axiom,
% 157.36/157.40 ! [V_k,V_j,V_i] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_mult__le__mono1,axiom,
% 157.36/157.40 ! [V_k,V_j,V_i] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__cube,axiom,
% 157.36/157.40 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__square,axiom,
% 157.36/157.40 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__refl,axiom,
% 157.36/157.40 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__le__linear,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_eq__imp__le,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( V_m = V_n
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__trans,axiom,
% 157.36/157.40 ! [V_k,V_j,V_i] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__antisym,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.36/157.40 => V_m = V_n ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__le__self,axiom,
% 157.36/157.40 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__le__mono2,axiom,
% 157.36/157.40 ! [V_l,V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__le__mono,axiom,
% 157.36/157.40 ! [V_l,V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__diff__cancel,axiom,
% 157.36/157.40 ! [V_n,V_i] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 157.36/157.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_eq__diff__iff,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.36/157.40 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
% 157.36/157.40 <=> V_m_2 = V_n_2 ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_Nat_Odiff__diff__eq,axiom,
% 157.36/157.40 ! [V_n,V_m,V_k] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 157.36/157.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__diff__iff,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__diff__iff,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__less__mono,axiom,
% 157.36/157.40 ! [V_c,V_b,V_a] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__less__le,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 & V_m_2 != V_n_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__eq__less__or__eq,axiom,
% 157.36/157.40 ! [V_n_2,V_m_2] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.40 | V_m_2 = V_n_2 ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__imp__le__nat,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_le__neq__implies__less,axiom,
% 157.36/157.40 ! [V_n,V_m] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.40 => ( V_m != V_n
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_termination__basic__simps_I5_J,axiom,
% 157.36/157.40 ! [V_y,V_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__subset__induct,axiom,
% 157.36/157.40 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.40 => ( ! [B_a,B_F] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 157.36/157.40 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 157.36/157.40 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.36/157.40 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_finite__conv__nat__seg__image,axiom,
% 157.36/157.40 ! [V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__Diff2__less,axiom,
% 157.36/157.40 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__Diff1__less,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__insert,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__commute,axiom,
% 157.36/157.40 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__mult__assoc,axiom,
% 157.36/157.40 ! [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)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_nat__mult__commute,axiom,
% 157.36/157.40 ! [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) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__mult__distrib2,axiom,
% 157.36/157.40 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__mult__distrib,axiom,
% 157.36/157.40 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_SUP2__iff,axiom,
% 157.36/157.40 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 157.36/157.40 <=> ? [B_x] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.40 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one__idem_Oidem,axiom,
% 157.36/157.40 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.40 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 157.36/157.40 ! [V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.36/157.40 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.36/157.40 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__image,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__singleton,axiom,
% 157.36/157.40 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__singleton__def,axiom,
% 157.36/157.40 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 157.36/157.40 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 157.36/157.40 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one_Oeq__fold,axiom,
% 157.36/157.40 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__insert__le,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__seteq,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 157.36/157.40 => V_A_2 = V_B_2 ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__mono,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__image__le,axiom,
% 157.36/157.40 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__Diff__subset,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.36/157.40 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__on__iff__eq__card,axiom,
% 157.36/157.40 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_eq__card__imp__inj__on,axiom,
% 157.36/157.40 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
% 157.36/157.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_diff__card__le__card__Diff,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_pigeonhole,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
% 157.36/157.40 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__quotient__disjoint,axiom,
% 157.36/157.40 ! [V_r_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 157.36/157.40 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_psubset__card__mono,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_comp__cong,axiom,
% 157.36/157.40 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 157.36/157.40 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
% 157.36/157.40 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__def,axiom,
% 157.36/157.40 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_less__by__empty,axiom,
% 157.36/157.40 ! [V_B_2,T_b,V_A_2] :
% 157.36/157.40 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__bij__eq,axiom,
% 157.36/157.40 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 157.36/157.40 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.36/157.40 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__psubset,axiom,
% 157.36/157.40 ! [V_A_2,V_B_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_folding__one__idem_Oin__idem,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.36/157.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.40 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__insert__idem,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__Un2,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,T_b] :
% 157.36/157.40 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.36/157.40 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.40 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__Diff1__le,axiom,
% 157.36/157.40 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_card__inj__on__le,axiom,
% 157.36/157.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.36/157.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.36/157.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_inj__on__iff__card__le,axiom,
% 157.36/157.40 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.36/157.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.36/157.40 => ( ? [B_f] :
% 157.36/157.40 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 157.36/157.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) )
% 157.36/157.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 157.36/157.40
% 157.36/157.40 fof(fact_fold1__in,axiom,
% 157.36/157.40 ! [V_A_2,T_b] :
% 157.36/157.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.36/157.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.41 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__Diff__singleton,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__Diff__singleton__if,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 157.36/157.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_hom__fold1__commute,axiom,
% 157.36/157.41 ! [V_N_2,V_h_2,T_b] :
% 157.36/157.41 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.36/157.41 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.36/157.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.41 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__Diff__insert,axiom,
% 157.36/157.41 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__Suc__Diff1,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 157.36/157.41 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 157.36/157.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.36/157.41 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.36/157.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.36/157.41 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_fold__image__reindex,axiom,
% 157.36/157.41 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 157.36/157.41 ( class_Groups_Oab__semigroup__mult(T_d)
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 157.36/157.41 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_pigeonhole__infinite,axiom,
% 157.36/157.41 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.41 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.36/157.41 => ? [B_x] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.36/157.41 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_lessI,axiom,
% 157.36/157.41 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__mono,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__Suc__1,axiom,
% 157.36/157.41 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__UNIV__unit,axiom,
% 157.36/157.41 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_one__reorient,axiom,
% 157.36/157.41 ! [V_x_2,T_b] :
% 157.36/157.41 ( class_Groups_Oone(T_b)
% 157.36/157.41 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 157.36/157.41 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__inject,axiom,
% 157.36/157.41 ! [V_y,V_x] :
% 157.36/157.41 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 157.36/157.41 => V_x = V_y ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat_Oinject,axiom,
% 157.36/157.41 ! [V_nat_H_2,V_nat_2] :
% 157.36/157.41 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 157.36/157.41 <=> V_nat_2 = V_nat_H_2 ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__n__not__n,axiom,
% 157.36/157.41 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 157.36/157.41
% 157.36/157.41 fof(fact_n__not__Suc__n,axiom,
% 157.36/157.41 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_inj__Suc,axiom,
% 157.36/157.41 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult_Ocomm__neutral,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__1__right,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Omonoid__mult(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__1,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__1__left,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Omonoid__mult(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__less__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__Suc__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.36/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 | V_m_2 = V_n_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__less__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__less__less__Suc__eq,axiom,
% 157.36/157.41 ! [V_m_2,V_n_2] :
% 157.36/157.41 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 157.36/157.41 <=> V_n_2 = V_m_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__antisym,axiom,
% 157.36/157.41 ! [V_m,V_n] :
% 157.36/157.41 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 157.36/157.41 => V_m = V_n ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__SucI,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__lessI,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__trans__Suc,axiom,
% 157.36/157.41 ! [V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__SucE,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 157.36/157.41 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => V_m = V_n ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__lessD,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__less__SucD,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__n__not__le__n,axiom,
% 157.36/157.41 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__less__eq__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__Suc__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.36/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__le__mono,axiom,
% 157.36/157.41 ! [V_m_2,V_n_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__SucI,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__SucE,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 157.36/157.41 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__leD,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__Suc__Suc,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__diff__diff,axiom,
% 157.36/157.41 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__mult__cancel1,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
% 157.36/157.41 <=> V_m_2 = V_n_2 ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_fold__image__distrib,axiom,
% 157.36/157.41 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.36/157.41 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__mult__1,axiom,
% 157.36/157.41 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__1__eq__mult__iff,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 157.36/157.41 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.36/157.41 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__mult__1__right,axiom,
% 157.36/157.41 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__mult__eq__1__iff,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.36/157.41 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.36/157.41 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_fold__image__empty,axiom,
% 157.36/157.41 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__eq__Suc__le,axiom,
% 157.36/157.41 ! [V_m_2,V_n_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__Suc__eq__le,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__le__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__imp__less__Suc,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__leI,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__less__Suc__eq,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 157.36/157.41 <=> V_n_2 = V_m_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__le__lessD,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__less__Suc,axiom,
% 157.36/157.41 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__mult__less__cancel1,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__diff__le,axiom,
% 157.36/157.41 ! [V_m,V_n] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.36/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__mult__le__cancel1,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__eq__Suc__le__raw,axiom,
% 157.36/157.41 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 157.36/157.41 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.41 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_folding__image_Oeq__fold,axiom,
% 157.36/157.41 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.36/157.41 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.36/157.41 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__insert__if,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
% 157.36/157.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__insert__disjoint,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_fold__image__insert,axiom,
% 157.36/157.41 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 157.36/157.41 ( class_Groups_Oab__semigroup__mult(T_c)
% 157.36/157.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.36/157.41 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__insert,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_image__eq__fold__image,axiom,
% 157.36/157.41 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__1__mult,axiom,
% 157.36/157.41 ! [V_n,V_m,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_finite__fun__UNIVD1,axiom,
% 157.36/157.41 ! [T_c,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 157.36/157.41 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.36/157.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card_Oremove,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card_Oinsert__remove,axiom,
% 157.36/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__zeroE,axiom,
% 157.36/157.41 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le0,axiom,
% 157.36/157.41 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__Suc,axiom,
% 157.36/157.41 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_bot__nat__def,axiom,
% 157.36/157.41 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__is__1,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.36/157.41 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.36/157.41 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.36/157.41 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_one__is__add,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
% 157.36/157.41 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.36/157.41 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.36/157.41 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__zero__left,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Omult__zero(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__zero__right,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Omult__zero(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__eq__0__iff,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oring__no__zero__divisors(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_no__zero__divisors,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ono__zero__divisors(T_a)
% 157.36/157.41 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.36/157.41 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_divisors__zero,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ono__zero__divisors(T_a)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 157.36/157.41 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 157.36/157.41 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_inj__on__add__nat,axiom,
% 157.36/157.41 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__gr__0,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
% 157.36/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 157.36/157.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_plus__nat_Oadd__0,axiom,
% 157.36/157.41 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Nat_Oadd__0__right,axiom,
% 157.36/157.41 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__commute,axiom,
% 157.36/157.41 ! [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) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__left__commute,axiom,
% 157.36/157.41 ! [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)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__is__0,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__assoc,axiom,
% 157.36/157.41 ! [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)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__left__cancel,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( 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)
% 157.36/157.41 <=> V_m_2 = V_n_2 ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__right__cancel,axiom,
% 157.36/157.41 ! [V_n_2,V_k_2,V_m_2] :
% 157.36/157.41 ( 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)
% 157.36/157.41 <=> V_m_2 = V_n_2 ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__eq__self__zero,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 157.36/157.41 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__nonpos__nonpos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__increasing2,axiom,
% 157.36/157.41 ! [V_a,V_b,V_c,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__increasing,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__nonneg__eq__0__iff,axiom,
% 157.36/157.41 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__nonneg__nonneg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 157.36/157.41 ! [V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 157.36/157.41 ! [V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__0__left,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Omonoid__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__0,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__reorient,axiom,
% 157.36/157.41 ! [V_x_2,T_b] :
% 157.36/157.41 ( class_Groups_Ozero(T_b)
% 157.36/157.41 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 157.36/157.41 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_double__zero__sym,axiom,
% 157.36/157.41 ! [V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.36/157.41 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 157.36/157.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__0__right,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Omonoid__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add_Ocomm__neutral,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oab__semigroup__add(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__left__cancel,axiom,
% 157.36/157.41 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Ocancel__semigroup__add(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)
% 157.36/157.41 <=> V_b_2 = V_ca_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__right__cancel,axiom,
% 157.36/157.41 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 157.36/157.41 ( class_Groups_Ocancel__semigroup__add(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)
% 157.36/157.41 <=> V_b_2 = V_ca_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__left__imp__eq,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 157.36/157.41 => ( 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)
% 157.36/157.41 => V_b = V_c ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__imp__eq,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( 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)
% 157.36/157.41 => V_b = V_c ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__right__imp__eq,axiom,
% 157.36/157.41 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 157.36/157.41 => ( 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)
% 157.36/157.41 => V_b = V_c ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 157.36/157.41 ! [V_d,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 157.36/157.41 ! [V_d,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__0__iff,axiom,
% 157.36/157.41 ! [V_a_2,V_b_2,T_b] :
% 157.36/157.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.36/157.41 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 157.36/157.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 157.36/157.41 ! [V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 157.36/157.41 ! [V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 157.36/157.41 ! [V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__pos__pos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__neg__neg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_pos__add__strict,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_crossproduct__eq,axiom,
% 157.36/157.41 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 157.36/157.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
% 157.36/157.41 <=> ( V_w_2 = V_x_2
% 157.36/157.41 | V_y_2 = V_z_2 ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_combine__common__factor,axiom,
% 157.36/157.41 ! [V_c,V_b,V_e,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Osemiring(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 157.36/157.41 ! [V_b,V_m,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__class_Odistrib,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_crossproduct__noteq,axiom,
% 157.36/157.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.36/157.41 => ( ( V_a_2 != V_b_2
% 157.36/157.41 & V_ca_2 != V_d_2 )
% 157.36/157.41 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 157.36/157.41 ! [V_z,V_y,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__scale__eq__noteq,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 157.36/157.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 157.36/157.41 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 157.36/157.41 => ( ( V_a = V_b
% 157.36/157.41 & V_c != V_d )
% 157.36/157.41 => 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)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_sum__squares__eq__zero__iff,axiom,
% 157.36/157.41 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__add__0,axiom,
% 157.36/157.41 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__neq__one,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Ozero__neq__one(T_a)
% 157.36/157.41 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_one__neq__zero,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Ozero__neq__one(T_a)
% 157.36/157.41 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_sum__squares__ge__zero,axiom,
% 157.36/157.41 ! [V_y,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_sum__squares__le__zero__iff,axiom,
% 157.36/157.41 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_sum__squares__gt__zero__iff,axiom,
% 157.36/157.41 ! [V_y_2,V_x_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
% 157.36/157.41 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__sum__squares__lt__zero,axiom,
% 157.36/157.41 ! [V_y,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring(T_a)
% 157.36/157.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__two,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__nonpos__neg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__neg__nonpos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__strict__increasing2,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__strict__increasing,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__nonneg__pos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__pos__nonneg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__diff__split__asm,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_Pa_2] :
% 157.36/157.41 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 157.36/157.41 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.36/157.41 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.36/157.41 | ? [B_d] :
% 157.36/157.41 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 157.36/157.41 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__diff__split,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_Pa_2] :
% 157.36/157.41 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 157.36/157.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.36/157.41 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.36/157.41 & ! [B_d] :
% 157.36/157.41 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 157.36/157.41 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_convex__bound__le,axiom,
% 157.36/157.41 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__1(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__imp__le__left,axiom,
% 157.36/157.41 ! [V_b,V_a,V_c,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__imp__le__right,axiom,
% 157.36/157.41 ! [V_b,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__right__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__cancel__left,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__cancel__right,axiom,
% 157.36/157.41 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__imp__less__left,axiom,
% 157.36/157.41 ! [V_b,V_a,V_c,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__imp__less__right,axiom,
% 157.36/157.41 ! [V_b,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__strict__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__strict__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__strict__right__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__cancel__left,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__cancel__right,axiom,
% 157.36/157.41 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__diff__cancel,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ogroup__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__add__cancel,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ogroup__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__Suc__right,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__Suc,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__Suc__shift,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_termination__basic__simps_I2_J,axiom,
% 157.36/157.41 ! [V_y,V_z,V_x] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_termination__basic__simps_I1_J,axiom,
% 157.36/157.41 ! [V_z,V_y,V_x] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__lessD1,axiom,
% 157.36/157.41 ! [V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__eq__less,axiom,
% 157.36/157.41 ! [V_n,V_m,V_l,V_k] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 157.36/157.41 => ( 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)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__mono,axiom,
% 157.36/157.41 ! [V_l,V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__mono1,axiom,
% 157.36/157.41 ! [V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_trans__less__add2,axiom,
% 157.36/157.41 ! [V_m,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_trans__less__add1,axiom,
% 157.36/157.41 ! [V_m,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__left__cancel__less,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__add__less2,axiom,
% 157.36/157.41 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__add__less1,axiom,
% 157.36/157.41 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_termination__basic__simps_I4_J,axiom,
% 157.36/157.41 ! [V_y,V_z,V_x] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_termination__basic__simps_I3_J,axiom,
% 157.36/157.41 ! [V_z,V_y,V_x] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__leE,axiom,
% 157.36/157.41 ! [V_n,V_k,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 157.36/157.41 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__leD1,axiom,
% 157.36/157.41 ! [V_n,V_k,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__leD2,axiom,
% 157.36/157.41 ! [V_n,V_k,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__mono,axiom,
% 157.36/157.41 ! [V_l,V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__mono1,axiom,
% 157.36/157.41 ! [V_k,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_trans__le__add2,axiom,
% 157.36/157.41 ! [V_m,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_trans__le__add1,axiom,
% 157.36/157.41 ! [V_m,V_j,V_i] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat__add__left__cancel__le,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__iff__add,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__add1,axiom,
% 157.36/157.41 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__add2,axiom,
% 157.36/157.41 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__eq__if,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 157.36/157.41 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__cancel2,axiom,
% 157.36/157.41 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__cancel,axiom,
% 157.36/157.41 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__diff__left,axiom,
% 157.36/157.41 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__add__inverse,axiom,
% 157.36/157.41 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__add__inverse2,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__mult__distrib,axiom,
% 157.36/157.41 ! [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)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__mult__distrib2,axiom,
% 157.36/157.41 ! [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)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__eq__if,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.36/157.41 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_right__minus__eq,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Ogroup__add(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.36/157.41 <=> V_a_2 = V_b_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_eq__iff__diff__eq__0,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Oab__group__add(T_b)
% 157.36/157.41 => ( V_a_2 = V_b_2
% 157.36/157.41 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__self,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ogroup__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__0__right,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Groups_Ogroup__add(T_a)
% 157.36/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Zero__not__Suc,axiom,
% 157.36/157.41 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat_Osimps_I2_J,axiom,
% 157.36/157.41 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__not__Zero,axiom,
% 157.36/157.41 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_nat_Osimps_I3_J,axiom,
% 157.36/157.41 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Zero__neq__Suc,axiom,
% 157.36/157.41 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__neq__Zero,axiom,
% 157.36/157.41 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_gr0I,axiom,
% 157.36/157.41 ! [V_n] :
% 157.36/157.41 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_gr__implies__not0,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__nat__zero__code,axiom,
% 157.36/157.41 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_neq0__conv,axiom,
% 157.36/157.41 ! [V_n_2] :
% 157.36/157.41 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__less0,axiom,
% 157.36/157.41 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__0__eq,axiom,
% 157.36/157.41 ! [V_n_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 157.36/157.41 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 157.36/157.41 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__one,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_eq__add__iff2,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oring(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 157.36/157.41 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_eq__add__iff1,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oring(T_b)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 157.36/157.41 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diffs0__imp__equal,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 => V_m = V_n ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__self__eq__0,axiom,
% 157.36/157.41 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_minus__nat_Odiff__0,axiom,
% 157.36/157.41 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__0__eq__0,axiom,
% 157.36/157.41 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__cancel2,axiom,
% 157.36/157.41 ! [V_n_2,V_k_2,V_m_2] :
% 157.36/157.41 ( 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)
% 157.36/157.41 <=> ( V_m_2 = V_n_2
% 157.36/157.41 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__cancel1,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.36/157.41 ( 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)
% 157.36/157.41 <=> ( V_m_2 = V_n_2
% 157.36/157.41 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__is__0,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.36/157.41 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__0__right,axiom,
% 157.36/157.41 ! [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) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__0,axiom,
% 157.36/157.41 ! [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) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 157.36/157.41 ! [V_m,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 157.36/157.41 ! [V_a,V_m,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 157.36/157.41 ! [V_m,T_a] :
% 157.36/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.36/157.41 => 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) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__le__square,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__le__mult__iff,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 157.36/157.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__le__0__iff,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__nonneg__nonneg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__nonneg__nonpos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__nonneg__nonpos2,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__nonpos__nonneg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__nonpos__nonpos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__right__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__mult__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__comm__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__right__mono__neg,axiom,
% 157.36/157.41 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__left__mono__neg,axiom,
% 157.36/157.41 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__mono_H,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_split__mult__pos__le,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_a)
% 157.36/157.41 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_split__mult__neg__le,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.36/157.41 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__left__mono__neg,axiom,
% 157.36/157.41 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__right__mono__neg,axiom,
% 157.36/157.41 ! [V_c,V_a,V_b,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_comm__mult__strict__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__left__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__right__mono,axiom,
% 157.36/157.41 ! [V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__neg__neg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__neg__pos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__cancel__left__neg,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__mult__pos2,axiom,
% 157.36/157.41 ! [V_a,V_b,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__mult__pos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__pos__neg2,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__pos__neg,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__pos__pos,axiom,
% 157.36/157.41 ! [V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__cancel__left__pos,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__cancel__left__disj,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__cancel__right__disj,axiom,
% 157.36/157.41 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
% 157.36/157.41 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 157.36/157.41 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__square__less__zero,axiom,
% 157.36/157.41 ! [V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__ring(T_a)
% 157.36/157.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__one__le__zero,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__le__one,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_not__one__less__zero,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_zero__less__one,axiom,
% 157.36/157.41 ! [T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semidom(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__eq__plus1,axiom,
% 157.36/157.41 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_Suc__eq__plus1__left,axiom,
% 157.36/157.41 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_convex__bound__lt,axiom,
% 157.36/157.41 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 157.36/157.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card__def,axiom,
% 157.36/157.41 ! [V_A_2,T_b] :
% 157.36/157.41 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 157.36/157.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_card_Oeq__fold__g,axiom,
% 157.36/157.41 ! [V_A_2,T_b] :
% 157.36/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.36/157.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__le__less__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__less__le__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__add__iff1,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__add__iff2,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__iff2,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__iff1,axiom,
% 157.36/157.41 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Rings_Oordered__ring(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__left__le__imp__le,axiom,
% 157.36/157.41 ! [V_b,V_a,V_c,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__right__le__imp__le,axiom,
% 157.36/157.41 ! [V_b,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__imp__less__left,axiom,
% 157.36/157.41 ! [V_b,V_a,V_c,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__left__less__imp__less,axiom,
% 157.36/157.41 ! [V_b,V_a,V_c,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__imp__less__right,axiom,
% 157.36/157.41 ! [V_b,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__right__less__imp__less,axiom,
% 157.36/157.41 ! [V_b,V_c,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__le__less__imp__less,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__less__le__imp__less,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__mono_H,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__strict__mono,axiom,
% 157.36/157.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__le__cancel__left__neg,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__le__cancel__left__pos,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.36/157.41 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__iff__Suc__add,axiom,
% 157.36/157.41 ! [V_n_2,V_m_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.36/157.41 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__Suc2,axiom,
% 157.36/157.41 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__add__Suc1,axiom,
% 157.36/157.41 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__right__le__one__le,axiom,
% 157.36/157.41 ! [V_y,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__idom(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__left__le__one__le,axiom,
% 157.36/157.41 ! [V_y,V_x,T_a] :
% 157.36/157.41 ( class_Rings_Olinordered__idom(T_a)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 157.36/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__Suc__right,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_mult__Suc,axiom,
% 157.36/157.41 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_less__diff__conv,axiom,
% 157.36/157.41 ! [V_k_2,V_j_2,V_i_2] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__diff__inverse,axiom,
% 157.36/157.41 ! [V_n,V_m] :
% 157.36/157.41 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_le__iff__diff__le__0,axiom,
% 157.36/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.36/157.41 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.36/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.36/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_diff__add__assoc2,axiom,
% 157.36/157.41 ! [V_i,V_j,V_k] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.36/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ).
% 157.36/157.41
% 157.36/157.41 fof(fact_add__diff__assoc2,axiom,
% 157.36/157.41 ! [V_i,V_j,V_k] :
% 157.36/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.36/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ).
% 157.36/157.41
% 157.51/157.41 fof(fact_diff__add__assoc,axiom,
% 157.51/157.41 ! [V_i,V_j,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__imp__diff__is__add,axiom,
% 157.51/157.41 ! [V_k_2,V_j_2,V_i_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.51/157.41 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 157.51/157.41 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__add__diff__inverse2,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__diff__conv2,axiom,
% 157.51/157.41 ! [V_i_2,V_j_2,V_k_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_add__diff__assoc,axiom,
% 157.51/157.41 ! [V_i,V_j,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__add__diff__inverse,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__add__diff,axiom,
% 157.51/157.41 ! [V_m,V_n,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_le__diff__conv,axiom,
% 157.51/157.41 ! [V_i_2,V_k_2,V_j_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__diff__right,axiom,
% 157.51/157.41 ! [V_i,V_j,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_less__iff__diff__less__0,axiom,
% 157.51/157.41 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.41 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_less__Suc__eq__0__disj,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.51/157.41 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.41 | ? [B_j] :
% 157.51/157.41 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 157.51/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_less__Suc0,axiom,
% 157.51/157.41 ! [V_n_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 157.51/157.41 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_gr0__conv__Suc,axiom,
% 157.51/157.41 ! [V_n_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.51/157.41 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card_Oempty,axiom,
% 157.51/157.41 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__infinite,axiom,
% 157.51/157.41 ! [V_A_2,T_b] :
% 157.51/157.41 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__eq__1__iff,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2] :
% 157.51/157.41 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.51/157.41 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.51/157.41 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_zero__less__diff,axiom,
% 157.51/157.41 ! [V_m_2,V_n_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__less,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__0__less__mult__iff,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 157.51/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__less__cancel1,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__less__cancel2,axiom,
% 157.51/157.41 ! [V_n_2,V_k_2,V_m_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__less__mono1,axiom,
% 157.51/157.41 ! [V_k,V_j,V_i] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__less__mono2,axiom,
% 157.51/157.41 ! [V_k,V_j,V_i] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__is__0__eq_H,axiom,
% 157.51/157.41 ! [V_n,V_m] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__is__0__eq,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2] :
% 157.51/157.41 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_One__nat__def,axiom,
% 157.51/157.41 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__eq__self__implies__10,axiom,
% 157.51/157.41 ! [V_n,V_m] :
% 157.51/157.41 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 157.51/157.41 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.51/157.41 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_Suc__pred_H,axiom,
% 157.51/157.41 ! [V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.41 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__Suc__diff__eq2,axiom,
% 157.51/157.41 ! [V_m,V_j,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__Suc__diff__eq1,axiom,
% 157.51/157.41 ! [V_m,V_j,V_k] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_linorder__neqE__linordered__idom,axiom,
% 157.51/157.41 ! [V_y,V_x,T_a] :
% 157.51/157.41 ( class_Rings_Olinordered__idom(T_a)
% 157.51/157.41 => ( V_x != V_y
% 157.51/157.41 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 157.51/157.41 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 157.51/157.41 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 157.51/157.41 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 157.51/157.41 ! [V_rx,V_ly,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 157.51/157.41 ! [V_rx,V_ly,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 157.51/157.41 ! [V_ry,V_rx,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 157.51/157.41 ! [V_ry,V_rx,V_lx,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 157.51/157.41 ! [V_b,V_a,T_a] :
% 157.51/157.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.41 => 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) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__eq__0__iff,axiom,
% 157.51/157.41 ! [V_A_2,T_b] :
% 157.51/157.41 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.41 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.41 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_Sup__fin_Oidem,axiom,
% 157.51/157.41 ! [V_x,T_a] :
% 157.51/157.41 ( class_Lattices_Olattice(T_a)
% 157.51/157.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__ge__0__finite,axiom,
% 157.51/157.41 ! [V_A_2,T_b] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 157.51/157.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_Suc__pred,axiom,
% 157.51/157.41 ! [V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.41 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_diff__Suc__less,axiom,
% 157.51/157.41 ! [V_i,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_n__less__m__mult__n,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_n__less__n__mult__m,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_one__less__mult,axiom,
% 157.51/157.41 ! [V_m,V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_one__le__mult__iff,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 157.51/157.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__le__cancel1,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_mult__le__cancel2,axiom,
% 157.51/157.41 ! [V_n_2,V_k_2,V_m_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.51/157.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__less__Suc2,axiom,
% 157.51/157.41 ! [V_i_2,V_M_2] :
% 157.51/157.41 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.51/157.41 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__less,axiom,
% 157.51/157.41 ! [V_i_2,V_M_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.51/157.41 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__less__Suc,axiom,
% 157.51/157.41 ! [V_i_2,V_M_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.51/157.41 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card__gt__0__iff,axiom,
% 157.51/157.41 ! [V_A_2,T_b] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 157.51/157.41 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.41 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_finite__UNIV__card__ge__0,axiom,
% 157.51/157.41 ! [T_b] :
% 157.51/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.51/157.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_Suc__diff__1,axiom,
% 157.51/157.41 ! [V_n] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.41 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_card_Oinsert,axiom,
% 157.51/157.41 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.41 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__less__add__iff1,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__less__add__iff2,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__eq__add__iff2,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.51/157.41 => ( 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)
% 157.51/157.41 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__diff__add__eq2,axiom,
% 157.51/157.41 ! [V_n,V_m,V_u,V_j,V_i] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.51/157.41 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 157.51/157.41
% 157.51/157.41 fof(fact_nat__le__add__iff2,axiom,
% 157.51/157.41 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.51/157.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.51/157.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 157.51/157.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__eq__add__iff1,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.51/157.42 => ( 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)
% 157.51/157.42 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__diff__add__eq1,axiom,
% 157.51/157.42 ! [V_n,V_m,V_u,V_i,V_j] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__le__add__iff1,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.42 ( 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)
% 157.51/157.42 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 | V_m_2 = V_n_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_left__add__mult__distrib,axiom,
% 157.51/157.42 ! [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) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__mult__less__cancel1,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__mult__eq__cancel1,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.42 => ( 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)
% 157.51/157.42 <=> V_m_2 = V_n_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__mult__le__cancel1,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_k_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_semilattice__big_OF__eq,axiom,
% 157.51/157.42 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.51/157.42 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_triple_Osize_I1_J,axiom,
% 157.51/157.42 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_even__less__0__iff,axiom,
% 157.51/157.42 ! [V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Olinordered__idom(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_triple_Osize_I2_J,axiom,
% 157.51/157.42 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__monoid__big_OF__eq,axiom,
% 157.51/157.42 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.51/157.42 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Suc__eq,axiom,
% 157.51/157.42 ! [V_k_2,V_A_2,T_b] :
% 157.51/157.42 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 157.51/157.42 <=> ? [B_b,B_B] :
% 157.51/157.42 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 157.51/157.42 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 157.51/157.42 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 157.51/157.42 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oremove,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 157.51/157.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Osingleton,axiom,
% 157.51/157.42 ! [V_x_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oin__idem,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_OF__eq,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Osubset__idem,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 157.51/157.42 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.51/157.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Ounion__idem,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oinsert,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.51/157.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_double__eq__0__iff,axiom,
% 157.51/157.42 ! [V_a_2,T_b] :
% 157.51/157.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.51/157.42 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Oclosed,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__odd__less__0,axiom,
% 157.51/157.42 ! [V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Olinordered__idom(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I4_J,axiom,
% 157.51/157.42 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Pow,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Plus__conv__if,axiom,
% 157.51/157.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.51/157.42 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) )
% 157.51/157.42 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I12_J,axiom,
% 157.51/157.42 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Ohom__commute,axiom,
% 157.51/157.42 ! [V_N_2,V_h_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__power,axiom,
% 157.51/157.42 ! [V_n_2,V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 157.51/157.42 ! [V_q,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 157.51/157.42 ! [V_q,V_p,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 157.51/157.42 ! [V_q,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 157.51/157.42 ! [V_q,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 157.51/157.42 ! [V_q,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => 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) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 157.51/157.42 ! [V_q,V_p,V_x,T_a] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__0,axiom,
% 157.51/157.42 ! [T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__add,axiom,
% 157.51/157.42 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__mult,axiom,
% 157.51/157.42 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__diff,axiom,
% 157.51/157.42 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__1,axiom,
% 157.51/157.42 ! [T_b] :
% 157.51/157.42 ( class_Rings_Oring__1(T_b)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I10_J,axiom,
% 157.51/157.42 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I9_J,axiom,
% 157.51/157.42 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I2_J,axiom,
% 157.51/157.42 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_com_Osize_I1_J,axiom,
% 157.51/157.42 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__eq__if,axiom,
% 157.51/157.42 ! [V_p,V_m] :
% 157.51/157.42 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.51/157.42 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__double__eq__0__iff,axiom,
% 157.51/157.42 ! [V_a_2,T_b] :
% 157.51/157.42 ( class_Int_Oring__char__0(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__PlusD_I2_J,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__PlusD_I1_J,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__Plus,axiom,
% 157.51/157.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__Plus__iff,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 157.51/157.42 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Plus,axiom,
% 157.51/157.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Ints__odd__nonzero,axiom,
% 157.51/157.42 ! [V_a_2,T_b] :
% 157.51/157.42 ( class_Int_Oring__char__0(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__strict__mono,axiom,
% 157.51/157.42 ! [V_n,V_b,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_one__less__power,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__increasing__iff,axiom,
% 157.51/157.42 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__le__imp__le__exp,axiom,
% 157.51/157.42 ! [V_n,V_m,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__decreasing,axiom,
% 157.51/157.42 ! [V_a,V_N,V_n,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__strict__decreasing,axiom,
% 157.51/157.42 ! [V_a,V_N,V_n,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__Suc__less__one,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zpower__zadd__distrib,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zpower__zpower,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_field__power__not__zero,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 157.51/157.42 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__mult__distrib,axiom,
% 157.51/157.42 ! [V_n,V_b,V_a,T_a] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__commutes,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__one,axiom,
% 157.51/157.42 ! [V_n,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => 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) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__mult,axiom,
% 157.51/157.42 ! [V_n,V_m,V_a,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => 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) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__one__right,axiom,
% 157.51/157.42 ! [V_a,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zero__le__power,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__mono,axiom,
% 157.51/157.42 ! [V_n,V_b,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zero__less__power,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__eq__0__iff,axiom,
% 157.51/157.42 ! [V_n_2,V_a_2,T_b] :
% 157.51/157.42 ( ( class_Power_Opower(T_b)
% 157.51/157.42 & class_Rings_Omult__zero(T_b)
% 157.51/157.42 & class_Rings_Ono__zero__divisors(T_b)
% 157.51/157.42 & class_Rings_Ozero__neq__one(T_b) )
% 157.51/157.42 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.42 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.42 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_one__le__power,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__0__Suc,axiom,
% 157.51/157.42 ! [V_n,T_a] :
% 157.51/157.42 ( ( class_Power_Opower(T_a)
% 157.51/157.42 & class_Rings_Osemiring__0(T_a) )
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__inject__exp,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
% 157.51/157.42 <=> V_m_2 = V_n_2 ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__Suc2,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__Suc,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Power_Opower(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__0,axiom,
% 157.51/157.42 ! [V_a,T_a] :
% 157.51/157.42 ( class_Power_Opower(T_a)
% 157.51/157.42 => 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) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__add,axiom,
% 157.51/157.42 ! [V_n,V_m,V_a,T_a] :
% 157.51/157.42 ( class_Groups_Omonoid__mult(T_a)
% 157.51/157.42 => 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)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__Suc__0,axiom,
% 157.51/157.42 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 157.51/157.42 ! [V_m_2,V_x_2] :
% 157.51/157.42 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.51/157.42 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__zero__less__power__iff,axiom,
% 157.51/157.42 ! [V_n_2,V_x_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 157.51/157.42 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__power__less__imp__less,axiom,
% 157.51/157.42 ! [V_n,V_m,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__less__imp__less__base,axiom,
% 157.51/157.42 ! [V_b,V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__le__imp__le__base,axiom,
% 157.51/157.42 ! [V_b,V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__inject__base,axiom,
% 157.51/157.42 ! [V_b,V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.51/157.42 => V_a = V_b ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__less__power__Suc,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__gt1__lemma,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__0__left,axiom,
% 157.51/157.42 ! [V_n,T_a] :
% 157.51/157.42 ( ( class_Power_Opower(T_a)
% 157.51/157.42 & class_Rings_Osemiring__0(T_a) )
% 157.51/157.42 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 => 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) )
% 157.51/157.42 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.42 => 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) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__gt1,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__strict__increasing,axiom,
% 157.51/157.42 ! [V_a,V_N,V_n,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__less__imp__less__exp,axiom,
% 157.51/157.42 ! [V_n,V_m,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__strict__increasing__iff,axiom,
% 157.51/157.42 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__increasing,axiom,
% 157.51/157.42 ! [V_a,V_N,V_n,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__one__le__power,axiom,
% 157.51/157.42 ! [V_n,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__Suc__less,axiom,
% 157.51/157.42 ! [V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__eq__imp__eq__base,axiom,
% 157.51/157.42 ! [V_b,V_n,V_a,T_a] :
% 157.51/157.42 ( class_Rings_Olinordered__semidom(T_a)
% 157.51/157.42 => ( 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)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.42 => V_a = V_b ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_UNIV__Plus__UNIV,axiom,
% 157.51/157.42 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Plus__eq__empty__conv,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.51/157.42 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 157.51/157.42 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power__power__power,axiom,
% 157.51/157.42 ! [T_b] :
% 157.51/157.42 ( class_Power_Opower(T_b)
% 157.51/157.42 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__gen__delta,axiom,
% 157.51/157.42 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_ex__least__nat__less,axiom,
% 157.51/157.42 ! [V_n_2,V_Pa_2] :
% 157.51/157.42 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 157.51/157.42 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 157.51/157.42 => ? [B_k] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 157.51/157.42 & ! [B_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 157.51/157.42 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 157.51/157.42 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fold__Un__disjoint,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_diff__Suc,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf1E,axiom,
% 157.51/157.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 157.51/157.42 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 157.51/157.42 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf1I,axiom,
% 157.51/157.42 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 157.51/157.42 ( hBOOL(hAPP(V_A_2,V_x_2))
% 157.51/157.42 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_IntE,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.51/157.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_IntI,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__Int,axiom,
% 157.51/157.42 ! [V_Ga_2,V_F_2,T_b] :
% 157.51/157.42 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.51/157.42 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_pos__zmult__eq__1__iff,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.51/157.42 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.51/157.42 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zmult__zless__mono2,axiom,
% 157.51/157.42 ! [V_k,V_j,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__zmult__distrib,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__zmult__distrib2,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zmult__assoc,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zmult__commute,axiom,
% 157.51/157.42 ! [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) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zdiff__zmult__distrib2,axiom,
% 157.51/157.42 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zdiff__zmult__distrib,axiom,
% 157.51/157.42 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zmult__1__right,axiom,
% 157.51/157.42 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zmult__1,axiom,
% 157.51/157.42 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oidem,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf1D2,axiom,
% 157.51/157.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 157.51/157.42 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf1D1,axiom,
% 157.51/157.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 157.51/157.42 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__assoc,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__left__commute,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__left__absorb,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__commute,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__absorb,axiom,
% 157.51/157.42 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__apply,axiom,
% 157.51/157.42 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__assoc,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__aci_I2_J,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf_Oassoc,axiom,
% 157.51/157.42 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__left__commute,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__aci_I3_J,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf_Oleft__commute,axiom,
% 157.51/157.42 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__left__idem,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__aci_I4_J,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf_Oleft__idem,axiom,
% 157.51/157.42 ! [V_b,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__commute,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__aci_I1_J,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf_Ocommute,axiom,
% 157.51/157.42 ! [V_b,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__fun__def,axiom,
% 157.51/157.42 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__idem,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf_Oidem,axiom,
% 157.51/157.42 ! [V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Pow__Int__eq,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__ord_I1_J,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__le1,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__ord_I2_J,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__le2,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__iff__inf,axiom,
% 157.51/157.42 ! [V_y_2,V_x_2,T_b] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.51/157.42 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__inf__iff,axiom,
% 157.51/157.42 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.51/157.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__infI1,axiom,
% 157.51/157.42 ! [V_b,V_x,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__infI2,axiom,
% 157.51/157.42 ! [V_a,V_x,V_b,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__absorb1,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__absorb2,axiom,
% 157.51/157.42 ! [V_x,V_y,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__infI,axiom,
% 157.51/157.42 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__greatest,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__mono,axiom,
% 157.51/157.42 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__infE,axiom,
% 157.51/157.42 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
% 157.51/157.42 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.51/157.42 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_less__infI1,axiom,
% 157.51/157.42 ! [V_b,V_x,V_a,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_less__infI2,axiom,
% 157.51/157.42 ! [V_a,V_x,V_b,T_a] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_a)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__bot__right,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__bot__left,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__inf__distrib2,axiom,
% 157.51/157.42 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__distrib2,axiom,
% 157.51/157.42 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__inf__distrib1,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__distrib1,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__inf__absorb,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__sup__absorb,axiom,
% 157.51/157.42 ! [V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__eq__top__iff,axiom,
% 157.51/157.42 ! [V_y_2,V_x_2,T_b] :
% 157.51/157.42 ( class_Lattices_Obounded__lattice__top(T_b)
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 157.51/157.42 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 157.51/157.42 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__top__right,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__top__left,axiom,
% 157.51/157.42 ! [V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_IntD2,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_IntD1,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__iff,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.51/157.42 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_disjoint__iff__not__equal,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 <=> ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.42 => ! [B_xa] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 157.51/157.42 => B_x != B_xa ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__empty__right,axiom,
% 157.51/157.42 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__empty__left,axiom,
% 157.51/157.42 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_insert__inter__insert,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__mono,axiom,
% 157.51/157.42 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__greatest,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__absorb1,axiom,
% 157.51/157.42 ! [V_A_2,V_B_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__absorb2,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__lower2,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__lower1,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__UNIV__right,axiom,
% 157.51/157.42 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__UNIV__left,axiom,
% 157.51/157.42 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Un__Int__crazy,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Un__Int__distrib2,axiom,
% 157.51/157.42 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__Un__distrib2,axiom,
% 157.51/157.42 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Un__Int__distrib,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__Un__distrib,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__Int2,axiom,
% 157.51/157.42 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__Int__distrib2,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__Diff,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__Int__distrib,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inj__on__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.51/157.42 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.51/157.42 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_vimage__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__timesf,axiom,
% 157.51/157.42 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__1,axiom,
% 157.51/157.42 ! [V_A_2,T_c,T_b] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__Un__Int,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Ounion__inter,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fun__left__comm__idem__inf,axiom,
% 157.51/157.42 ! [T_b] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.42 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__Int__eq,axiom,
% 157.51/157.42 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Collect__conj__eq,axiom,
% 157.51/157.42 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_UN__simps_I5_J,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_UN__simps_I4_J,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_UN__extend__simps_I5_J,axiom,
% 157.51/157.42 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__UN__distrib,axiom,
% 157.51/157.42 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_UN__extend__simps_I4_J,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__UN__distrib2,axiom,
% 157.51/157.42 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Ounion__disjoint,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__Un__disjoint,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__zero,axiom,
% 157.51/157.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Rings_Ocomm__semiring__1(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ? [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.42 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__zero__iff,axiom,
% 157.51/157.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 157.51/157.42 & class_Rings_Ono__zero__divisors(T_c) )
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
% 157.51/157.42 <=> ? [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.42 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__empty,axiom,
% 157.51/157.42 ! [V_f_2,T_c,T_b] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oempty,axiom,
% 157.51/157.42 ! [V_g_2,T_c,T_b] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oinfinite,axiom,
% 157.51/157.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__infinite,axiom,
% 157.51/157.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__eq__1__iff,axiom,
% 157.51/157.42 ! [V_f_2,V_F_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.51/157.42 <=> ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 157.51/157.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_distrib__inf__le,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_distrib__sup__le,axiom,
% 157.51/157.42 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.42 ( class_Lattices_Olattice(T_a)
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__right,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.51/157.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__left,axiom,
% 157.51/157.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.51/157.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__right__if0,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.51/157.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__left__if0,axiom,
% 157.51/157.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.51/157.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__right__if1,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__insert__left__if1,axiom,
% 157.51/157.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_image__Int__subset,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__triv,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Un__Int__assoc__eq,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Odistrib,axiom,
% 157.51/157.42 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Un__Diff__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__Un,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Diff__Int,axiom,
% 157.51/157.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Image__Int__subset,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__Collect,axiom,
% 157.51/157.42 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Int__def,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__case__0,axiom,
% 157.51/157.42 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_nat__case__Suc,axiom,
% 157.51/157.42 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__pos__nat__iff,axiom,
% 157.51/157.42 ! [V_f_2,V_S_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
% 157.51/157.42 <=> ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__reindex__cong,axiom,
% 157.51/157.42 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.51/157.42 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.51/157.42 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.51/157.42 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__reindex,axiom,
% 157.51/157.42 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.51/157.42 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__delta,axiom,
% 157.51/157.42 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__delta_H,axiom,
% 157.51/157.42 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__Sup__absorb,axiom,
% 157.51/157.42 ! [V_a_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__constant,axiom,
% 157.51/157.42 ! [V_y_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inj__on__image__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.51/157.42 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_image__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.51/157.42 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power_Opower_Opower__0,axiom,
% 157.51/157.42 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 157.51/157.42
% 157.51/157.42 fof(fact_power_Opower_Opower__Suc,axiom,
% 157.51/157.42 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_image__vimage__eq,axiom,
% 157.51/157.42 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_if__image__distrib,axiom,
% 157.51/157.42 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.51/157.42 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__insert,axiom,
% 157.51/157.42 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oinsert,axiom,
% 157.51/157.42 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oreindex,axiom,
% 157.51/157.42 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_OF__eq,axiom,
% 157.51/157.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oeq__fold,axiom,
% 157.51/157.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fold1__belowI,axiom,
% 157.51/157.42 ! [V_a_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_below__fold1__iff,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
% 157.51/157.42 <=> ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Un__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Diff__subset__Int,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oinsert__remove,axiom,
% 157.51/157.42 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding__one_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding__one_Ounion__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 157.51/157.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card__Un__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inj__on__Un,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.51/157.42 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.51/157.42 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.51/157.42 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fold__image__Un__Int,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fold1__Un,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Sup__fin_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Oremove,axiom,
% 157.51/157.42 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_folding_Ounion,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.51/157.42 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_card_Ounion__inter__neutral,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.51/157.42 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_fold__image__Un__one,axiom,
% 157.51/157.42 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.51/157.42 => ( ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 157.51/157.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.51/157.42 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__Un__one,axiom,
% 157.51/157.42 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.51/157.42 => ( ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 157.51/157.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 157.51/157.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.42 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oremove,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 157.51/157.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__Sup1__distrib,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_inf__Sup2__distrib,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__diff1__eq,axiom,
% 157.51/157.42 ! [V_z_2,V_w_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zless__linear,axiom,
% 157.51/157.42 ! [V_y,V_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 157.51/157.42 | V_x = V_y
% 157.51/157.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zless__le,axiom,
% 157.51/157.42 ! [V_w_2,V_z_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 157.51/157.42 & V_z_2 != V_w_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_less__bin__lemma,axiom,
% 157.51/157.42 ! [V_l_2,V_k_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__strict__right__mono,axiom,
% 157.51/157.42 ! [V_k,V_j,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__0,axiom,
% 157.51/157.42 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__0__right,axiom,
% 157.51/157.42 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__commute,axiom,
% 157.51/157.42 ! [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) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__left__commute,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__assoc,axiom,
% 157.51/157.42 ! [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)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__zless__mono,axiom,
% 157.51/157.42 ! [V_z,V_z_H,V_w,V_w_H] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zadd__left__mono,axiom,
% 157.51/157.42 ! [V_k,V_j,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zless__imp__add1__zle,axiom,
% 157.51/157.42 ! [V_z,V_w] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_le__imp__0__less,axiom,
% 157.51/157.42 ! [V_z] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_add1__zle__eq,axiom,
% 157.51/157.42 ! [V_z_2,V_w_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__add1__eq__le,axiom,
% 157.51/157.42 ! [V_z_2,V_w_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_int__one__le__iff__zero__less,axiom,
% 157.51/157.42 ! [V_z_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_odd__nonzero,axiom,
% 157.51/157.42 ! [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) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_int__0__neq__1,axiom,
% 157.51/157.42 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_int__0__less__1,axiom,
% 157.51/157.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zless__add1__eq,axiom,
% 157.51/157.42 ! [V_z_2,V_w_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 157.51/157.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 157.51/157.42 | V_w_2 = V_z_2 ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_odd__less__0,axiom,
% 157.51/157.42 ! [V_z_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Osingleton,axiom,
% 157.51/157.42 ! [V_x_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__Collect__bounded__ex,axiom,
% 157.51/157.42 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2)))))
% 157.51/157.42 <=> ! [B_y] :
% 157.51/157.42 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_finite__image__set,axiom,
% 157.51/157.42 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 157.51/157.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.51/157.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__Inf2__distrib,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__Inf1__distrib,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Odistrib__lattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_sup__Inf__absorb,axiom,
% 157.51/157.42 ! [V_a_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oin__idem,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_OF__eq,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Osubset__idem,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Ounion__idem,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__le__Sup,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 157.51/157.42 ! [V_n_2,V_m_2] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 157.51/157.42 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oinsert,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.51/157.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Ounion__inter,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 157.51/157.42 ! [V_B_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_self__quotient__aux2,axiom,
% 157.51/157.42 ! [V_q,V_r,V_a] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.42 => ( 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))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_self__quotient__aux1,axiom,
% 157.51/157.42 ! [V_q,V_r,V_a] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.42 => ( 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))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 157.51/157.42 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 157.51/157.42 ( 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)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_unique__quotient__lemma__neg,axiom,
% 157.51/157.42 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zdiv__mono2__lemma,axiom,
% 157.51/157.42 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 157.51/157.42 ( 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)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_unique__quotient__lemma,axiom,
% 157.51/157.42 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__refl,axiom,
% 157.51/157.42 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__linear,axiom,
% 157.51/157.42 ! [V_w,V_z] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 157.51/157.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__trans,axiom,
% 157.51/157.42 ! [V_k,V_j,V_i] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_zle__antisym,axiom,
% 157.51/157.42 ! [V_w,V_z] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 157.51/157.42 => V_z = V_w ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_q__pos__lemma,axiom,
% 157.51/157.42 ! [V_r_H,V_q_H,V_b_H] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_q__neg__lemma,axiom,
% 157.51/157.42 ! [V_r_H,V_q_H,V_b_H] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 157.51/157.42 ! [V_n,V_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 157.51/157.42 ! [V_y,V_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 157.51/157.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 157.51/157.42 ! [V_y,V_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Oclosed,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_add__Max__commute,axiom,
% 157.51/157.42 ! [V_k_2,V_N_2,T_b] :
% 157.51/157.42 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Max_Osingleton,axiom,
% 157.51/157.42 ! [V_x_2,T_b] :
% 157.51/157.42 ( class_Orderings_Olinorder(T_b)
% 157.51/157.42 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Max__ge,axiom,
% 157.51/157.42 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.42 ( class_Orderings_Olinorder(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Max__in,axiom,
% 157.51/157.42 ! [V_A_2,T_b] :
% 157.51/157.42 ( class_Orderings_Olinorder(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Max__mono,axiom,
% 157.51/157.42 ! [V_N_2,V_M_2,T_b] :
% 157.51/157.42 ( class_Orderings_Olinorder(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 157.51/157.42 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 157.51/157.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_add__Min__commute,axiom,
% 157.51/157.42 ! [V_k_2,V_N_2,T_b] :
% 157.51/157.42 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_tsub__def,axiom,
% 157.51/157.42 ! [V_x,V_y] :
% 157.51/157.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.51/157.42 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.51/157.42 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_int__power__div__base,axiom,
% 157.51/157.42 ! [V_k,V_m] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.51/157.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.51/157.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_setprod__diff1,axiom,
% 157.51/157.42 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 157.51/157.42 ( class_Fields_Ofield(T_c)
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.42 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 157.51/157.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 157.51/157.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_Inf__fin_Ohom__commute,axiom,
% 157.51/157.42 ! [V_N_2,V_h_2,T_b] :
% 157.51/157.42 ( class_Lattices_Olattice(T_b)
% 157.51/157.42 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.51/157.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.42 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_strong__setprod__reindex__cong,axiom,
% 157.51/157.42 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.51/157.42 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.51/157.42 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.51/157.42 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.51/157.42 => ( ! [B_x] :
% 157.51/157.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.42 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
% 157.51/157.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 157.51/157.42
% 157.51/157.42 fof(fact_divide__zero__left,axiom,
% 157.51/157.42 ! [V_a,T_a] :
% 157.51/157.42 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.42 => 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) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__zero,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 157.51/157.43 => 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) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_add__divide__distrib,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => 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)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_times__divide__eq__right,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => 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) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_diff__divide__distrib,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__1,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zero,axiom,
% 157.51/157.43 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_power__divide,axiom,
% 157.51/157.43 ! [V_n,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => 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)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__by__0,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__0,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__by__1,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nonzero__eq__divide__eq,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_b)
% 157.51/157.43 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 157.51/157.43 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nonzero__divide__eq__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_b)
% 157.51/157.43 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 157.51/157.43 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__eq__imp,axiom,
% 157.51/157.43 ! [V_a,V_b,V_c,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_eq__divide__imp,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 157.51/157.43 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_right__inverse__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,T_b] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_b)
% 157.51/157.43 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 157.51/157.43 <=> V_a_2 = V_b_2 ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__self,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring(T_a)
% 157.51/157.43 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__self__if,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 157.51/157.43 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.51/157.43 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nonzero__power__divide,axiom,
% 157.51/157.43 ! [V_n,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => 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)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 157.51/157.43 ! [V_y,V_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__neg__pos__less0,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_power__one__over,axiom,
% 157.51/157.43 ! [V_n,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => 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) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__self,axiom,
% 157.51/157.43 ! [V_a] :
% 157.51/157.43 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__mult1__if,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.51/157.43 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self2__is__id,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self1__is__id,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__mult2,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__mult1,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__self,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_setprod__dividef,axiom,
% 157.51/157.43 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_c)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min_Osingleton,axiom,
% 157.51/157.43 ! [V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__eq__0__iff,axiom,
% 157.51/157.43 ! [V_k_2,V_i_2] :
% 157.51/157.43 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 157.51/157.43 ! [V_i_2,V_k_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__mono2,axiom,
% 157.51/157.43 ! [V_b,V_b_H,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__nonneg__neg__le0,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__pos__pos__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__nonpos__pos__le0,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__mono2__neg,axiom,
% 157.51/157.43 ! [V_b,V_b_H,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__neg__neg__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__mono1,axiom,
% 157.51/157.43 ! [V_b,V_a_H,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__mono1__neg,axiom,
% 157.51/157.43 ! [V_b,V_a_H,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_int__div__less__self,axiom,
% 157.51/157.43 ! [V_k,V_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zmult2__eq,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self2,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self1,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__add__self1,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__add__self2,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min__le,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min__in,axiom,
% 157.51/157.43 ! [V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_power__diff,axiom,
% 157.51/157.43 ! [V_m,V_n,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.51/157.43 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min__antimono,axiom,
% 157.51/157.43 ! [V_N_2,V_M_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 157.51/157.43 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divmod__int__rel__div__eq,axiom,
% 157.51/157.43 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 157.51/157.43 ( 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)
% 157.51/157.43 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.51/157.43 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__zdiv,axiom,
% 157.51/157.43 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.51/157.43 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 157.51/157.43 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.51/157.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.51/157.43 => ! [B_i] :
% 157.51/157.43 ( ? [B_j] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 157.51/157.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ! [B_i] :
% 157.51/157.43 ( ? [B_j] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 157.51/157.43 ! [V_y,V_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_tsub__eq,axiom,
% 157.51/157.43 ! [V_x,V_y] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.51/157.43 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__divide__eq,axiom,
% 157.51/157.43 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__le__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__le__divide__eq,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__divide__le__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__imp__div__pos__le,axiom,
% 157.51/157.43 ! [V_z,V_x,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__imp__le__div__pos,axiom,
% 157.51/157.43 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__le__dividend,axiom,
% 157.51/157.43 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__le__mono,axiom,
% 157.51/157.43 ! [V_k,V_n,V_m] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult2__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__1,axiom,
% 157.51/157.43 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__less,axiom,
% 157.51/157.43 ! [V_n,V_m] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nat__mult__div__cancel__disj,axiom,
% 157.51/157.43 ! [V_n,V_m,V_k] :
% 157.51/157.43 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.51/157.43 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__le__mono2,axiom,
% 157.51/157.43 ! [V_k,V_n,V_m] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nat__mult__div__cancel1,axiom,
% 157.51/157.43 ! [V_n,V_m,V_k] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self1__is__m,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult__self__is__m,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__less__dividend,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__if,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__geq,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__div,axiom,
% 157.51/157.43 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.51/157.43 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.51/157.43 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.51/157.43 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => ! [B_i,B_j] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 157.51/157.43 => ( 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)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__div__geq,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__div_H,axiom,
% 157.51/157.43 ! [V_n_2,V_m_2,V_Pa_2] :
% 157.51/157.43 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 157.51/157.43 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.51/157.43 | ? [B_q] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
% 157.51/157.43 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__div__lemma,axiom,
% 157.51/157.43 ! [V_m_2,V_q_2,V_n_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) )
% 157.51/157.43 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_times__divide__times__eq,axiom,
% 157.51/157.43 ! [V_w,V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zero__le__divide__iff,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__le__0__iff,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__right__mono,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__right__mono__neg,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zero__less__divide__iff,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__less__0__iff,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.51/157.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__pos__pos,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__pos__neg,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__neg__pos,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__neg__neg,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__strict__right__mono,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__strict__right__mono__neg,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_frac__eq__eq,axiom,
% 157.51/157.43 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 157.51/157.43 ( class_Fields_Ofield(T_b)
% 157.51/157.43 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
% 157.51/157.43 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__divide__mult__cancel__left,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__divide__mult__cancel__right,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__eq__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_b)
% 157.51/157.43 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 157.51/157.43 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 157.51/157.43 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_eq__divide__eq,axiom,
% 157.51/157.43 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_b)
% 157.51/157.43 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 157.51/157.43 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 157.51/157.43 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.51/157.43 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__nonpos__neg,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__nonpos__pos,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_frac__le,axiom,
% 157.51/157.43 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_frac__less,axiom,
% 157.51/157.43 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_frac__less2,axiom,
% 157.51/157.43 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__nonneg__neg,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__nonneg__pos,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__strict__left__mono__neg,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__strict__left__mono,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__divide__less__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__less__divide__eq,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__imp__less__div__pos,axiom,
% 157.51/157.43 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__imp__div__pos__less,axiom,
% 157.51/157.43 ! [V_z,V_x,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__divide__less__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__less__divide__eq,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__less__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_less__divide__eq,axiom,
% 157.51/157.43 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.51/157.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_add__frac__eq,axiom,
% 157.51/157.43 ! [V_w,V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__add__eq__iff,axiom,
% 157.51/157.43 ! [V_y,V_x,V_z,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_add__frac__num,axiom,
% 157.51/157.43 ! [V_z,V_x,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_add__divide__eq__iff,axiom,
% 157.51/157.43 ! [V_y,V_x,V_z,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_add__num__frac,axiom,
% 157.51/157.43 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.51/157.43 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_diff__divide__eq__iff,axiom,
% 157.51/157.43 ! [V_y,V_x,V_z,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__diff__eq__iff,axiom,
% 157.51/157.43 ! [V_y,V_x,V_z,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_diff__frac__eq,axiom,
% 157.51/157.43 ! [V_w,V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Fields_Ofield(T_a)
% 157.51/157.43 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_less__half__sum,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_gt__half__sum,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__left__mono__neg,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divide__left__mono,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__divide__le__eq,axiom,
% 157.51/157.43 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__le__divide__eq,axiom,
% 157.51/157.43 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.51/157.43 ( class_Fields_Olinordered__field(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.51/157.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_setprod__Un,axiom,
% 157.51/157.43 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.51/157.43 ( class_Fields_Ofield(T_c)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.51/157.43 => ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.43 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 157.51/157.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_setprod__mono__one__left,axiom,
% 157.51/157.43 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.51/157.43 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.51/157.43 => ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 157.51/157.43 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.51/157.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_setprod__mono__one__right,axiom,
% 157.51/157.43 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.51/157.43 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.51/157.43 => ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 157.51/157.43 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.51/157.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_field__le__mult__one__interval,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.51/157.43 => ( ! [B_z] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__pos__lemma,axiom,
% 157.51/157.43 ! [V_n_2,V_Pa_2,V_k_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 157.51/157.43 <=> ! [B_i,B_j] :
% 157.51/157.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__neg__lemma,axiom,
% 157.51/157.43 ! [V_n_2,V_Pa_2,V_k_2] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 157.51/157.43 <=> ! [B_i,B_j] :
% 157.51/157.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mod__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__self,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__by__0,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__0,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__cong,axiom,
% 157.51/157.43 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__simps_I1_J,axiom,
% 157.51/157.43 ! [V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__simps_I2_J,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__left__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__right__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__self1,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__add__self2,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__cong,axiom,
% 157.51/157.43 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__simps_I4_J,axiom,
% 157.51/157.43 ! [V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__mult2,axiom,
% 157.51/157.43 ! [V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__mult1,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__left__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__right__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__diff__cong,axiom,
% 157.51/157.43 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Oring__div(T_a)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.51/157.43 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__diff__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Oring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__diff__left__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Oring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__diff__right__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Oring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__self,axiom,
% 157.51/157.43 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zero,axiom,
% 157.51/157.43 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__simps_I3_J,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zmult1__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiff__zmod__left,axiom,
% 157.51/157.43 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiff__zmod__right,axiom,
% 157.51/157.43 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zpower__zmod,axiom,
% 157.51/157.43 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self2__is__0,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self1__is__0,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self2,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self1,axiom,
% 157.51/157.43 ! [V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__by__1,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__div__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__le__nonneg__dividend,axiom,
% 157.51/157.43 ! [V_k,V_m] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 157.51/157.43 ! [V_y,V_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__mod__bound,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__mod__bound,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__eq__0__iff,axiom,
% 157.51/157.43 ! [V_d_2,V_m_2] :
% 157.51/157.43 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_DIVISION__BY__ZERO,axiom,
% 157.51/157.43 ! [V_a] :
% 157.51/157.43 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zdiv__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zadd1__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mod__equality,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mod__equality2,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__div__equality,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__div__equality2,axiom,
% 157.51/157.43 ! [V_a,V_b,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Divides_Osemiring__div(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__mod__sign,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_pos__mod__conj,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__pos__pos__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__mod__sign,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_neg__mod__conj,axiom,
% 157.51/157.43 ! [V_a,V_b] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__neg__neg__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zdiv__equality,axiom,
% 157.51/157.43 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zmult1__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zmod__equality,axiom,
% 157.51/157.43 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zdiv__zmod__equality2,axiom,
% 157.51/157.43 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmult__div__cancel,axiom,
% 157.51/157.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zdiv__equality_H,axiom,
% 157.51/157.43 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__pos__neg__trivial,axiom,
% 157.51/157.43 ! [V_b,V_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_divmod__int__rel__mod__eq,axiom,
% 157.51/157.43 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 157.51/157.43 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 157.51/157.43 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.51/157.43 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmult2__lemma__aux2,axiom,
% 157.51/157.43 ! [V_q,V_r,V_b,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmult2__lemma__aux1,axiom,
% 157.51/157.43 ! [V_q,V_r,V_b,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmult2__lemma__aux4,axiom,
% 157.51/157.43 ! [V_q,V_b,V_r,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmult2__lemma__aux3,axiom,
% 157.51/157.43 ! [V_q,V_b,V_r,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__zmod,axiom,
% 157.51/157.43 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.51/157.43 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 157.51/157.43 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 157.51/157.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.51/157.43 => ! [B_i,B_j] :
% 157.51/157.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 157.51/157.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 => ! [B_i,B_j] :
% 157.51/157.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.51/157.43 & 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) )
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_zmod__zmult2__eq,axiom,
% 157.51/157.43 ! [V_b,V_a,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min_Oremove,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 157.51/157.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Max_Oremove,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 157.51/157.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_setprod__pos__nat,axiom,
% 157.51/157.43 ! [V_f_2,V_S_2,T_b] :
% 157.51/157.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.51/157.43 => ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 157.51/157.43 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.51/157.43 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.51/157.43 => ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.51/157.43 => hAPP(V_g_2,B_x) = V_z_2 )
% 157.51/157.43 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_finite__UN__I,axiom,
% 157.51/157.43 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.51/157.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( ! [B_a] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.51/157.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 157.51/157.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_inj__on__diff__nat,axiom,
% 157.51/157.43 ! [V_k_2,V_N_2] :
% 157.51/157.43 ( ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 157.51/157.43 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Odistrib__inf__le,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Odistrib__sup__le,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup_Oidem,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf_Oidem,axiom,
% 157.51/157.43 ! [V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup_Ocommute,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__commute,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf_Ocommute,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__commute,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__inf__absorb,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__left__idem,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 157.51/157.43 ! [V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__left__idem,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__left__commute,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 157.51/157.43 ! [V_c,V_a,V_b,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__left__commute,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup_Oassoc,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__assoc,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf_Oassoc,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__assoc,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 157.51/157.43 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 157.51/157.43 ! [V_x,V_z,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Max_Oidem,axiom,
% 157.51/157.43 ! [V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min_Oidem,axiom,
% 157.51/157.43 ! [V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__max__iff__disj,axiom,
% 157.51/157.43 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 157.51/157.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__supE,axiom,
% 157.51/157.43 ! [V_x,V_b,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
% 157.51/157.43 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.51/157.43 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__mono,axiom,
% 157.51/157.43 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__least,axiom,
% 157.51/157.43 ! [V_z,V_x,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__supI,axiom,
% 157.51/157.43 ! [V_b,V_x,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__absorb1,axiom,
% 157.51/157.43 ! [V_x,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Osup__absorb2,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__supI2,axiom,
% 157.51/157.43 ! [V_a,V_b,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__supI1,axiom,
% 157.51/157.43 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__sup__iff,axiom,
% 157.51/157.43 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__iff__sup,axiom,
% 157.51/157.43 ! [V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.51/157.43 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__maxI2,axiom,
% 157.51/157.43 ! [V_x,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__maxI1,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__le__iff__disj,axiom,
% 157.51/157.43 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 157.51/157.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__infE,axiom,
% 157.51/157.43 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
% 157.51/157.43 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.51/157.43 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__mono,axiom,
% 157.51/157.43 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__greatest,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__infI,axiom,
% 157.51/157.43 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__absorb2,axiom,
% 157.51/157.43 ! [V_x,V_y,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__absorb1,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__infI2,axiom,
% 157.51/157.43 ! [V_a,V_x,V_b,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__infI1,axiom,
% 157.51/157.43 ! [V_b,V_x,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__inf__iff,axiom,
% 157.51/157.43 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ole__iff__inf,axiom,
% 157.51/157.43 ! [V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.51/157.43 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__le2,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oinf__le1,axiom,
% 157.51/157.43 ! [V_y,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_less__max__iff__disj,axiom,
% 157.51/157.43 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 157.51/157.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__less__iff__conj,axiom,
% 157.51/157.43 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oless__supI2,axiom,
% 157.51/157.43 ! [V_a,V_b,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oless__supI1,axiom,
% 157.51/157.43 ! [V_b,V_a,V_x,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__less__iff__conj,axiom,
% 157.51/157.43 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__less__iff__disj,axiom,
% 157.51/157.43 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 157.51/157.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 157.51/157.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oless__infI2,axiom,
% 157.51/157.43 ! [V_a,V_x,V_b,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Oless__infI1,axiom,
% 157.51/157.43 ! [V_b,V_x,V_a,T_a] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_a)
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__add__distrib__left,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__add__distrib__left,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__diff__distrib__left,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__diff__distrib__left,axiom,
% 157.51/157.43 ! [V_z,V_y,V_x,T_a] :
% 157.51/157.43 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.51/157.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_sup__max,axiom,
% 157.51/157.43 ! [T_b] :
% 157.51/157.43 ( ( class_Lattices_Osemilattice__sup(T_b)
% 157.51/157.43 & class_Orderings_Olinorder(T_b) )
% 157.51/157.43 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 157.51/157.43 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__0L,axiom,
% 157.51/157.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__0R,axiom,
% 157.51/157.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 157.51/157.43
% 157.51/157.43 fof(fact_inf__min,axiom,
% 157.51/157.43 ! [T_b] :
% 157.51/157.43 ( ( class_Lattices_Osemilattice__inf(T_b)
% 157.51/157.43 & class_Orderings_Olinorder(T_b) )
% 157.51/157.43 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__0L,axiom,
% 157.51/157.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__0R,axiom,
% 157.51/157.43 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__less,axiom,
% 157.51/157.43 ! [V_n,V_m] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__Suc__Suc,axiom,
% 157.51/157.43 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__Suc__Suc,axiom,
% 157.51/157.43 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__less__eq__dividend,axiom,
% 157.51/157.43 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__distrib2,axiom,
% 157.51/157.43 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__distrib,axiom,
% 157.51/157.43 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__diff,axiom,
% 157.51/157.43 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 157.51/157.43 ! [T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 157.51/157.43 ! [T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__1,axiom,
% 157.51/157.43 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__Suc,axiom,
% 157.51/157.43 ! [V_n,V_m] :
% 157.51/157.43 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.51/157.43 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__less__divisor,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__eq__0__iff,axiom,
% 157.51/157.43 ! [V_d_2,V_m_2] :
% 157.51/157.43 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__geq,axiom,
% 157.51/157.43 ! [V_n,V_m] :
% 157.51/157.43 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__if,axiom,
% 157.51/157.43 ! [V_n,V_m] :
% 157.51/157.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 157.51/157.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self3,axiom,
% 157.51/157.43 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_le__mod__geq,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_nat__minus__add__max,axiom,
% 157.51/157.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__add1__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__Suc2,axiom,
% 157.51/157.43 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_max__Suc1,axiom,
% 157.51/157.43 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__le__divisor,axiom,
% 157.51/157.43 ! [V_m,V_n] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult__self4,axiom,
% 157.51/157.43 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Max_Oin__idem,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min_Oin__idem,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.51/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__mult2__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mult1__eq,axiom,
% 157.51/157.43 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Divides_Omod__div__equality_H,axiom,
% 157.51/157.43 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mult__div__cancel,axiom,
% 157.51/157.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_div__mod__equality_H,axiom,
% 157.51/157.43 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Max_OF__eq,axiom,
% 157.51/157.43 ! [V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min_OF__eq,axiom,
% 157.51/157.43 ! [V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__Suc1,axiom,
% 157.51/157.43 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__Suc2,axiom,
% 157.51/157.43 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_split__mod,axiom,
% 157.51/157.43 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.51/157.43 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 157.51/157.43 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 157.51/157.43 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.51/157.43 => ! [B_i,B_j] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 157.51/157.43 => ( 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)
% 157.51/157.43 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_mod__lemma,axiom,
% 157.51/157.43 ! [V_q,V_b,V_r,V_c] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Ofold1__belowI,axiom,
% 157.51/157.43 ! [V_a_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 157.51/157.43 <=> ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_fold1__below__iff,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 157.51/157.43 <=> ? [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_strict__below__fold1__iff,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 157.51/157.43 <=> ! [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_fold1__strict__below__iff,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 157.51/157.43 <=> ? [B_x] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.51/157.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Suc__times__mod__eq,axiom,
% 157.51/157.43 ! [V_m,V_k] :
% 157.51/157.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 157.51/157.43 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Max__insert,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.51/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.51/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.51/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ).
% 157.51/157.43
% 157.51/157.43 fof(fact_Min__insert,axiom,
% 157.51/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.51/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max_Osubset__idem,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Min_Osubset__idem,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max__Un,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Min__Un,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max_Oinsert,axiom,
% 157.60/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Min_Oinsert,axiom,
% 157.60/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_fold1__antimono,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max_Oinsert__remove,axiom,
% 157.60/157.43 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.60/157.43 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max_Ounion__inter,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.43 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 157.60/157.43
% 157.60/157.43 fof(fact_Max_Ounion__disjoint,axiom,
% 157.60/157.43 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.43 ( class_Orderings_Olinorder(T_b)
% 157.60/157.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Min_Oinsert__remove,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.60/157.44 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Min_Ounion__inter,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Min_Ounion__disjoint,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_dual__min,axiom,
% 157.60/157.44 ! [T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_dual__max,axiom,
% 157.60/157.44 ! [T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_max__ord__max,axiom,
% 157.60/157.44 ! [T_b] :
% 157.60/157.44 ( class_Orderings_Oord(T_b)
% 157.60/157.44 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__ord__min,axiom,
% 157.60/157.44 ! [T_b] :
% 157.60/157.44 ( class_Orderings_Oord(T_b)
% 157.60/157.44 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_sup__nat__def,axiom,
% 157.60/157.44 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_inf__nat__def,axiom,
% 157.60/157.44 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__le__Sup,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 157.60/157.44 ! [V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 157.60/157.44 ! [V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 157.60/157.44 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 157.60/157.44 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.60/157.44 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.60/157.44 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 157.60/157.44 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 157.60/157.44 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Max_Oclosed,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Min_Oclosed,axiom,
% 157.60/157.44 ! [V_A_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 157.60/157.44 ! [V_N_2,V_h_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.60/157.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 157.60/157.44 ! [V_N_2,V_h_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.60/157.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Max_Ohom__commute,axiom,
% 157.60/157.44 ! [V_N_2,V_h_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.60/157.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Min_Ohom__commute,axiom,
% 157.60/157.44 ! [V_N_2,V_h_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.60/157.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff1,axiom,
% 157.60/157.44 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff1__ring,axiom,
% 157.60/157.44 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Rings_Oring(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__commute,axiom,
% 157.60/157.44 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__0,axiom,
% 157.60/157.44 ! [V_A_2,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__addf,axiom,
% 157.60/157.44 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__right__distrib,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__0(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__left__distrib,axiom,
% 157.60/157.44 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__0(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__product,axiom,
% 157.60/157.44 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__0(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__subtractf,axiom,
% 157.60/157.44 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__divide__distrib,axiom,
% 157.60/157.44 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Fields_Ofield(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oempty,axiom,
% 157.60/157.44 ! [V_g_2,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__empty,axiom,
% 157.60/157.44 ! [V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oinfinite,axiom,
% 157.60/157.44 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__infinite,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__eq__0__iff,axiom,
% 157.60/157.44 ! [V_f_2,V_F_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.44 <=> ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 157.60/157.44 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Odistrib,axiom,
% 157.60/157.44 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__eq__setsum,axiom,
% 157.60/157.44 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__eq__Suc0__iff,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.60/157.44 <=> ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.44 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.60/157.44 & ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.60/157.44 => ( B_x != B_xa
% 157.60/157.44 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__reindex,axiom,
% 157.60/157.44 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.60/157.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__eq__1__iff,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.60/157.44 <=> ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.44 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.60/157.44 & ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.60/157.44 => ( B_x != B_xa
% 157.60/157.44 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__delta,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__delta_H,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__setsum__restrict,axiom,
% 157.60/157.44 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oinsert,axiom,
% 157.60/157.44 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__insert,axiom,
% 157.60/157.44 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.60/157.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__Un__Int,axiom,
% 157.60/157.44 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff,axiom,
% 157.60/157.44 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oreindex,axiom,
% 157.60/157.44 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_OF__eq,axiom,
% 157.60/157.44 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oeq__fold,axiom,
% 157.60/157.44 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff__nat,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__restrict__set_H,axiom,
% 157.60/157.44 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__restrict__set,axiom,
% 157.60/157.44 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__image__gen,axiom,
% 157.60/157.44 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oinsert__remove,axiom,
% 157.60/157.44 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__Un__disjoint,axiom,
% 157.60/157.44 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__Un,axiom,
% 157.60/157.44 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff1__nat,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__Un__nat,axiom,
% 157.60/157.44 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Oremove,axiom,
% 157.60/157.44 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff1_H,axiom,
% 157.60/157.44 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__mono2,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 => ( ! [B_b] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_arith__series__nat,axiom,
% 157.60/157.44 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__Un__zero,axiom,
% 157.60/157.44 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 157.60/157.44 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 157.60/157.44 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.60/157.44 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__mono3,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.44 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__lessThan,axiom,
% 157.60/157.44 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__eq__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 157.60/157.44 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__0,axiom,
% 157.60/157.44 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__Suc,axiom,
% 157.60/157.44 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__lessThan,axiom,
% 157.60/157.44 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__lessThan__UNIV,axiom,
% 157.60/157.44 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 157.60/157.44 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__lessThan__Suc,axiom,
% 157.60/157.44 ! [V_n_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__iff,axiom,
% 157.60/157.44 ! [V_k_2,V_i_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oord(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__subset__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__strict__subset__iff,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_single__Diff__lessThan,axiom,
% 157.60/157.44 ! [V_k_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__multicount,axiom,
% 157.60/157.44 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 157.60/157.44 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_arith__series__general,axiom,
% 157.60/157.44 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Rings_Ocomm__semiring__1(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__reindex__nonzero,axiom,
% 157.60/157.44 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.44 => ! [B_y] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 157.60/157.44 => ( B_x != B_y
% 157.60/157.44 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 157.60/157.44 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__multicount__gen,axiom,
% 157.60/157.44 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 157.60/157.44 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__nonneg__0,axiom,
% 157.60/157.44 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oordered__ab__group__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.60/157.44 => ( ! [B_i] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 157.60/157.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 157.60/157.44 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 157.60/157.44 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__eq__iff,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Nat_Osemiring__char__0(T_b)
% 157.60/157.44 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 157.60/157.44 <=> V_m_2 = V_n_2 ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_inj__int,axiom,
% 157.60/157.44 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 157.60/157.44 ! [V_A_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 157.60/157.44 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 157.60/157.44 ! [V_A_2] :
% 157.60/157.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 157.60/157.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__setsum,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__setprod,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__0,axiom,
% 157.60/157.44 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__eq__0__conv,axiom,
% 157.60/157.44 ! [V_n_2] :
% 157.60/157.44 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.44 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 157.60/157.44 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zero__zle__int,axiom,
% 157.60/157.44 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 157.60/157.44 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 157.60/157.44 ! [V_Pa_2] :
% 157.60/157.44 ( ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.44 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 157.60/157.44 ! [V_Pa_2] :
% 157.60/157.44 ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.44 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__less__0__conv,axiom,
% 157.60/157.44 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zless__int,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zle__int,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zadd__int,axiom,
% 157.60/157.44 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zadd__int__left,axiom,
% 157.60/157.44 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 157.60/157.44 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zle__iff__zadd,axiom,
% 157.60/157.44 ! [V_z_2,V_w_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 157.60/157.44 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zero__le__imp__of__nat,axiom,
% 157.60/157.44 ! [V_m,T_a] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__0__le__iff,axiom,
% 157.60/157.44 ! [V_n,T_a] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__less__0__iff,axiom,
% 157.60/157.44 ! [V_m,T_a] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__mult,axiom,
% 157.60/157.44 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zmult__int,axiom,
% 157.60/157.44 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 157.60/157.44 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__0,axiom,
% 157.60/157.44 ! [T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__less__iff,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_less__imp__of__nat__less,axiom,
% 157.60/157.44 ! [V_n,V_m,T_a] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__less__imp__less,axiom,
% 157.60/157.44 ! [V_n,V_m,T_a] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__1,axiom,
% 157.60/157.44 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 157.60/157.44 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__le__iff,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__add,axiom,
% 157.60/157.44 ! [V_n,V_m,T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__mult,axiom,
% 157.60/157.44 ! [V_n,V_m,T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zmod__int,axiom,
% 157.60/157.44 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 157.60/157.44 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zdiv__int,axiom,
% 157.60/157.44 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 157.60/157.44 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__1,axiom,
% 157.60/157.44 ! [T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Ints__of__nat,axiom,
% 157.60/157.44 ! [V_n_2,T_b] :
% 157.60/157.44 ( class_Rings_Oring__1(T_b)
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__power,axiom,
% 157.60/157.44 ! [V_n,V_m,T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__power,axiom,
% 157.60/157.44 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zpower__int,axiom,
% 157.60/157.44 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 157.60/157.44 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 157.60/157.44 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__setsum,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_inj__of__nat,axiom,
% 157.60/157.44 ! [T_b] :
% 157.60/157.44 ( class_Nat_Osemiring__char__0(T_b)
% 157.60/157.44 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__le__0__conv,axiom,
% 157.60/157.44 ! [V_n_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.44 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__Suc0__eq__1,axiom,
% 157.60/157.44 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zless__iff__Suc__zadd,axiom,
% 157.60/157.44 ! [V_z_2,V_w_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 157.60/157.44 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__Suc,axiom,
% 157.60/157.44 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__setprod,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.60/157.44 & class_Rings_Osemiring__1(T_b) )
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zdiff__int,axiom,
% 157.60/157.44 ! [V_m,V_n] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__Suc,axiom,
% 157.60/157.44 ! [V_m,T_a] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__diff,axiom,
% 157.60/157.44 ! [V_m,V_n,T_a] :
% 157.60/157.44 ( class_Rings_Oring__1(T_a)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 157.60/157.44 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__constant,axiom,
% 157.60/157.44 ! [V_A_2,V_y_2,T_c,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zero__less__int__conv,axiom,
% 157.60/157.44 ! [V_n_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zmult__zless__mono2__lemma,axiom,
% 157.60/157.44 ! [V_k,V_j,V_i] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__0__less__iff,axiom,
% 157.60/157.44 ! [V_n_2,T_b] :
% 157.60/157.44 ( class_Rings_Olinordered__semidom(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zdiff__int__split,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,V_Pa_2] :
% 157.60/157.44 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 157.60/157.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 157.60/157.44 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 157.60/157.44 ! [V_n_2,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__bounded,axiom,
% 157.60/157.44 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.44 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 157.60/157.44 & class_Rings_Osemiring__1(T_c) )
% 157.60/157.44 => ( ! [B_i] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 157.60/157.44 ! [V_x_2,V_y_2,V_ca_2] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 157.60/157.44 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.60/157.44 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.60/157.44 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__nonneg__leq__bound,axiom,
% 157.60/157.44 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 157.60/157.44 ( class_Groups_Oordered__ab__group__add(T_c)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.60/157.44 => ( ! [B_i] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 157.60/157.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
% 157.60/157.44 <=> V_x_2 = V_y_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( V_A_2 = V_B_2
% 157.60/157.44 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__int__eq,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] :
% 157.60/157.44 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
% 157.60/157.44 <=> V_m_2 = V_n_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_infinite__UNIV__int,axiom,
% 157.60/157.44 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.60/157.44 => V_b_2 = V_d_2 ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.60/157.44 => V_a_2 = V_ca_2 ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__eq__iff,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 157.60/157.44 <=> ( V_a_2 = V_ca_2
% 157.60/157.44 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__add__Un,axiom,
% 157.60/157.44 ! [V_k_2,V_j_2,V_i_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.60/157.44 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan0,axiom,
% 157.60/157.44 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeast0LessThan,axiom,
% 157.60/157.44 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_subset__card__intvl__is__intvl,axiom,
% 157.60/157.44 ! [V_k_2,V_A_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
% 157.60/157.44 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__Suc__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__empty,axiom,
% 157.60/157.44 ! [V_a_2,V_b_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 157.60/157.44 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__empty__iff,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__subset__iff,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 157.60/157.44 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I17_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 157.60/157.44 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__diff,axiom,
% 157.60/157.44 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I11_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__add__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__add__nat__ivl,axiom,
% 157.60/157.44 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__diff__nat__ivl,axiom,
% 157.60/157.44 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 157.60/157.44 ! [V_i_2,V_inc_2,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.44 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 157.60/157.44 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 157.60/157.44 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.44 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThan__singleton,axiom,
% 157.60/157.44 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__UN__finite__eq,axiom,
% 157.60/157.44 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I8_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I2_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 157.60/157.44 ! [V_k_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__head__upt__Suc,axiom,
% 157.60/157.44 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThanSuc,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__op__ivl__Suc,axiom,
% 157.60/157.44 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_geometric__sum,axiom,
% 157.60/157.44 ! [V_n_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Fields_Ofield(T_b)
% 157.60/157.44 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ex__nat__less__eq,axiom,
% 157.60/157.44 ! [V_Pa_2,V_n_2] :
% 157.60/157.44 ( ? [B_m] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.60/157.44 <=> ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_all__nat__less__eq,axiom,
% 157.60/157.44 ! [V_Pa_2,V_n_2] :
% 157.60/157.44 ( ! [B_m] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.60/157.44 <=> ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__finite2__subset,axiom,
% 157.60/157.44 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 157.60/157.44 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__finite2__eq,axiom,
% 157.60/157.44 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 157.60/157.44 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
% 157.60/157.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__finite__subset,axiom,
% 157.60/157.44 ! [V_C_2,V_A_2,T_b] :
% 157.60/157.44 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atLeastLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__add__int__atLeastLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I3_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThan__0,axiom,
% 157.60/157.44 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_sum__diff__distrib,axiom,
% 157.60/157.44 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 157.60/157.44 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x)))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__natinterval__difff,axiom,
% 157.60/157.44 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_gauss__sum,axiom,
% 157.60/157.44 ! [V_n_2,T_b] :
% 157.60/157.44 ( class_Rings_Ocomm__semiring__1(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__greaterThanLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__greaterThanLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThan__eq__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 157.60/157.44 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I12_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I13_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I7_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ex__nat__less,axiom,
% 157.60/157.44 ! [V_Pa_2,V_n_2] :
% 157.60/157.44 ( ? [B_m] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.60/157.44 <=> ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_all__nat__less,axiom,
% 157.60/157.44 ! [V_Pa_2,V_n_2] :
% 157.60/157.44 ( ! [B_m] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.60/157.44 <=> ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastatMost__empty__iff2,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastatMost__empty__iff,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastatMost__empty,axiom,
% 157.60/157.44 ! [V_a_2,V_b_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastatMost__subset__iff,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 157.60/157.44 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.60/157.44 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastAtMost__singleton,axiom,
% 157.60/157.44 ! [V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 157.60/157.44 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.44 <=> ( V_a_2 = V_b_2
% 157.60/157.44 & V_b_2 = V_ca_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastAtMost__singleton_H,axiom,
% 157.60/157.44 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( V_a_2 = V_b_2
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I18_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__Suc__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 157.60/157.44 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThanLessThan__empty,axiom,
% 157.60/157.44 ! [V_k_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 157.60/157.44 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__add__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThan__iff,axiom,
% 157.60/157.44 ! [V_k_2,V_i_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oord(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThan__subset__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastAtMostSuc__conv,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 157.60/157.44 ! [V_k_2,V_f_2] :
% 157.60/157.44 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I21_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I15_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__atLeastAtMost,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastatMost__psubset__iff,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 157.60/157.44 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.60/157.44 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 157.60/157.44 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 157.60/157.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I4_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__head__Suc,axiom,
% 157.60/157.44 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I9_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__greaterThanLessThan,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__greaterThanLessThan,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThan__Suc,axiom,
% 157.60/157.44 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__cl__ivl__Suc,axiom,
% 157.60/157.44 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__ub__add__nat,axiom,
% 157.60/157.44 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I15_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I6_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__le__eq__Un0,axiom,
% 157.60/157.44 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I19_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I4_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I5_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 157.60/157.44 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__greaterThanAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atLeastAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__greaterThanAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_finite__atMost,axiom,
% 157.60/157.44 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 157.60/157.44 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 157.60/157.44 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__int,axiom,
% 157.60/157.44 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atMost__eq__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 157.60/157.44 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__greaterThanAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I9_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I3_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__0,axiom,
% 157.60/157.44 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 157.60/157.44 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_eq__nat__nat__iff,axiom,
% 157.60/157.44 ! [V_z_H_2,V_z_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 157.60/157.44 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 157.60/157.44 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ex__nat,axiom,
% 157.60/157.44 ! [V_Pa_2] :
% 157.60/157.44 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.44 <=> ? [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.44 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_all__nat,axiom,
% 157.60/157.44 ! [V_Pa_2] :
% 157.60/157.44 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.44 <=> ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.60/157.44 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 157.60/157.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atLeastAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 157.60/157.44 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 157.60/157.44 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThanAtMost__empty,axiom,
% 157.60/157.44 ! [V_k_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 157.60/157.44 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 157.60/157.44 ! [V_l_2,V_k_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 157.60/157.44 ! [V_l_2,V_k_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
% 157.60/157.44 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeast0AtMost,axiom,
% 157.60/157.44 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I20_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 157.60/157.44 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I14_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_lessThan__Suc__atMost,axiom,
% 157.60/157.44 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atMost,axiom,
% 157.60/157.44 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__le__0,axiom,
% 157.60/157.44 ! [V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.44 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__0__iff,axiom,
% 157.60/157.44 ! [V_i_2] :
% 157.60/157.44 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__mono__iff,axiom,
% 157.60/157.44 ! [V_w_2,V_z_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zless__nat__conj,axiom,
% 157.60/157.44 ! [V_z_2,V_w_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atMost__Suc,axiom,
% 157.60/157.44 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atMost__iff,axiom,
% 157.60/157.44 ! [V_k_2,V_i_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oord(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__1,axiom,
% 157.60/157.44 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__nat__eq,axiom,
% 157.60/157.44 ! [V_z] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_int__eq__iff,axiom,
% 157.60/157.44 ! [V_z_2,V_m_2] :
% 157.60/157.44 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 157.60/157.44 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 157.60/157.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__0__le,axiom,
% 157.60/157.44 ! [V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zless__nat__eq__int__zless,axiom,
% 157.60/157.44 ! [V_z_2,V_m_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atMost__subset__iff,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__greaterThanAtMost,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__atLeastLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_zero__less__nat__eq,axiom,
% 157.60/157.44 ! [V_z_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__less__eq__zless,axiom,
% 157.60/157.44 ! [V_z_2,V_w_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__eq__iff2,axiom,
% 157.60/157.44 ! [V_w_2,V_m_2] :
% 157.60/157.44 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 157.60/157.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__eq__iff,axiom,
% 157.60/157.44 ! [V_m_2,V_w_2] :
% 157.60/157.44 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 157.60/157.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__le__eq__zle,axiom,
% 157.60/157.44 ! [V_z_2,V_w_2] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_split__nat,axiom,
% 157.60/157.44 ! [V_i_2,V_Pa_2] :
% 157.60/157.44 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 157.60/157.44 <=> ( ! [B_n] :
% 157.60/157.44 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 157.60/157.44 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.44 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__add__distrib,axiom,
% 157.60/157.44 ! [V_z_H,V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 157.60/157.44 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__mult__distrib,axiom,
% 157.60/157.44 ! [V_z_H,V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__diff__distrib,axiom,
% 157.60/157.44 ! [V_z,V_z_H] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 157.60/157.44 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__mod__distrib,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__div__distrib,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I22_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I16_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__atMost__UNIV,axiom,
% 157.60/157.44 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__greaterThanAtMost,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 157.60/157.44 ! [V_n,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__power__eq,axiom,
% 157.60/157.44 ! [V_n,V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 157.60/157.44 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__atMost__Suc,axiom,
% 157.60/157.44 ! [V_n_2,V_f_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_atMost__0,axiom,
% 157.60/157.44 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I10_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 157.60/157.44 ! [V_y,V_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I11_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_card__greaterThanLessThan__int,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I5_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_simp__from__to,axiom,
% 157.60/157.44 ! [V_i_2,V_j_2] :
% 157.60/157.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
% 157.60/157.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 157.60/157.44 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__atLeastAtMostL1,axiom,
% 157.60/157.44 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Int__atLeastAtMostR1,axiom,
% 157.60/157.44 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_UN__le__add__shift,axiom,
% 157.60/157.44 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__int_I1_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Oorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_one__less__nat__eq,axiom,
% 157.60/157.44 ! [V_z_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__less__iff,axiom,
% 157.60/157.44 ! [V_m_2,V_w_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 157.60/157.44 ! [V_z] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.44 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 157.60/157.44 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I16_J,axiom,
% 157.60/157.44 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_setsum__head,axiom,
% 157.60/157.44 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 157.60/157.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I2_J,axiom,
% 157.60/157.44 ! [V_u_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I10_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_ivl__disj__un_I7_J,axiom,
% 157.60/157.44 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.44 ( class_Orderings_Olinorder(T_b)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__aux__def,axiom,
% 157.60/157.44 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__morphism__nat__int,axiom,
% 157.60/157.44 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_bset_I8_J,axiom,
% 157.60/157.44 ! [V_B_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_aset_I6_J,axiom,
% 157.60/157.44 ! [V_A_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_aset_I4_J,axiom,
% 157.60/157.44 ! [V_A_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( B_x != V_t_2
% 157.60/157.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_bset_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 157.60/157.44 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_aset_I3_J,axiom,
% 157.60/157.44 ! [V_A_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 157.60/157.44 => ( ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 157.60/157.44 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 157.60/157.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_aset_I5_J,axiom,
% 157.60/157.44 ! [V_A_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 157.60/157.44 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_nat__set__def,axiom,
% 157.60/157.44 ! [V_S_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_S_2)
% 157.60/157.44 <=> ! [B_x] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 157.60/157.44 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => ( V_A_2 = V_B_2
% 157.60/157.44 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 157.60/157.44 ! [V_y_2,V_x_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.60/157.44 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 157.60/157.44 ! [V_x_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 157.60/157.44 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 157.60/157.44 ! [V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 157.60/157.44 ! [V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 157.60/157.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 157.60/157.44 ! [V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 157.60/157.44 ! [V_B_2,V_A_2] :
% 157.60/157.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 157.60/157.44 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.44 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_bset_I4_J,axiom,
% 157.60/157.44 ! [V_B_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( B_x != V_t_2
% 157.60/157.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_bset_I7_J,axiom,
% 157.60/157.44 ! [V_B_2,V_t_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 157.60/157.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 157.60/157.44
% 157.60/157.44 fof(fact_bset_I6_J,axiom,
% 157.60/157.44 ! [V_t_2,V_B_2,V_D_2] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.44 => ! [B_x] :
% 157.60/157.44 ( ! [B_xa] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.44 => ! [B_xb] :
% 157.60/157.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.60/157.44 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_aset_I8_J,axiom,
% 157.60/157.45 ! [V_t_2,V_A_2,V_D_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.45 => ! [B_x] :
% 157.60/157.45 ( ! [B_xa] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.45 => ! [B_xb] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.60/157.45 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 157.60/157.45 ! [V_A_2,V_x_2] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.60/157.45 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 157.60/157.45 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 157.60/157.45 ! [V_y,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 157.60/157.45 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 157.60/157.45 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 157.60/157.45 ! [V_y,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 157.60/157.45 ! [V_y,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 157.60/157.45 ! [V_y,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 157.60/157.45 ! [V_n,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 157.60/157.45 ! [V_y,V_x] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_is__nat__def,axiom,
% 157.60/157.45 ! [V_x_2] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.60/157.45 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 157.60/157.45 ! [V_x_2,V_A_2] :
% 157.60/157.45 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 157.60/157.45 ! [V_n_2,V_m_2] :
% 157.60/157.45 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 157.60/157.45 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 157.60/157.45 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 157.60/157.45 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.45 ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 157.60/157.45 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.45 ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_periodic__finite__ex,axiom,
% 157.60/157.45 ! [V_Pa_2,V_d_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.60/157.45 => ( ! [B_x,B_k] :
% 157.60/157.45 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.45 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 157.60/157.45 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.45 <=> ? [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2)))
% 157.60/157.45 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_bset_I5_J,axiom,
% 157.60/157.45 ! [V_t_2,V_B_2,V_D_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.45 => ! [B_x] :
% 157.60/157.45 ( ! [B_xa] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.45 => ! [B_xb] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.60/157.45 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_aset_I7_J,axiom,
% 157.60/157.45 ! [V_t_2,V_A_2,V_D_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.60/157.45 => ! [B_x] :
% 157.60/157.45 ( ! [B_xa] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 157.60/157.45 => ! [B_xb] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.60/157.45 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__Suc,axiom,
% 157.60/157.45 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__un_I12_J,axiom,
% 157.60/157.45 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_decr__mult__lemma,axiom,
% 157.60/157.45 ! [V_k_2,V_Pa_2,V_d_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.60/157.45 => ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__eq__iff,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 157.60/157.45 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__iff,axiom,
% 157.60/157.45 ! [V_k_2,V_i_2,T_b] :
% 157.60/157.45 ( class_Orderings_Oord(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__subset__iff,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Orderings_Oorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__0,axiom,
% 157.60/157.45 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atLeast__Suc__greaterThan,axiom,
% 157.60/157.45 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__un_I14_J,axiom,
% 157.60/157.45 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__int_I8_J,axiom,
% 157.60/157.45 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Oorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Int__atLeastAtMostR2,axiom,
% 157.60/157.45 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Int__atLeastAtMostL2,axiom,
% 157.60/157.45 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_UN__atLeast__UNIV,axiom,
% 157.60/157.45 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__int_I6_J,axiom,
% 157.60/157.45 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Oorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_atMost__Int__atLeast,axiom,
% 157.60/157.45 ! [V_n_2,T_b] :
% 157.60/157.45 ( class_Orderings_Oorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__un_I1_J,axiom,
% 157.60/157.45 ! [V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ivl__disj__un_I13_J,axiom,
% 157.60/157.45 ! [V_u_2,V_l_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_incr__mult__lemma,axiom,
% 157.60/157.45 ! [V_k_2,V_Pa_2,V_d_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.60/157.45 => ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__less__imp__eq__int,axiom,
% 157.60/157.45 ! [V_k] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.60/157.45 => ? [B_n] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 157.60/157.45 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__mono__zero__left,axiom,
% 157.60/157.45 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.60/157.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 157.60/157.45 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__mono__zero__right,axiom,
% 157.60/157.45 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.60/157.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 157.60/157.45 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__strict__mono,axiom,
% 157.60/157.45 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.45 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.45 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 157.60/157.45 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.45 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.45 => ( V_A_2 = V_B_2
% 157.60/157.45 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.45 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_incr__lemma,axiom,
% 157.60/157.45 ! [V_x,V_z,V_d] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_decr__lemma,axiom,
% 157.60/157.45 ! [V_z,V_x,V_d] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__abs,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__abs__ge__zero,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__minus__commute,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__le__D1,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__ge__self,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__add__abs,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__mult,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__mult__self,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__one,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__abs,axiom,
% 157.60/157.45 ! [V_n,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__idempotent,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__eq__0,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__zero,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__divide,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__of__nat,axiom,
% 157.60/157.45 ! [V_n,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__int__eq,axiom,
% 157.60/157.45 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__setsum__abs,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__setprod,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Fields_Olinordered__field(T_b)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__ge__zero,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__le__zero__iff,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__of__nonneg,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__of__pos,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__less__abs__iff,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
% 157.60/157.45 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__not__less__zero,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__triangle__ineq,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__mult__less,axiom,
% 157.60/157.45 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__triangle__ineq2__sym,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__triangle__ineq2,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__triangle__ineq3,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nonzero__abs__divide,axiom,
% 157.60/157.45 ! [V_a,V_b,T_a] :
% 157.60/157.45 ( class_Fields_Olinordered__field(T_a)
% 157.60/157.45 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__zmult__eq__1,axiom,
% 157.60/157.45 ! [V_n,V_m] :
% 157.60/157.45 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__mult__pos,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__eq__mult,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oordered__ring__abs(T_a)
% 157.60/157.45 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.60/157.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 157.60/157.45 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.60/157.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__diff__triangle__ineq,axiom,
% 157.60/157.45 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__triangle__ineq4,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__le__power__abs,axiom,
% 157.60/157.45 ! [V_n,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__div__pos,axiom,
% 157.60/157.45 ! [V_x,V_y,T_a] :
% 157.60/157.45 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zabs__less__one__iff,axiom,
% 157.60/157.45 ! [V_z_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 157.60/157.45 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__abs__mult__distrib,axiom,
% 157.60/157.45 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__le__zpower__abs,axiom,
% 157.60/157.45 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__less__zpower__abs__iff,axiom,
% 157.60/157.45 ! [V_n_2,V_x_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
% 157.60/157.45 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 157.60/157.45 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 157.60/157.45 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.45 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.60/157.45 => ( V_A_2 = V_B_2
% 157.60/157.45 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.45 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_int__val__lemma,axiom,
% 157.60/157.45 ! [V_k_2,V_f_2,V_n_2] :
% 157.60/157.45 ( ! [B_i] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.60/157.45 => ? [B_i] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.45 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat0__intermed__int__val,axiom,
% 157.60/157.45 ! [V_k_2,V_f_2,V_n_2] :
% 157.60/157.45 ( ! [B_i] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.60/157.45 => ? [B_i] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.45 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 157.60/157.45 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__nat__eq__if,axiom,
% 157.60/157.45 ! [V_z_2,V_z_H_2] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__SucD,axiom,
% 157.60/157.45 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 157.60/157.45 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 157.60/157.45 => ? [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__cases,axiom,
% 157.60/157.45 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 157.60/157.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_inj__uminus,axiom,
% 157.60/157.45 ! [V_A_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ComplI,axiom,
% 157.60/157.45 ! [V_A_2,V_ca_2,T_b] :
% 157.60/157.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__minus__cancel,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__diff__eq,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oab__group__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__subset__Compl__iff,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__anti__mono,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__less__iff__less,axiom,
% 157.60/157.45 ! [V_a_2,V_b_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__less__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__minus__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__mono,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__imp__neg__le,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__le__compl__iff,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__le__iff__le,axiom,
% 157.60/157.45 ! [V_a_2,V_b_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__le__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__minus__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__equal__zero,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__equal__0__iff__equal,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_equal__neg__zero,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__0__equal__iff__equal,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 157.60/157.45 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__zero,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__add__cancel,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__minus__cancel,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__add,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__add__distrib,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oab__group__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__mult__right,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oring(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__mult__left,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oring(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__mult__commute,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__mult__minus,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_square__eq__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Oidom(T_b)
% 157.60/157.45 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 157.60/157.45 <=> ( V_a_2 = V_b_2
% 157.60/157.45 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_fun__Compl__def,axiom,
% 157.60/157.45 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Ouminus(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__minus,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_double__compl,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_uminus__apply,axiom,
% 157.60/157.45 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Ouminus(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_equation__minus__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.60/157.45 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__equation__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 157.60/157.45 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__equal__iff__equal,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.60/157.45 <=> V_a_2 = V_b_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__eq__compl__iff,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_b)
% 157.60/157.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 157.60/157.45 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_double__complement,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__eq__Compl__iff,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
% 157.60/157.45 <=> V_A_2 = V_B_2 ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mod__minus__cong,axiom,
% 157.60/157.45 ! [V_a_H,V_b,V_a,T_a] :
% 157.60/157.45 ( class_Divides_Oring__div(T_a)
% 157.60/157.45 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mod__minus__eq,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Divides_Oring__div(T_a)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__divide__left,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Odivision__ring(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__divide__divide,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__divide__right,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__iff,axiom,
% 157.60/157.45 ! [V_A_2,V_ca_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.60/157.45 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ComplD,axiom,
% 157.60/157.45 ! [V_A_2,V_ca_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.60/157.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ComplE,axiom,
% 157.60/157.45 ! [V_A_2,V_ca_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.60/157.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_vimage__Compl,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__0,axiom,
% 157.60/157.45 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__int,axiom,
% 157.60/157.45 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__1,axiom,
% 157.60/157.45 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_setsum__negf,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Collect__neg__eq,axiom,
% 157.60/157.45 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__0__le__iff__le,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__minus__self__iff,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__le__0__iff__le,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__le__self__iff,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__minus__self__iff,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__less__nonneg,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__less__0__iff__less,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__0__less__iff__less,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_right__minus,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_b)
% 157.60/157.45 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.60/157.45 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_left__minus,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ab__left__minus,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oab__group__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__unique,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__0,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Rings_Ocomm__ring__1(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__def,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_ab__diff__minus,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oab__group__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__minus__eq__add,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Ogroup__add(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_square__eq__1__iff,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.60/157.45 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.45 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.45 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Rings_Ocomm__ring__1(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_inf__compl__bot,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__inf__bot,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__eq,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__bot__eq,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__top__eq,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__inf,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__sup,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sup__compl__top,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__sup__top,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nonzero__minus__divide__right,axiom,
% 157.60/157.45 ! [V_a,V_b,T_a] :
% 157.60/157.45 ( class_Rings_Odivision__ring(T_a)
% 157.60/157.45 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nonzero__minus__divide__divide,axiom,
% 157.60/157.45 ! [V_a,V_b,T_a] :
% 157.60/157.45 ( class_Rings_Odivision__ring(T_a)
% 157.60/157.45 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__ge__minus__self,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__le__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 157.60/157.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.60/157.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__leI,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__le__D2,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__less__iff,axiom,
% 157.60/157.45 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 157.60/157.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.60/157.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_subset__Compl__self__eq,axiom,
% 157.60/157.45 ! [V_A_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.60/157.45 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__UNIV__eq,axiom,
% 157.60/157.45 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__empty__eq,axiom,
% 157.60/157.45 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_finite__compl,axiom,
% 157.60/157.45 ! [V_A_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.60/157.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__disjoint,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__disjoint2,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__partition,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__partition2,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__Un,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__Int,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__max__eq__min,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__min__eq__max,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__atLeastAtMost,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__power__minus,axiom,
% 157.60/157.45 ! [V_n,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__Diff__eq,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Diff__eq,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Diff__Compl,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Ints__minus,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Oring__1(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__eq,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__atLeast,axiom,
% 157.60/157.45 ! [V_k_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__lessThan,axiom,
% 157.60/157.45 ! [V_k_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Collect__imp__eq,axiom,
% 157.60/157.45 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__greaterThan,axiom,
% 157.60/157.45 ! [V_k_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Compl__atMost,axiom,
% 157.60/157.45 ! [V_k_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__eq__ge__0,axiom,
% 157.60/157.45 ! [V_x_2] :
% 157.60/157.45 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__def,axiom,
% 157.60/157.45 ! [V_Z_2] :
% 157.60/157.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__nat,axiom,
% 157.60/157.45 ! [V_z] :
% 157.60/157.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 157.60/157.45 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__nat,axiom,
% 157.60/157.45 ! [V_z] :
% 157.60/157.45 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__of__nonpos,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__minus__le__zero,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__if,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oabs__if(T_a)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__of__neg,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__minus,axiom,
% 157.60/157.45 ! [V_n,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_disjoint__eq__subset__Compl,axiom,
% 157.60/157.45 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.45 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_surj__Compl__image__subset,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.60/157.45 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__atLeastLessThan,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__lessThan,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__greaterThan,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__atMost,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_image__uminus__atLeast,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.60/157.45 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Pow__Compl,axiom,
% 157.60/157.45 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_compl__unique,axiom,
% 157.60/157.45 ! [V_y,V_x,T_a] :
% 157.60/157.45 ( class_Lattices_Oboolean__algebra(T_a)
% 157.60/157.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 157.60/157.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_inj__image__Compl__subset,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_vimage__if,axiom,
% 157.60/157.45 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.60/157.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.60/157.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.60/157.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.60/157.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__gcd_Osimps,axiom,
% 157.60/157.45 ! [V_x,V_y] :
% 157.60/157.45 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.45 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 157.60/157.45 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.45 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__Max__eq__Min,axiom,
% 157.60/157.45 ! [V_S_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.45 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__Min__eq__Max,axiom,
% 157.60/157.45 ! [V_S_2,T_b] :
% 157.60/157.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.45 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 157.60/157.45 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__neg,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__1__neg,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__if,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Groups_Osgn__if(T_a)
% 157.60/157.45 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.60/157.45 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negative__zle,axiom,
% 157.60/157.45 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negative__zless,axiom,
% 157.60/157.45 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zdiv__zminus__zminus,axiom,
% 157.60/157.45 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zdiv__zminus2,axiom,
% 157.60/157.45 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmult__zminus,axiom,
% 157.60/157.45 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zminus__0,axiom,
% 157.60/157.45 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zminus__zadd__distrib,axiom,
% 157.60/157.45 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zminus__zmod,axiom,
% 157.60/157.45 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus__zminus,axiom,
% 157.60/157.45 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus2,axiom,
% 157.60/157.45 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__sgn,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => 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) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zsgn__def,axiom,
% 157.60/157.45 ! [V_i] :
% 157.60/157.45 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.45 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__0__0,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn0,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Groups_Osgn__if(T_a)
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__times,axiom,
% 157.60/157.45 ! [V_b,V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => 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)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zadd__zminus__inverse2,axiom,
% 157.60/157.45 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negative__eq__positive,axiom,
% 157.60/157.45 ! [V_m_2,V_n_2] :
% 157.60/157.45 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
% 157.60/157.45 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.45 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__int__zless__negative,axiom,
% 157.60/157.45 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus2__not__zero,axiom,
% 157.60/157.45 ! [V_l,V_k] :
% 157.60/157.45 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus1__not__zero,axiom,
% 157.60/157.45 ! [V_l,V_k] :
% 157.60/157.45 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__int__def__symmetric,axiom,
% 157.60/157.45 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__int__def,axiom,
% 157.60/157.45 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_int__zle__neg,axiom,
% 157.60/157.45 ! [V_m_2,V_n_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
% 157.60/157.45 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.45 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negative__zle__0,axiom,
% 157.60/157.45 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__less,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__greater,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__zminus__int,axiom,
% 157.60/157.45 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus1__eq__if,axiom,
% 157.60/157.45 ! [V_b,V_a] :
% 157.60/157.45 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.45 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zmod__zminus2__eq__if,axiom,
% 157.60/157.45 ! [V_b,V_a] :
% 157.60/157.45 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.45 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zabs__def,axiom,
% 157.60/157.45 ! [V_i] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__zminus__int,axiom,
% 157.60/157.45 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__sgn,axiom,
% 157.60/157.45 ! [V_k,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__sgn__abs,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__zle__0__negative,axiom,
% 157.60/157.45 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negative__zless__0,axiom,
% 157.60/157.45 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__pos,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.60/157.45 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_sgn__1__pos,axiom,
% 157.60/157.45 ! [V_a_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__mult__distrib__neg,axiom,
% 157.60/157.45 ! [V_z_H,V_z] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zdiv__zminus1__eq__if,axiom,
% 157.60/157.45 ! [V_a,V_b] :
% 157.60/157.45 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 157.60/157.45 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zdiv__zminus2__eq__if,axiom,
% 157.60/157.45 ! [V_a,V_b] :
% 157.60/157.45 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 157.60/157.45 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_z3div__def,axiom,
% 157.60/157.45 ! [V_k,V_l] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.45 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.45 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_z3mod__def,axiom,
% 157.60/157.45 ! [V_k,V_l] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.45 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.45 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__of__nat,axiom,
% 157.60/157.45 ! [V_k,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__mod__eq__lemma,axiom,
% 157.60/157.45 ! [V_y,V_n,V_x] :
% 157.60/157.45 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 157.60/157.45 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zminus__zminus,axiom,
% 157.60/157.45 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__minus,axiom,
% 157.60/157.45 ! [V_z,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__int__eq,axiom,
% 157.60/157.45 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__eq__iff,axiom,
% 157.60/157.45 ! [V_z_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Int_Oring__char__0(T_b)
% 157.60/157.45 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 157.60/157.45 <=> V_w_2 = V_z_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__eq__0__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Int_Oring__char__0(T_b)
% 157.60/157.45 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__0__eq__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Int_Oring__char__0(T_b)
% 157.60/157.45 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 157.60/157.45 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__0,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__le__iff,axiom,
% 157.60/157.45 ! [V_z_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__less__iff,axiom,
% 157.60/157.45 ! [V_z_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__add,axiom,
% 157.60/157.45 ! [V_z,V_w,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__mult,axiom,
% 157.60/157.45 ! [V_z,V_w,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__1,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__diff,axiom,
% 157.60/157.45 ! [V_z,V_w,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__of__nat__eq,axiom,
% 157.60/157.45 ! [V_n,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Ints__of__int,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Rings_Oring__1(T_b)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__power,axiom,
% 157.60/157.45 ! [V_n,V_z,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__setsum,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( class_Rings_Oring__1(T_b)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__setprod,axiom,
% 157.60/157.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.45 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.60/157.45 & class_Rings_Oring__1(T_b) )
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__0__le__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__le__0__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__0__less__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__less__0__iff,axiom,
% 157.60/157.45 ! [V_z_2,T_b] :
% 157.60/157.45 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__nat__nat,axiom,
% 157.60/157.45 ! [V_z,T_a] :
% 157.60/157.45 ( class_Rings_Oring__1(T_a)
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_negD,axiom,
% 157.60/157.45 ! [V_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osize_I5_J,axiom,
% 157.60/157.45 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osize_I13_J,axiom,
% 157.60/157.45 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_fold__image__1,axiom,
% 157.60/157.45 ! [V_f_2,V_S_2,T_b,T_c] :
% 157.60/157.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.45 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.60/157.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I4_J,axiom,
% 157.60/157.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 157.60/157.45 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
% 157.60/157.45 <=> ( V_fun_2 = V_fun_H_2
% 157.60/157.45 & V_com1_2 = V_com1_H_2
% 157.60/157.45 & V_com2_2 = V_com2_H_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I26_J,axiom,
% 157.60/157.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I27_J,axiom,
% 157.60/157.45 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I44_J,axiom,
% 157.60/157.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I45_J,axiom,
% 157.60/157.45 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I14_J,axiom,
% 157.60/157.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I15_J,axiom,
% 157.60/157.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ).
% 157.60/157.45
% 157.60/157.45 fof(fact_hoare__derivs_OIf,axiom,
% 157.60/157.45 ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 157.60/157.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.60/157.45 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)),V_d_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.60/157.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_card_Oneutral,axiom,
% 157.60/157.45 ! [V_A_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mod__induct__0,axiom,
% 157.60/157.45 ! [V_i_2,V_Pa_2,V_p_2] :
% 157.60/157.45 ( ! [B_i] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 157.60/157.45 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 157.60/157.45 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 157.60/157.45 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_fold__image__cong,axiom,
% 157.60/157.45 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.60/157.45 ( class_Groups_Oab__semigroup__mult(T_c)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( ! [B_x] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.45 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 157.60/157.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_peek__and__def,axiom,
% 157.60/157.45 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 157.60/157.45 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 157.60/157.45 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Loop,axiom,
% 157.60/157.45 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 157.60/157.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.60/157.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OWhile(V_b_2,V_ca_2),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Max__eqI,axiom,
% 157.60/157.45 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( ! [B_y] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.45 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Min__eqI,axiom,
% 157.60/157.45 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.45 ( class_Orderings_Olinorder(T_b)
% 157.60/157.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.45 => ( ! [B_y] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.45 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_expand__Suc,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__nat__number__of__eq,axiom,
% 157.60/157.45 ! [V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__number__of,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Int_Oring__char__0(T_b) )
% 157.60/157.45 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.60/157.45 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__reorient,axiom,
% 157.60/157.45 ! [V_x_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Int_Onumber(T_b)
% 157.60/157.45 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 157.60/157.45 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I5_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 157.60/157.45 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 157.60/157.45 <=> ( V_fun_2 = V_fun_H_2
% 157.60/157.45 & V_com_2 = V_com_H_2 ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__nat__number__of__lemma,axiom,
% 157.60/157.45 ! [V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_of__int__number__of__eq,axiom,
% 157.60/157.45 ! [V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__eq,axiom,
% 157.60/157.45 ! [V_k,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I52_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I53_J,axiom,
% 157.60/157.45 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I28_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I29_J,axiom,
% 157.60/157.45 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I46_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I47_J,axiom,
% 157.60/157.45 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I16_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osimps_I17_J,axiom,
% 157.60/157.45 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__number__of__eq__not__less,axiom,
% 157.60/157.45 ! [V_w_2,V_v_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Orderings_Olinorder(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_right__distrib__number__of,axiom,
% 157.60/157.45 ! [V_c,V_b,V_v,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Rings_Osemiring(T_b) )
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_left__distrib__number__of,axiom,
% 157.60/157.45 ! [V_v,V_b,V_a,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Rings_Osemiring(T_b) )
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_left__diff__distrib__number__of,axiom,
% 157.60/157.45 ! [V_v,V_b,V_a,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Rings_Oring(T_b) )
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_right__diff__distrib__number__of,axiom,
% 157.60/157.45 ! [V_c,V_b,V_v,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Rings_Oring(T_b) )
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__number__of,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__number__of,axiom,
% 157.60/157.45 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_min__number__of,axiom,
% 157.60/157.45 ! [V_v,V_u,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Orderings_Oord(T_b) )
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_max__number__of,axiom,
% 157.60/157.45 ! [V_v,V_u,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber(T_b)
% 157.60/157.45 & class_Orderings_Oord(T_b) )
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__add,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__number__of__eq,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__number__of__left,axiom,
% 157.60/157.45 ! [V_z,V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__mult,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_arith__simps_I32_J,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__number__of__left,axiom,
% 157.60/157.45 ! [V_z,V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__diff,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__minus,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_arith__simps_I30_J,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Ints__number__of,axiom,
% 157.60/157.45 ! [V_w_2,T_b] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__eq__eq__number__of1,axiom,
% 157.60/157.45 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 157.60/157.45 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 157.60/157.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__eq__eq__number__of,axiom,
% 157.60/157.45 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 157.60/157.45 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) )
% 157.60/157.45 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__divide__eq__number__of,axiom,
% 157.60/157.45 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 157.60/157.45 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2 )
% 157.60/157.45 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__divide__eq__number__of1,axiom,
% 157.60/157.45 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 157.60/157.45 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 157.60/157.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.45 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__number__of__diff1,axiom,
% 157.60/157.45 ! [V_c,V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__number__of__mult,axiom,
% 157.60/157.45 ! [V_z,V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__number__of__eq,axiom,
% 157.60/157.45 ! [V_w,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__less__eq__number__of1,axiom,
% 157.60/157.45 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__less__eq__number__of,axiom,
% 157.60/157.45 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__divide__eq__number__of,axiom,
% 157.60/157.45 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__divide__eq__number__of1,axiom,
% 157.60/157.45 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_abs__number__of,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_a) )
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__number__of__diff2,axiom,
% 157.60/157.45 ! [V_w,V_c,V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__divide__eq__number__of1,axiom,
% 157.60/157.45 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__divide__eq__number__of,axiom,
% 157.60/157.45 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__le__eq__number__of,axiom,
% 157.60/157.45 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__le__eq__number__of1,axiom,
% 157.60/157.45 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.60/157.45 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.45 & class_Int_Onumber(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osize_I14_J,axiom,
% 157.60/157.45 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_com_Osize_I6_J,axiom,
% 157.60/157.45 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_one__mod__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_one__div__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__number__of__odd__number__of,axiom,
% 157.60/157.45 ! [V_v_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__nat__number__of,axiom,
% 157.60/157.45 ! [V_n,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__numeral__code_I5_J,axiom,
% 157.60/157.45 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__number__of__Bit1,axiom,
% 157.60/157.45 ! [V_w_2] :
% 157.60/157.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 157.60/157.45 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__is__id,axiom,
% 157.60/157.45 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 157.60/157.45
% 157.60/157.45 fof(fact_times__numeral__code_I5_J,axiom,
% 157.60/157.45 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_plus__numeral__code_I9_J,axiom,
% 157.60/157.45 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__number__of__int__code,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__eq__number__of__int__code,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__int__code_I16_J,axiom,
% 157.60/157.45 ! [V_k2_2,V_k1_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I17_J,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__eq__int__code_I16_J,axiom,
% 157.60/157.45 ! [V_k2_2,V_k1_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I34_J,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I51_J,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 157.60/157.45 <=> V_k_2 = V_l_2 ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_int__number__of__def,axiom,
% 157.60/157.45 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_bin__less__0__simps_I4_J,axiom,
% 157.60/157.45 ! [V_w_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Bit1__def,axiom,
% 157.60/157.45 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of,axiom,
% 157.60/157.45 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__def,axiom,
% 157.60/157.45 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__Bit1,axiom,
% 157.60/157.45 ! [V_w_2] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__Bit1,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__number__of__odd,axiom,
% 157.60/157.45 ! [V_z_2,V_w_2,T_b] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zpower__number__of__odd,axiom,
% 157.60/157.45 ! [V_z_2,V_w_2] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__numeral__code_I6_J,axiom,
% 157.60/157.45 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__imp__number__of__eq__0,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_int__eq__iff__number__of,axiom,
% 157.60/157.45 ! [V_v_2,V_m_2] :
% 157.60/157.45 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
% 157.60/157.45 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 157.60/157.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H_2,V_v_2] :
% 157.60/157.45 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
% 157.60/157.45 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 157.60/157.45 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 157.60/157.45 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__add__left,axiom,
% 157.60/157.45 ! [V_k,V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_int__nat__number__of,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mod__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.60/157.45 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_div__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power__nat__number__of__number__of,axiom,
% 157.60/157.45 ! [V_w,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__nat__number__of__add,axiom,
% 157.60/157.45 ! [V_n,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.45 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_2,V_v_H_2] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_min__number__of__Suc,axiom,
% 157.60/157.45 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_min__Suc__number__of,axiom,
% 157.60/157.45 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_succ__Pls,axiom,
% 157.60/157.45 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I39_J,axiom,
% 157.60/157.45 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I46_J,axiom,
% 157.60/157.45 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__Pls,axiom,
% 157.60/157.45 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__Pls,axiom,
% 157.60/157.45 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__bin__simps_I1_J,axiom,
% 157.60/157.45 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I19_J,axiom,
% 157.60/157.45 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_succ__pred,axiom,
% 157.60/157.45 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Pls__def,axiom,
% 157.60/157.45 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__Pls,axiom,
% 157.60/157.45 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__Pls__right,axiom,
% 157.60/157.45 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I2_J,axiom,
% 157.60/157.45 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_semiring__norm_I112_J,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__Pls,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__numeral__0__right,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__numeral__0,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_bin__less__0__simps_I1_J,axiom,
% 157.60/157.45 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__Pls,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_semiring__norm_I113_J,axiom,
% 157.60/157.45 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_zero__is__num__zero,axiom,
% 157.60/157.45 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I22_J,axiom,
% 157.60/157.45 ! [V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I12_J,axiom,
% 157.60/157.45 ! [V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__diff__number__of,axiom,
% 157.60/157.45 ! [V_m,V_v] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_not__neg__number__of__Pls,axiom,
% 157.60/157.45 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__add__1,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__1__add__number__of,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__iff__pred__less,axiom,
% 157.60/157.45 ! [V_l_2,V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_minus__Bit1,axiom,
% 157.60/157.45 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_pred__def,axiom,
% 157.60/157.45 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__diff__1,axiom,
% 157.60/157.45 ! [V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__numeral__1,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__numeral__1__right,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__Numeral0,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.60/157.45 & class_Int_Onumber__ring(T_a) )
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_numeral__1__eq__1,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_semiring__norm_I110_J,axiom,
% 157.60/157.45 ! [T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__0__number__of,axiom,
% 157.60/157.45 ! [V_v_2] :
% 157.60/157.45 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_eq__number__of__0,axiom,
% 157.60/157.45 ! [V_v_2] :
% 157.60/157.45 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of2,axiom,
% 157.60/157.45 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I5_J,axiom,
% 157.60/157.45 ! [V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_rel__simps_I29_J,axiom,
% 157.60/157.45 ! [V_k_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H_2,V_v_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 157.60/157.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 157.60/157.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__Numeral1,axiom,
% 157.60/157.45 ! [V_x,T_a] :
% 157.60/157.45 ( ( class_Fields_Ofield(T_a)
% 157.60/157.45 & class_Int_Onumber__ring(T_a) )
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_divide__numeral__1,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( ( class_Fields_Ofield(T_a)
% 157.60/157.45 & class_Int_Onumber__ring(T_a) )
% 157.60/157.45 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H_2,V_v_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 157.60/157.45 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 157.60/157.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_one__is__num__one,axiom,
% 157.60/157.45 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Numeral1__eq1__nat,axiom,
% 157.60/157.45 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__numeral__1__eq__1,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 157.60/157.45 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_succ__def,axiom,
% 157.60/157.45 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__special_I1_J,axiom,
% 157.60/157.45 ! [V_y_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__special_I3_J,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__special_I1_J,axiom,
% 157.60/157.45 ! [V_y_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__special_I3_J,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__0__number__of,axiom,
% 157.60/157.45 ! [V_v_2] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_numeral__3__eq__3,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_numeral__1__eq__Suc__0,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_power3__eq__cube,axiom,
% 157.60/157.45 ! [V_a,T_a] :
% 157.60/157.45 ( class_Groups_Omonoid__mult(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 157.60/157.45 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc3__eq__add__3,axiom,
% 157.60/157.45 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 157.60/157.45 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__succ,axiom,
% 157.60/157.45 ! [V_k,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_number__of__pred,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__special_I4_J,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_le__special_I2_J,axiom,
% 157.60/157.45 ! [V_y_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__special_I2_J,axiom,
% 157.60/157.45 ! [V_y_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_less__special_I4_J,axiom,
% 157.60/157.45 ! [V_x_2,T_b] :
% 157.60/157.45 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.45 & class_Rings_Olinordered__idom(T_b) )
% 157.60/157.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 157.60/157.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__special_I3_J,axiom,
% 157.60/157.45 ! [V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_add__special_I2_J,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 157.60/157.45 ! [V_m,V_n] :
% 157.60/157.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_nat__number__of__mult__left,axiom,
% 157.60/157.45 ! [V_k,V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mult__nat__number__of,axiom,
% 157.60/157.45 ! [V_v_H,V_v] :
% 157.60/157.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.60/157.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_neg__number__of__pred__iff__0,axiom,
% 157.60/157.45 ! [V_v_2] :
% 157.60/157.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 157.60/157.45 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 157.60/157.45 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 157.60/157.45 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 157.60/157.45 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_div__Suc__eq__div__add3,axiom,
% 157.60/157.45 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__div__eq__add3__div,axiom,
% 157.60/157.45 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 157.60/157.45 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__special_I2_J,axiom,
% 157.60/157.45 ! [V_v,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_diff__special_I1_J,axiom,
% 157.60/157.45 ! [V_w,T_a] :
% 157.60/157.45 ( class_Int_Onumber__ring(T_a)
% 157.60/157.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 157.60/157.45
% 157.60/157.45 fof(fact_Suc__eq__number__of,axiom,
% 157.60/157.45 ! [V_v_2,V_n_2] :
% 157.60/157.45 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__number__of__Suc,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2] :
% 157.60/157.46 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__case__number__of,axiom,
% 157.60/157.46 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__Suc__number__of,axiom,
% 157.60/157.46 ! [V_v_2,V_n_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__number__of__Suc,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_le__Suc__number__of,axiom,
% 157.60/157.46 ! [V_v_2,V_n_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_le__number__of__Suc,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Suc__nat__number__of,axiom,
% 157.60/157.46 ! [V_v] :
% 157.60/157.46 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__Suc__number__of,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__number__of__Suc,axiom,
% 157.60/157.46 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__case__add__eq__if,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__rec__add__eq__if,axiom,
% 157.60/157.46 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__special_I4_J,axiom,
% 157.60/157.46 ! [V_x_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__special_I2_J,axiom,
% 157.60/157.46 ! [V_y_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__rec__number__of,axiom,
% 157.60/157.46 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_iszero__def,axiom,
% 157.60/157.46 ! [V_z_2,T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => ( c_Int_Oiszero(T_b,V_z_2)
% 157.60/157.46 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_iszero__0,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.46 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_not__iszero__1,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.46 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__rec__0,axiom,
% 157.60/157.46 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__rec__Suc,axiom,
% 157.60/157.46 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_iszero__Numeral0,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_iszero__number__of__Bit1,axiom,
% 157.60/157.46 ! [V_w,T_a] :
% 157.60/157.46 ( ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 & class_Int_Oring__char__0(T_a) )
% 157.60/157.46 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_not__iszero__Numeral1,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__number__of__eq,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__special_I1_J,axiom,
% 157.60/157.46 ! [V_y_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__special_I3_J,axiom,
% 157.60/157.46 ! [V_x_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_neg__zmod__mult__2,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmod__number__of__Bit1,axiom,
% 157.60/157.46 ! [V_v,V_w] :
% 157.60/157.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_arith__series__int,axiom,
% 157.60/157.46 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pos__zdiv__mult__2,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I49_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I50_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_minus__Bit0,axiom,
% 157.60/157.46 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__Bit0,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I48_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 157.60/157.46 <=> V_k_2 = V_l_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Bit0__def,axiom,
% 157.60/157.46 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Bit0__Bit0,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I14_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__int__code_I13_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I31_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__eq__int__code_I13_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I7_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Bit0__Pls,axiom,
% 157.60/157.46 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I38_J,axiom,
% 157.60/157.46 ! [V_l_2] :
% 157.60/157.46 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 157.60/157.46 <=> c_Int_OPls = V_l_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I44_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 157.60/157.46 <=> V_k_2 = c_Int_OPls ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_bin__less__0__simps_I3_J,axiom,
% 157.60/157.46 ! [V_w_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I21_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I27_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I32_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__eq__int__code_I14_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I4_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I10_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I16_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__int__code_I15_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Bit0__Bit1,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Bit1__Bit0,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I3_J,axiom,
% 157.60/157.46 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I10_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I9_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zdiv__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_neg__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 157.60/157.46 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__Bit1,axiom,
% 157.60/157.46 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__Bit0,axiom,
% 157.60/157.46 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_iszero__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w_2,T_b] :
% 157.60/157.46 ( ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 & class_Int_Oring__char__0(T_b) )
% 157.60/157.46 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 157.60/157.46 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_succ__Bit0,axiom,
% 157.60/157.46 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_succ__Bit1,axiom,
% 157.60/157.46 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I15_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__int__code_I14_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I33_J,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__eq__int__code_I15_J,axiom,
% 157.60/157.46 ! [V_k2_2,V_k1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_card__UNIV__bool,axiom,
% 157.60/157.46 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__Bit1,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I8_J,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Bit1__Bit1,axiom,
% 157.60/157.46 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__number__of__even,axiom,
% 157.60/157.46 ! [V_w_2,V_z_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zpower__number__of__even,axiom,
% 157.60/157.46 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_double__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_number__of1,axiom,
% 157.60/157.46 ! [V_n] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 157.60/157.46 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__number__of__even__number__of,axiom,
% 157.60/157.46 ! [V_w_2,V_v_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__2__right,axiom,
% 157.60/157.46 ! [V_z,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__2,axiom,
% 157.60/157.46 ! [V_z,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_one__add__one__is__two,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__eq__power2,axiom,
% 157.60/157.46 ! [V_a_2,T_b] :
% 157.60/157.46 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.60/157.46 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__power2,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_numeral__2__eq__2,axiom,
% 157.60/157.46 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_semiring__norm_I115_J,axiom,
% 157.60/157.46 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__eq__square,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Groups_Omonoid__mult(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 157.60/157.46 ! [V_x,T_a] :
% 157.60/157.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 157.60/157.46 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__2__eq__Suc,axiom,
% 157.60/157.46 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__2__eq__Suc_H,axiom,
% 157.60/157.46 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_one__power2,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__minus,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Rings_Oring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__mult__2,axiom,
% 157.60/157.46 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__mult__2__right,axiom,
% 157.60/157.46 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__even__eq,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Groups_Omonoid__mult(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 157.60/157.46 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 157.60/157.46 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__abs,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_abs__power2,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__1__add__1,axiom,
% 157.60/157.46 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod2__Suc__Suc,axiom,
% 157.60/157.46 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div2__Suc__Suc,axiom,
% 157.60/157.46 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmod__number__of__Bit0,axiom,
% 157.60/157.46 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__self__div__2,axiom,
% 157.60/157.46 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ).
% 157.60/157.46
% 157.60/157.46 fof(fact_half__gt__zero__iff,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.60/157.46 & class_Int_Onumber__ring(T_b) )
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_half__gt__zero,axiom,
% 157.60/157.46 ! [V_r,T_a] :
% 157.60/157.46 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.60/157.46 & class_Int_Onumber__ring(T_a) )
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__le__power2,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__le__imp__le,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__eq__imp__eq,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.46 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.60/157.46 => V_x = V_y ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__less__power2,axiom,
% 157.60/157.46 ! [V_a_2,T_b] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 157.60/157.46 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__less__0,axiom,
% 157.60/157.46 ! [V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sum__power2__eq__zero__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__eq__square__number__of,axiom,
% 157.60/157.46 ! [V_w,T_b] :
% 157.60/157.46 ( ( class_Groups_Omonoid__mult(T_b)
% 157.60/157.46 & class_Int_Onumber(T_b) )
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__2__cases,axiom,
% 157.60/157.46 ! [V_n] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 157.60/157.46 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__2,axiom,
% 157.60/157.46 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__eq__1__iff,axiom,
% 157.60/157.46 ! [V_a_2,T_b] :
% 157.60/157.46 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.60/157.46 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.46 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 157.60/157.46 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 157.60/157.46 ! [V_n,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__minus__even,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Rings_Oring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__less__imp__less,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__semidom(T_a)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sum__power2__ge__zero,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sum__power2__le__zero__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.46 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sum__power2__gt__zero__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 157.60/157.46 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.46 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_not__sum__power2__lt__zero,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__sum,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__le__even__power_H,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 157.60/157.46 ! [V_n,V_x,T_a] :
% 157.60/157.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__odd__eq,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Groups_Omonoid__mult(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__minus1__even,axiom,
% 157.60/157.46 ! [V_n,T_a] :
% 157.60/157.46 ( class_Rings_Oring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zdiv__number__of__Bit1,axiom,
% 157.60/157.46 ! [V_v,V_w] :
% 157.60/157.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod2__gr__0,axiom,
% 157.60/157.46 ! [V_m_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 157.60/157.46 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__2__gt__zero,axiom,
% 157.60/157.46 ! [V_n] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power2__diff,axiom,
% 157.60/157.46 ! [V_y,V_x,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_odd__power__less__zero,axiom,
% 157.60/157.46 ! [V_n,V_a,T_a] :
% 157.60/157.46 ( class_Rings_Olinordered__idom(T_a)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__minus1__odd,axiom,
% 157.60/157.46 ! [V_n,T_a] :
% 157.60/157.46 ( class_Rings_Oring__1(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 157.60/157.46 ! [V_n] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_of__nat__double,axiom,
% 157.60/157.46 ! [V_x,T_a] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_a)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.60/157.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pos__zmod__mult__2,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_neg__zdiv__mult__2,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_int__of__code,axiom,
% 157.60/157.46 ! [V_k] :
% 157.60/157.46 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.46 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
% 157.60/157.46 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_of__int__num,axiom,
% 157.60/157.46 ! [V_k_2,T_b] :
% 157.60/157.46 ( class_Rings_Oring__1(T_b)
% 157.60/157.46 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 157.60/157.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__m1__odd,axiom,
% 157.60/157.46 ! [V_n,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_power__m1__even,axiom,
% 157.60/157.46 ! [V_n,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I45_J,axiom,
% 157.60/157.46 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I42_J,axiom,
% 157.60/157.46 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I37_J,axiom,
% 157.60/157.46 c_Int_OPls != c_Int_OMin ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I40_J,axiom,
% 157.60/157.46 c_Int_OMin != c_Int_OPls ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral__zero__minus__one,axiom,
% 157.60/157.46 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I24_J,axiom,
% 157.60/157.46 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I7_J,axiom,
% 157.60/157.46 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I47_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 157.60/157.46 <=> V_k_2 = c_Int_OMin ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I43_J,axiom,
% 157.60/157.46 ! [V_l_2] :
% 157.60/157.46 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 157.60/157.46 <=> c_Int_OMin = V_l_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Bit1__Min,axiom,
% 157.60/157.46 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 157.60/157.46
% 157.60/157.46 fof(fact_bin__less__0__simps_I2_J,axiom,
% 157.60/157.46 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I20_J,axiom,
% 157.60/157.46 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I23_J,axiom,
% 157.60/157.46 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I30_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I26_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I3_J,axiom,
% 157.60/157.46 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I6_J,axiom,
% 157.60/157.46 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I13_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I9_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I28_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I8_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__number__of__Pls__Min,axiom,
% 157.60/157.46 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Int_OMin__def,axiom,
% 157.60/157.46 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__Min,axiom,
% 157.60/157.46 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_neg__number__of__Min,axiom,
% 157.60/157.46 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__Pls,axiom,
% 157.60/157.46 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Min__right,axiom,
% 157.60/157.46 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add__Min,axiom,
% 157.60/157.46 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__Min,axiom,
% 157.60/157.46 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nonzero__number__of__Min,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_succ__Min,axiom,
% 157.60/157.46 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I2_J,axiom,
% 157.60/157.46 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__minus1__right,axiom,
% 157.60/157.46 ! [V_z,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult__minus1,axiom,
% 157.60/157.46 ! [V_z,T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_arith__simps_I31_J,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_number__of__Min,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_abs__minus__one,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 & class_Rings_Olinordered__idom(T_a) )
% 157.60/157.46 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divide__minus1,axiom,
% 157.60/157.46 ! [V_x,T_a] :
% 157.60/157.46 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.60/157.46 & class_Int_Onumber__ring(T_a) )
% 157.60/157.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I11_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__simps_I25_J,axiom,
% 157.60/157.46 ! [V_k_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmod__minus1__right,axiom,
% 157.60/157.46 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I4_J,axiom,
% 157.60/157.46 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_minus__Min,axiom,
% 157.60/157.46 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 157.60/157.46 ! [V_n,V_m] :
% 157.60/157.46 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.60/157.46 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.60/157.46 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmult__eq__1__iff,axiom,
% 157.60/157.46 ! [V_n_2,V_m_2] :
% 157.60/157.46 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.60/157.46 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.60/157.46 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 157.60/157.46 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 157.60/157.46 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I6_J,axiom,
% 157.60/157.46 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_diff__bin__simps_I5_J,axiom,
% 157.60/157.46 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_of__int__m1,axiom,
% 157.60/157.46 ! [T_a] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zdiv__minus1__right,axiom,
% 157.60/157.46 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zero__code__numeral__code,axiom,
% 157.60/157.46 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_minus1__divide,axiom,
% 157.60/157.46 ! [V_x,T_a] :
% 157.60/157.46 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.60/157.46 & class_Int_Onumber__ring(T_a) )
% 157.60/157.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_abs__power__minus__one,axiom,
% 157.60/157.46 ! [V_n,T_a] :
% 157.60/157.46 ( ( class_Int_Onumber__ring(T_a)
% 157.60/157.46 & class_Rings_Olinordered__idom(T_a) )
% 157.60/157.46 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__eq__minus1,axiom,
% 157.60/157.46 ! [V_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__pos__neg__trivial,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmod__minus1,axiom,
% 157.60/157.46 ! [V_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_one__code__numeral__code,axiom,
% 157.60/157.46 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nitpick_OFrac__def,axiom,
% 157.60/157.46 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_int__ge__less__than2__def,axiom,
% 157.60/157.46 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_int__ge__less__than__def,axiom,
% 157.60/157.46 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inj__graph,axiom,
% 157.60/157.46 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nitpick_Oprod__def,axiom,
% 157.60/157.46 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__of__aux__code,axiom,
% 157.60/157.46 ! [V_n,V_i] :
% 157.60/157.46 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 157.60/157.46 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.46 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__def,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__correct,axiom,
% 157.60/157.46 ! [V_a,V_b] :
% 157.60/157.46 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmult2__lemma,axiom,
% 157.60/157.46 ! [V_c,V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osize_I1_J,axiom,
% 157.60/157.46 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nats__number__of,axiom,
% 157.60/157.46 ! [V_w_2,T_b] :
% 157.60/157.46 ( class_Int_Onumber__ring(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__equals__eq2,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_c,T_b] :
% 157.60/157.46 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
% 157.60/157.46 <=> V_R_2 = V_S_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inf__Int__eq2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sup__Un__eq2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_bot__empty__eq2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__subset__eq2,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rev__ImageI,axiom,
% 157.60/157.46 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Image__iff,axiom,
% 157.60/157.46 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 157.60/157.46 <=> ? [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_unique__remainder,axiom,
% 157.60/157.46 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 157.60/157.46 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => V_r = V_r_H ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_unique__quotient,axiom,
% 157.60/157.46 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 157.60/157.46 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => V_q = V_q_H ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_self__remainder,axiom,
% 157.60/157.46 ! [V_r,V_q,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__0,axiom,
% 157.60/157.46 ! [V_b] :
% 157.60/157.46 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_SUP__UN__eq2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_self__quotient,axiom,
% 157.60/157.46 ! [V_r,V_q,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__mod,axiom,
% 157.60/157.46 ! [V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__div,axiom,
% 157.60/157.46 ! [V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nats__0,axiom,
% 157.60/157.46 ! [T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__mod__div,axiom,
% 157.60/157.46 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nats__add,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nats__mult,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nats__1,axiom,
% 157.60/157.46 ! [T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_of__nat__in__Nats,axiom,
% 157.60/157.46 ! [V_n_2,T_b] :
% 157.60/157.46 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Image__singleton__iff,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__div__mod,axiom,
% 157.60/157.46 ! [V_a,V_b] :
% 157.60/157.46 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Image__singleton,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zadd1__lemma,axiom,
% 157.60/157.46 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
% 157.60/157.46 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
% 157.60/157.46 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zminus1__lemma,axiom,
% 157.60/157.46 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__relI,axiom,
% 157.60/157.46 ! [V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
% 157.60/157.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_zmult1__lemma,axiom,
% 157.60/157.46 ! [V_a,V_r,V_q,V_c,V_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 157.60/157.46 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__imageI,axiom,
% 157.60/157.46 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_norm__frac_Osimps,axiom,
% 157.60/157.46 ! [V_a_2,V_b_2] :
% 157.60/157.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 157.60/157.46 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_adjust__eq,axiom,
% 157.60/157.46 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sup2CI,axiom,
% 157.60/157.46 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 157.60/157.46 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sup2E,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 157.60/157.46 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inf2I,axiom,
% 157.60/157.46 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inf2E,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 157.60/157.46 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mem__splitI,axiom,
% 157.60/157.46 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_splitI,axiom,
% 157.60/157.46 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod__caseI,axiom,
% 157.60/157.46 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_bot2E,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_splitD_H,axiom,
% 157.60/157.46 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_ca_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_swap__inj__on,axiom,
% 157.60/157.46 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rev__predicate2D,axiom,
% 157.60/157.46 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_predicate2D,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inf2D1,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inf2D2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sup2I2,axiom,
% 157.60/157.46 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_sup2I1,axiom,
% 157.60/157.46 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Pair__inject,axiom,
% 157.60/157.46 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 157.60/157.46 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
% 157.60/157.46 => ~ ( V_a = V_a_H
% 157.60/157.46 => V_b != V_b_H ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Pair__eq,axiom,
% 157.60/157.46 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.46 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 157.60/157.46 <=> ( V_a_2 = V_a_H_2
% 157.60/157.46 & V_b_2 = V_b_H_2 ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__paired__All,axiom,
% 157.60/157.46 ! [T_c,T_b,V_Pa_2] :
% 157.60/157.46 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.46 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__weak__cong,axiom,
% 157.60/157.46 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 157.60/157.46 ( V_p_2 = V_q_2
% 157.60/157.46 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__twice,axiom,
% 157.60/157.46 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__conv,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod_Osimps_I2_J,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_splitD,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__eta,axiom,
% 157.60/157.46 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ).
% 157.60/157.46
% 157.60/157.46 fof(fact_The__split__eq,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__paired__The,axiom,
% 157.60/157.46 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_adjust__def,axiom,
% 157.60/157.46 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_in__rel__def,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__mod__code__numeral__def,axiom,
% 157.60/157.46 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 157.60/157.46 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 157.60/157.46 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__correct,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__div__mod,axiom,
% 157.60/157.46 ! [V_l,V_k] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.46 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__minus1,axiom,
% 157.60/157.46 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg_Osimps,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 157.60/157.46 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__eqn,axiom,
% 157.60/157.46 ! [V_a,V_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg__eqn__number__of,axiom,
% 157.60/157.46 ! [V_w,V_v] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 157.60/157.46 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 157.60/157.46 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nitpick_Orefl_H__def,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 157.60/157.46 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg_Osimps,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 157.60/157.46 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__0,axiom,
% 157.60/157.46 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__correct,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__div__mod,axiom,
% 157.60/157.46 ! [V_l,V_k] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.60/157.46 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__eqn,axiom,
% 157.60/157.46 ! [V_a,V_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.60/157.46 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.60/157.46 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg__eqn__number__of,axiom,
% 157.60/157.46 ! [V_w,V_v] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.60/157.46 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__def,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 157.60/157.46 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__step,axiom,
% 157.60/157.46 ! [V_m,V_n] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.60/157.46 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__pdivmod,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 157.60/157.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 157.60/157.46 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negateSnd__def,axiom,
% 157.60/157.46 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apsnd__conv,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apsnd__compose,axiom,
% 157.60/157.46 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__zero,axiom,
% 157.60/157.46 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__base,axiom,
% 157.60/157.46 ! [V_n,V_m] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.60/157.46 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negateSnd__eq,axiom,
% 157.60/157.46 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__div__mod,axiom,
% 157.60/157.46 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__rel__neg,axiom,
% 157.60/157.46 ! [V_qr,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__if,axiom,
% 157.60/157.46 ! [V_m_2,V_n_2] :
% 157.60/157.46 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 157.60/157.46 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
% 157.60/157.46 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 157.60/157.46 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pdivmod__def,axiom,
% 157.60/157.46 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pdivmod__posDivAlg,axiom,
% 157.60/157.46 ! [V_k,V_l] :
% 157.60/157.46 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) )
% 157.60/157.46 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__int__code,axiom,
% 157.60/157.46 ! [V_l_2,V_k_2] :
% 157.60/157.46 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 157.60/157.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 157.60/157.46 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 157.60/157.46 ! [V_a,V_r,V_q,V_c,V_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 157.60/157.46 ! [V_c,V_r,V_q,V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg_Opsimps,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 157.60/157.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) )
% 157.60/157.46 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__unique,axiom,
% 157.60/157.46 ! [V_qr_H,V_qr,V_n,V_m] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 157.60/157.46 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 157.60/157.46 => V_qr = V_qr_H ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 157.60/157.46 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__eq,axiom,
% 157.60/157.46 ! [V_qr,V_n,V_m] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 157.60/157.46 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__def,axiom,
% 157.60/157.46 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__eq,axiom,
% 157.60/157.46 ! [V_r,V_q,V_n,V_m] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__eq,axiom,
% 157.60/157.46 ! [V_r,V_q,V_n,V_m] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel,axiom,
% 157.60/157.46 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 157.60/157.46 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
% 157.60/157.46 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.60/157.46 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg_Opsimps,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 157.60/157.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) )
% 157.60/157.46 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_norm__frac_Opsimps,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 157.60/157.46 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.60/157.46 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.60/157.46 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_negDivAlg_Opinduct,axiom,
% 157.60/157.46 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 157.60/157.46 => ( ! [B_a,B_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 157.60/157.46 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b)))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_posDivAlg_Opinduct,axiom,
% 157.60/157.46 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 157.60/157.46 => ( ! [B_a,B_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 157.60/157.46 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 157.60/157.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_accp__subset,axiom,
% 157.60/157.46 ! [V_R2_2,V_R1_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__pos__neg__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_snd__eqD,axiom,
% 157.60/157.46 ! [V_a,V_y,V_x,T_a,T_b] :
% 157.60/157.46 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
% 157.60/157.46 => V_y = V_a ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_snd__conv,axiom,
% 157.60/157.46 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ).
% 157.60/157.46
% 157.60/157.46 fof(fact_snd__def,axiom,
% 157.60/157.46 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_snd__apsnd,axiom,
% 157.60/157.46 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apsnd__eq__conv,axiom,
% 157.60/157.46 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 157.60/157.46 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
% 157.60/157.46 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__int__def,axiom,
% 157.60/157.46 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_accp__downward,axiom,
% 157.60/157.46 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.60/157.46 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_accp_Oequations,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 157.60/157.46 <=> ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 157.60/157.46 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_accp_Osimps,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 157.60/157.46 <=> ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 157.60/157.46 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__neg__pos,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__pos__pos,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__pos__pos__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__pos__neg,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__neg__neg,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__gcd_Opsimps,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
% 157.60/157.46 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 157.60/157.46 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat_Osize_I2_J,axiom,
% 157.60/157.46 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_in__measure,axiom,
% 157.60/157.46 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mod__nat__def,axiom,
% 157.60/157.46 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat_Osize_I1_J,axiom,
% 157.60/157.46 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_irrefl__def,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Relation_Oirrefl(T_b,V_r_2)
% 157.60/157.46 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_norm__frac_Opinduct,axiom,
% 157.60/157.46 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 157.60/157.46 => ( ! [B_a,B_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__pos__neg__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Pair__fst__snd__eq,axiom,
% 157.60/157.46 ! [T_c,T_b,V_t_2,V_s_2] :
% 157.60/157.46 ( V_s_2 = V_t_2
% 157.60/157.46 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 157.60/157.46 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod__eqI,axiom,
% 157.60/157.46 ! [V_q,V_p,T_b,T_a] :
% 157.60/157.46 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 157.60/157.46 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 157.60/157.46 => V_p = V_q ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_fst__eqD,axiom,
% 157.60/157.46 ! [V_a,V_y,V_x,T_b,T_a] :
% 157.60/157.46 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
% 157.60/157.46 => V_x = V_a ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_fst__conv,axiom,
% 157.60/157.46 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ).
% 157.60/157.46
% 157.60/157.46 fof(fact_fst__def,axiom,
% 157.60/157.46 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_fst__apsnd,axiom,
% 157.60/157.46 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__collapse,axiom,
% 157.60/157.46 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ).
% 157.60/157.46
% 157.60/157.46 fof(fact_surjective__pairing,axiom,
% 157.60/157.46 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod__case__beta,axiom,
% 157.60/157.46 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__int__def,axiom,
% 157.60/157.46 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__beta,axiom,
% 157.60/157.46 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__comp__eq,axiom,
% 157.60/157.46 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__def,axiom,
% 157.60/157.46 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_split__comp,axiom,
% 157.60/157.46 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_The__split,axiom,
% 157.60/157.46 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__neg__pos,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__pos__pos,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__pos__pos__1__number__of,axiom,
% 157.60/157.46 ! [V_w] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__pos__neg,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__neg__neg,axiom,
% 157.60/157.46 ! [V_b,V_a] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.60/157.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod__size__simp,axiom,
% 157.60/157.46 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_exI__realizer,axiom,
% 157.60/157.46 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_conjI__realizer,axiom,
% 157.60/157.46 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 157.60/157.46 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 157.60/157.46 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 157.60/157.46 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 157.60/157.46 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_div__nat__def,axiom,
% 157.60/157.46 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_divmod__nat__rel__def,axiom,
% 157.60/157.46 ! [V_qr_2,V_n_2,V_m_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 157.60/157.46 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 157.60/157.46 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.46 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) )
% 157.60/157.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__def,axiom,
% 157.60/157.46 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__gcd_Opinduct,axiom,
% 157.60/157.46 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
% 157.60/157.46 => ( ! [B_x,B_y] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
% 157.60/157.46 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_inv__image__def,axiom,
% 157.60/157.46 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Rep__Integ__inject,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] :
% 157.60/157.46 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 157.60/157.46 <=> V_x_2 = V_y_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_in__inv__image,axiom,
% 157.60/157.46 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rp__inv__image__def,axiom,
% 157.60/157.46 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__class__nondisjoint,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_subset__equiv__class,axiom,
% 157.60/157.46 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__class__self,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_quotient__disj,axiom,
% 157.60/157.46 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( V_X_2 = V_Y_2
% 157.60/157.46 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__class__eq,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.46 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_quotient__eq__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 157.60/157.46 => ( V_X_2 = V_Y_2
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_quotient__eqI,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.46 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__equiv__class,axiom,
% 157.60/157.46 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.46 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__equiv__class__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.60/157.46 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__class__eq__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.46 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__class__subset,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__equiv__class__iff2,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.60/157.46 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_UN__equiv__class2,axiom,
% 157.60/157.46 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.60/157.46 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 157.60/157.46 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_UN__equiv__class,axiom,
% 157.60/157.46 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.46 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_in__finite__psubset,axiom,
% 157.60/157.46 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 157.60/157.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_congruent2__implies__congruent,axiom,
% 157.60/157.46 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.46 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_congruent2D,axiom,
% 157.60/157.46 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
% 157.60/157.46 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_congruentD,axiom,
% 157.60/157.46 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 157.60/157.46 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_congruent2__implies__congruent__UN,axiom,
% 157.60/157.46 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.60/157.46 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 157.60/157.46 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_finite__psubset__def,axiom,
% 157.60/157.46 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_UN__equiv__class__inject,axiom,
% 157.60/157.46 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.60/157.46 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.46 => ! [B_y] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.60/157.46 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 157.60/157.46 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_UN__equiv__class__type2,axiom,
% 157.60/157.46 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.60/157.46 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
% 157.60/157.46 => ( ! [B_x1] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 157.60/157.46 => ! [B_x2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_UN__equiv__class__type,axiom,
% 157.60/157.46 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.46 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.46 => ( ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mlex__leq,axiom,
% 157.60/157.46 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osize_I2_J,axiom,
% 157.60/157.46 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mlex__less,axiom,
% 157.60/157.46 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Oinject,axiom,
% 157.60/157.46 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 157.60/157.46 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 157.60/157.46 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 157.60/157.46 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 157.60/157.46 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Suc__code__numeral__minus__one,axiom,
% 157.60/157.46 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osize_I4_J,axiom,
% 157.60/157.46 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat_Osize_I4_J,axiom,
% 157.60/157.46 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_prod_Orecs,axiom,
% 157.60/157.46 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat__size,axiom,
% 157.60/157.46 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat_Osize_I3_J,axiom,
% 157.60/157.46 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osize_I3_J,axiom,
% 157.60/157.46 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_in__lex__prod,axiom,
% 157.60/157.46 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 157.60/157.46 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 157.60/157.46 | ( V_a_2 = V_a_H_2
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equivp__equiv,axiom,
% 157.60/157.46 ! [V_A_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 157.60/157.46 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apsnd__apfst,axiom,
% 157.60/157.46 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apfst__compose,axiom,
% 157.60/157.46 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_identity__equivp,axiom,
% 157.60/157.46 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equivp__def,axiom,
% 157.60/157.46 ! [V_R_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.46 <=> ! [B_x,B_y] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 157.60/157.46 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equivp__reflp,axiom,
% 157.60/157.46 ! [V_x_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equivp__symp,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equivp__transp,axiom,
% 157.60/157.46 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apfst__eq__conv,axiom,
% 157.60/157.46 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 157.60/157.46 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
% 157.60/157.46 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_fst__apfst,axiom,
% 157.60/157.46 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apfst__conv,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_snd__apfst,axiom,
% 157.60/157.46 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apsnd__apfst__commute,axiom,
% 157.60/157.46 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_apfst__apsnd,axiom,
% 157.60/157.46 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_same__fstI,axiom,
% 157.60/157.46 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 157.60/157.46 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__lessI2,axiom,
% 157.60/157.46 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_ImageE,axiom,
% 157.60/157.46 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 157.60/157.46 => ~ ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__lessI1,axiom,
% 157.60/157.46 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__leqI2,axiom,
% 157.60/157.46 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_smax__insertI,axiom,
% 157.60/157.46 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_smin__insertI,axiom,
% 157.60/157.46 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_smax__emptyI,axiom,
% 157.60/157.46 ! [V_Y_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 157.60/157.46 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_smin__emptyI,axiom,
% 157.60/157.46 ! [V_X_2] :
% 157.60/157.46 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__leqI1,axiom,
% 157.60/157.46 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wmin__insertI,axiom,
% 157.60/157.46 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wmax__insertI,axiom,
% 157.60/157.46 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Field__insert,axiom,
% 157.60/157.46 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Field__empty,axiom,
% 157.60/157.46 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mono__Field,axiom,
% 157.60/157.46 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Field__Un,axiom,
% 157.60/157.46 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_finite__Field,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.60/157.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wmin__emptyI,axiom,
% 157.60/157.46 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wmax__emptyI,axiom,
% 157.60/157.46 ! [V_X_2] :
% 157.60/157.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_min__weak__def,axiom,
% 157.60/157.46 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__weak__def,axiom,
% 157.60/157.46 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__on__def,axiom,
% 157.60/157.46 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__on__def_H,axiom,
% 157.60/157.46 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__on__empty,axiom,
% 157.60/157.46 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Image__Id__on,axiom,
% 157.60/157.46 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__on__iff,axiom,
% 157.60/157.46 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 157.60/157.46 <=> ( V_x_2 = V_y_2
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__on__eqI,axiom,
% 157.60/157.46 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 157.60/157.46 ( V_a_2 = V_b_2
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__strict__def,axiom,
% 157.60/157.46 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__ext__additive,axiom,
% 157.60/157.46 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_min__strict__def,axiom,
% 157.60/157.46 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__extp__max__ext__eq,axiom,
% 157.60/157.46 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__rpair__set,axiom,
% 157.60/157.46 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_min__rpair__set,axiom,
% 157.60/157.46 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rp__inv__image__rp,axiom,
% 157.60/157.46 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 157.60/157.46 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.60/157.46 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__intrel__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] :
% 157.60/157.46 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less__than__iff,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_intrel__iff,axiom,
% 157.60/157.46 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
% 157.60/157.46 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_equiv__intrel,axiom,
% 157.60/157.46 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pair__less__def,axiom,
% 157.60/157.46 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_measure__def,axiom,
% 157.60/157.46 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mlex__prod__def,axiom,
% 157.60/157.46 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_of__int,axiom,
% 157.60/157.46 ! [V_j_2,V_i_2,T_b] :
% 157.60/157.46 ( class_Rings_Oring__1(T_b)
% 157.60/157.46 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_One__int__def,axiom,
% 157.60/157.46 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_mult,axiom,
% 157.60/157.46 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Rep__Integ__inverse,axiom,
% 157.60/157.46 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 157.60/157.46
% 157.60/157.46 fof(fact_minus,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Zero__int__def,axiom,
% 157.60/157.46 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_int__def,axiom,
% 157.60/157.46 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_add,axiom,
% 157.60/157.46 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_nat,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_minus__int__def,axiom,
% 157.60/157.46 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_less,axiom,
% 157.60/157.46 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_le,axiom,
% 157.60/157.46 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_eq__Abs__Integ,axiom,
% 157.60/157.46 ! [V_z_2] :
% 157.60/157.46 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Integ__def,axiom,
% 157.60/157.46 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Id__onE,axiom,
% 157.60/157.46 ! [V_A_2,V_ca_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 157.60/157.46 => ~ ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.46 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Rep__Integ,axiom,
% 157.60/157.46 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition__Integ,axiom,
% 157.60/157.46 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 157.60/157.46 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_accp__acc__eq,axiom,
% 157.60/157.46 ! [V_x_2,V_r_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_acc__subset,axiom,
% 157.60/157.46 ! [V_R2_2,V_R1_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_acc__downward,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_acc_Osimps,axiom,
% 157.60/157.46 ! [V_r_2,V_a_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.60/157.46 <=> ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 157.60/157.46 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_ORep__range,axiom,
% 157.60/157.46 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_OAbs__image,axiom,
% 157.60/157.46 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_OAbs__inject,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 157.60/157.46 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 157.60/157.46 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_ORep__inject,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 157.60/157.46 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_ORep__inverse,axiom,
% 157.60/157.46 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_ORep,axiom,
% 157.60/157.46 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_type__definition_OAbs__inverse,axiom,
% 157.60/157.46 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.60/157.46 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 157.60/157.46 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__def,axiom,
% 157.60/157.46 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__extp_Oequations,axiom,
% 157.60/157.46 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 157.60/157.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.60/157.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.60/157.46 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.46 & ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.60/157.46 => ? [B_xa] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.60/157.46 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__ext_Ointros,axiom,
% 157.60/157.46 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 157.60/157.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 157.60/157.46 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.46 => ( ! [B_x] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 157.60/157.46 => ? [B_xa] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 157.60/157.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__compI,axiom,
% 157.60/157.46 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_ca_2)),V_s_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__UNION__distrib,axiom,
% 157.60/157.46 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__UNION__distrib2,axiom,
% 157.60/157.46 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__empty2,axiom,
% 157.60/157.46 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__empty1,axiom,
% 157.60/157.46 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__distrib,axiom,
% 157.60/157.46 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__distrib2,axiom,
% 157.60/157.46 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_rel__comp__mono,axiom,
% 157.60/157.46 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_O__assoc,axiom,
% 157.60/157.46 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_union__comp__emptyR,axiom,
% 157.60/157.46 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.60/157.46 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.46 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.46 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_union__comp__emptyL,axiom,
% 157.60/157.46 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 157.60/157.46 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.46 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.46 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__ext__compat,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_min__ext__compat,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__comp__rel__comp__eq,axiom,
% 157.60/157.46 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
% 157.60/157.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_reduction__pairI,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 157.60/157.46 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 157.60/157.46 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__less__than,axiom,
% 157.60/157.46 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__comp_Ointros,axiom,
% 157.60/157.46 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__empty,axiom,
% 157.60/157.46 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__inv__image,axiom,
% 157.60/157.46 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__lex__prod,axiom,
% 157.60/157.46 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 157.60/157.46 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 157.60/157.46 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__measure,axiom,
% 157.60/157.46 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__comp__self,axiom,
% 157.60/157.46 ! [V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.46 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_max__ext__wf,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__pair__less,axiom,
% 157.60/157.46 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_pred__comp_Oequations,axiom,
% 157.60/157.46 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 157.60/157.46 <=> ? [B_b] :
% 157.60/157.46 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 157.60/157.46 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__subset,axiom,
% 157.60/157.46 ! [V_p_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 157.60/157.46 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__Int2,axiom,
% 157.60/157.46 ! [V_r_H_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__Int1,axiom,
% 157.60/157.46 ! [V_r_H_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__finite__psubset,axiom,
% 157.60/157.46 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__mlex,axiom,
% 157.60/157.46 ! [V_f_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.46 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_min__ext__wf,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__less,axiom,
% 157.60/157.46 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__irrefl,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__asym,axiom,
% 157.60/157.46 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__not__sym,axiom,
% 157.60/157.46 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__not__refl,axiom,
% 157.60/157.46 ! [V_a_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__int__ge__less__than,axiom,
% 157.60/157.46 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__int__ge__less__than2,axiom,
% 157.60/157.46 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_acc__wfD,axiom,
% 157.60/157.46 ! [V_x_2,V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__acc__iff,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__no__loop,axiom,
% 157.60/157.46 ! [V_R_2,T_b] :
% 157.60/157.46 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.46 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__union__merge,axiom,
% 157.60/157.46 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 157.60/157.46 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 157.60/157.46 ! [V_r_2,T_b] :
% 157.60/157.46 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.46 <=> ~ ? [B_f] :
% 157.60/157.46 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 157.60/157.46
% 157.60/157.46 fof(fact_wfE__pf,axiom,
% 157.60/157.47 ! [V_A_2,V_R_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 157.60/157.47 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__union__compatible,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.47 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Orderings_Owellorder(T_b)
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reduction__pair__def,axiom,
% 157.60/157.47 ! [V_Pa_2,T_b] :
% 157.60/157.47 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.60/157.47 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reduction__pair__lemma,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 157.60/157.47 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 157.60/157.47 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Nitpick_Oone__frac__def,axiom,
% 157.60/157.47 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 157.60/157.47 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Nitpick_Ofrac__def,axiom,
% 157.60/157.47 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_pred__nat__def,axiom,
% 157.60/157.47 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__lenlex,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__same__fst,axiom,
% 157.60/157.47 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 157.60/157.47 ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.47 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 157.60/157.47 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__pred__nat,axiom,
% 157.60/157.47 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__lex,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__lexn,axiom,
% 157.60/157.47 ! [V_n_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__if__measure,axiom,
% 157.60/157.47 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 157.60/157.47 ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_lex__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_lexn_Osimps_I1_J,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Collect__split,axiom,
% 157.60/157.47 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_image__split__eq__Sigma,axiom,
% 157.60/157.47 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.60/157.47 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SigmaI,axiom,
% 157.60/157.47 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_RangeI,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__eq__cancel2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 157.60/157.47 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
% 157.60/157.47 <=> V_A_2 = V_B_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Diff__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__Diff__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Diff__distrib2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Id__on,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_accp__wfPD,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.60/157.47 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__accp__iff,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.60/157.47 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__empty1,axiom,
% 157.60/157.47 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_card__cartesian__product,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__cartesian__product,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__empty2,axiom,
% 157.60/157.47 ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__empty,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
% 157.60/157.47 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Compl__Times__UNIV2,axiom,
% 157.60/157.47 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Compl__Times__UNIV1,axiom,
% 157.60/157.47 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setprod__cartesian__product,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__subset,axiom,
% 157.60/157.47 ! [V_p_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
% 157.60/157.47 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Un__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__Un__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Un__distrib2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__comp__subset__Sigma,axiom,
% 157.60/157.47 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_swap__product,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__cartesian__product,axiom,
% 157.60/157.47 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_equiv__type,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Int__distrib2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__Int__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Int__distrib1,axiom,
% 157.60/157.47 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Id__on__subset__Times,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Diff__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UNIV__Times__UNIV,axiom,
% 157.60/157.47 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_mem__Sigma__iff,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 157.60/157.47 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SigmaD1,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SigmaD2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SigmaE2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 157.60/157.47 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__empty,axiom,
% 157.60/157.47 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__empty__iff,axiom,
% 157.60/157.47 ! [V_r_2,T_b,T_c] :
% 157.60/157.47 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Un__eq,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__Range,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_snd__eq__Range,axiom,
% 157.60/157.47 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_card__cartesian__product__singleton,axiom,
% 157.60/157.47 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Times__subset__cancel2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__subset,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__cartesian__productD1,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 157.60/157.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__cartesian__productD2,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 157.60/157.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Collect__split,axiom,
% 157.60/157.47 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SetCompr__Sigma__eq,axiom,
% 157.60/157.47 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fst__image__times,axiom,
% 157.60/157.47 ! [V_A_2,T_c,T_b,V_B_2] :
% 157.60/157.47 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_snd__image__times,axiom,
% 157.60/157.47 ! [V_B_2,T_c,T_b,V_A_2] :
% 157.60/157.47 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__iff,axiom,
% 157.60/157.47 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 157.60/157.47 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__insert,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Int__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_insert__times__insert,axiom,
% 157.60/157.47 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__equiv__class,axiom,
% 157.60/157.47 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_vimage__Times,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UN__Times__distrib,axiom,
% 157.60/157.47 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__def,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__quotient,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__in__rel,axiom,
% 157.60/157.47 ! [V_R_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.60/157.47 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__wf__eq,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
% 157.60/157.47 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 157.60/157.47 ( class_Rings_Osemiring__0(T_d)
% 157.60/157.47 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_RangeP__Range__eq,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 157.60/157.47 ! [V_A_2,V_I_2,T_c,T_b] :
% 157.60/157.47 ? [B_f] :
% 157.60/157.47 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_RangeP_Ointros,axiom,
% 157.60/157.47 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.60/157.47 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_image__id,axiom,
% 157.60/157.47 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_apfst__id,axiom,
% 157.60/157.47 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_apsnd__id,axiom,
% 157.60/157.47 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_id__def,axiom,
% 157.60/157.47 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_RangeP_Oequations,axiom,
% 157.60/157.47 ! [V_a2_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 157.60/157.47 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_id__apply,axiom,
% 157.60/157.47 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 157.60/157.47
% 157.60/157.47 fof(fact_vimage__id,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inj__on__id,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_id__o,axiom,
% 157.60/157.47 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_o__id,axiom,
% 157.60/157.47 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_o__eq__id__dest,axiom,
% 157.60/157.47 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.60/157.47 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2)
% 157.60/157.47 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_of__int__eq__id,axiom,
% 157.60/157.47 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_surj__id,axiom,
% 157.60/157.47 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inv__id,axiom,
% 157.60/157.47 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_folding_Oempty,axiom,
% 157.60/157.47 ! [V_F_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.60/157.47 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_split__Pair,axiom,
% 157.60/157.47 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__reindex__id,axiom,
% 157.60/157.47 ! [V_B_2,V_f_2,T_b,T_c] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setprod__reindex__id,axiom,
% 157.60/157.47 ! [V_B_2,V_f_2,T_b,T_c] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.60/157.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_surj__iff,axiom,
% 157.60/157.47 ! [V_f_2,T_b,T_c] :
% 157.60/157.47 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inv__o__cancel,axiom,
% 157.60/157.47 ! [V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.47 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inj__iff,axiom,
% 157.60/157.47 ! [V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.47 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setprod__Sigma,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__Sigma,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__image__Sigma,axiom,
% 157.60/157.47 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.60/157.47 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_card__SigmaI,axiom,
% 157.60/157.47 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.60/157.47 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__SigmaI,axiom,
% 157.60/157.47 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ! [B_a] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_RangeE,axiom,
% 157.60/157.47 ! [V_r_2,T_c,V_b_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 157.60/157.47 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SigmaE,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 157.60/157.47 => ~ ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 157.60/157.47 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__acyclicP,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__Un,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 157.60/157.47 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_DomainI,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__acyclic,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acyclic__subset,axiom,
% 157.60/157.47 ! [V_r_2,V_s_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Id__on,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__empty,axiom,
% 157.60/157.47 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__empty__iff,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] :
% 157.60/157.47 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__mono,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Un__eq,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__Domain,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fst__eq__Domain,axiom,
% 157.60/157.47 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__iff,axiom,
% 157.60/157.47 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 157.60/157.47 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__insert,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__acyclic__wf,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.60/157.47 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.60/157.47 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Int__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Diff__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Field__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Collect__split,axiom,
% 157.60/157.47 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_DomainP__Domain__eq,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Nitpick_Owf_H__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 157.60/157.47 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.47 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.60/157.47 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_DomainE,axiom,
% 157.60/157.47 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 157.60/157.47 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_DomainP_Ointros,axiom,
% 157.60/157.47 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.60/157.47 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_DomainP_Oequations,axiom,
% 157.60/157.47 ! [V_a1_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 157.60/157.47 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__surj,axiom,
% 157.60/157.47 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 157.60/157.47 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__inj__on,axiom,
% 157.60/157.47 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.60/157.47 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 157.60/157.47 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__map__pair__image,axiom,
% 157.60/157.47 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.47 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__imageI,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair_Ocomp,axiom,
% 157.60/157.47 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__compose,axiom,
% 157.60/157.47 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair_Ocompositionality,axiom,
% 157.60/157.47 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_snd__comp__map__pair,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fst__comp__map__pair,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fst__map__pair,axiom,
% 157.60/157.47 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_snd__prod__fun,axiom,
% 157.60/157.47 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__simp,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__ident,axiom,
% 157.60/157.47 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair_Oidentity,axiom,
% 157.60/157.47 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_apsnd__def,axiom,
% 157.60/157.47 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_apfst__def,axiom,
% 157.60/157.47 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair_Oid,axiom,
% 157.60/157.47 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__def,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_map__pair__surj__on,axiom,
% 157.60/157.47 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 157.60/157.47 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 157.60/157.47 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 157.60/157.47 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_prod__fun__imageE,axiom,
% 157.60/157.47 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 157.60/157.47 => ~ ! [B_x,B_y] :
% 157.60/157.47 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__def,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 & ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Rep__Integ__induct,axiom,
% 157.60/157.47 ! [V_Pa_2,V_y_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 157.60/157.47 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__Id__on,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__Un,axiom,
% 157.60/157.47 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 157.60/157.47 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__Int,axiom,
% 157.60/157.47 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 157.60/157.47 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__onD2,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__onD1,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__onD,axiom,
% 157.60/157.47 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reflp__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Predicate_Oreflp(T_b,V_r_2)
% 157.60/157.47 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__onI,axiom,
% 157.60/157.47 ! [V_A_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 157.60/157.47 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Rep__Integ__cases,axiom,
% 157.60/157.47 ! [V_y_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 157.60/157.47 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reflpE,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Predicate_Oreflp(T_b,V_r_2)
% 157.60/157.47 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__def_H,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 <=> ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) )
% 157.60/157.47 & ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Abs__Integ__cases,axiom,
% 157.60/157.47 ! [V_x_2] :
% 157.60/157.47 ~ ! [B_y] :
% 157.60/157.47 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Abs__Integ__induct,axiom,
% 157.60/157.47 ! [V_x_2,V_Pa_2] :
% 157.60/157.47 ( ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_ball__empty,axiom,
% 157.60/157.47 ! [V_Pa_2,T_b,B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Powp__def,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 157.60/157.47 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_congruent__def,axiom,
% 157.60/157.47 ! [V_f_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfP__SUP,axiom,
% 157.60/157.47 ! [T_b,V_r_2,T_c] :
% 157.60/157.47 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 157.60/157.47 => ( ! [B_i,B_j] :
% 157.60/157.47 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_mem__splitI2,axiom,
% 157.60/157.47 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 157.60/157.47 ( ! [B_a,B_b] :
% 157.60/157.47 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_mem__splitE,axiom,
% 157.60/157.47 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2)))
% 157.60/157.47 => ~ ! [B_x,B_y] :
% 157.60/157.47 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Eps__split,axiom,
% 157.60/157.47 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wfI__pf,axiom,
% 157.60/157.47 ! [V_R_2,T_b] :
% 157.60/157.47 ( ! [B_A] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
% 157.60/157.47 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 157.60/157.47 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__mono,axiom,
% 157.60/157.47 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_exE__some,axiom,
% 157.60/157.47 ! [T_b,V_ca_2,V_Pa_2] :
% 157.60/157.47 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.47 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_some__sym__eq__trivial,axiom,
% 157.60/157.47 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_some__eq__trivial,axiom,
% 157.60/157.47 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_some__eq__ex,axiom,
% 157.60/157.47 ! [T_b,V_Pa_2] :
% 157.60/157.47 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 157.60/157.47 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_someI__ex,axiom,
% 157.60/157.47 ! [T_b,V_Pa_2] :
% 157.60/157.47 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_someI,axiom,
% 157.60/157.47 ! [T_b,V_x_2,V_Pa_2] :
% 157.60/157.47 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.47 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_tfl__some,axiom,
% 157.60/157.47 ! [T_b,B_P] :
% 157.60/157.47 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 157.60/157.47 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_split__paired__Eps,axiom,
% 157.60/157.47 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Eps__split__eq,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inv__into__def,axiom,
% 157.60/157.47 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inv__def,axiom,
% 157.60/157.47 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acc_OaccI,axiom,
% 157.60/157.47 ! [V_r_2,V_x_2,T_b] :
% 157.60/157.47 ( ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_not__acc__down,axiom,
% 157.60/157.47 ! [V_R_2,V_x_2,T_b] :
% 157.60/157.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 157.60/157.47 => ~ ! [B_z] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_max__ext_Osimps,axiom,
% 157.60/157.47 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 157.60/157.47 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.60/157.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.60/157.47 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 & ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.60/157.47 => ? [B_xa] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__no__infinite__down__chainE,axiom,
% 157.60/157.47 ! [V_f_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osize_I3_J,axiom,
% 157.60/157.47 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osize_I11_J,axiom,
% 157.60/157.47 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I37_J,axiom,
% 157.60/157.47 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I36_J,axiom,
% 157.60/157.47 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I23_J,axiom,
% 157.60/157.47 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I22_J,axiom,
% 157.60/157.47 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I34_J,axiom,
% 157.60/157.47 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I35_J,axiom,
% 157.60/157.47 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I11_J,axiom,
% 157.60/157.47 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I10_J,axiom,
% 157.60/157.47 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I2_J,axiom,
% 157.60/157.47 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 157.60/157.47 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
% 157.60/157.47 <=> ( V_loc_2 = V_loc_H_2
% 157.60/157.47 & V_fun_2 = V_fun_H_2
% 157.60/157.47 & V_com_2 = V_com_H_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I39_J,axiom,
% 157.60/157.47 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_com_Osimps_I38_J,axiom,
% 157.60/157.47 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__reindex__cong,axiom,
% 157.60/157.47 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.60/157.47 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.60/157.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.60/157.47 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.60/157.47 => ( ! [B_a] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.60/157.47 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_scomp__unfold,axiom,
% 157.60/157.47 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_setsum__ivl__cong,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 157.60/157.47 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.47 & class_Orderings_Oord(T_b) )
% 157.60/157.47 => ( V_a_2 = V_ca_2
% 157.60/157.47 => ( V_b_2 = V_d_2
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 157.60/157.47 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 157.60/157.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_scomp__Pair,axiom,
% 157.60/157.47 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_scomp__scomp,axiom,
% 157.60/157.47 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Pair__scomp,axiom,
% 157.60/157.47 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_scomp__apply,axiom,
% 157.60/157.47 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_scomp__def,axiom,
% 157.60/157.47 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_iterate_Osimps,axiom,
% 157.60/157.47 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 157.60/157.47 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.47 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) )
% 157.60/157.47 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.47 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_less__eq,axiom,
% 157.60/157.47 ! [V_n_2,V_m_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_nat__intermed__int__val,axiom,
% 157.60/157.47 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 157.60/157.47 ( ! [B_i] :
% 157.60/157.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.60/157.47 => ? [B_i] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.47 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__trancl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_less__than__def,axiom,
% 157.60/157.47 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acyclic__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.47 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl_Or__into__trancl,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__subset__Field2,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__Int__subset,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_r__into__trancl_H,axiom,
% 157.60/157.47 ! [V_r_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__domain,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__range,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__trancl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__trans,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__into__trancl2,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_r__r__into__trancl,axiom,
% 157.60/157.47 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_R_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__mono,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__unfold,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__subset__Sigma,axiom,
% 157.60/157.47 ! [V_A_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_log_Osimps,axiom,
% 157.60/157.47 ! [V_i,V_b] :
% 157.60/157.47 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 157.60/157.47 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 157.60/157.47 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 157.60/157.47 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_minus__shift__def,axiom,
% 157.60/157.47 ! [V_r,V_l,V_k] :
% 157.60/157.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.60/157.47 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) )
% 157.60/157.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.60/157.47 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inc__shift__def,axiom,
% 157.60/157.47 ! [V_k,V_v] :
% 157.60/157.47 ( ( V_v = V_k
% 157.60/157.47 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 157.60/157.47 & ( V_v != V_k
% 157.60/157.47 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_range,axiom,
% 157.60/157.47 ! [V_s,V_k] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__insert,axiom,
% 157.60/157.47 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reflcl__set__eq,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_r__into__rtrancl,axiom,
% 157.60/157.47 ! [V_r_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 157.60/157.47 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_IdI,axiom,
% 157.60/157.47 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__into__rtrancl,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__closed__trancl,axiom,
% 157.60/157.47 ! [V_X_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
% 157.60/157.47 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__subset__rtrancl,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__subset,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__mono,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__Int__subset,axiom,
% 157.60/157.47 ! [V_r_2,V_s_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__rtrancl,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__Id,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Id__O__R,axiom,
% 157.60/157.47 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_R__O__Id,axiom,
% 157.60/157.47 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__rtrancl,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__unfold,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_r__comp__rtrancl__eq,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__idemp__self__comp,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_in__rtrancl__UnI,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 157.60/157.47 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__reflcl,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__reflcl__absorb,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__Un__rtrancl,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__idemp,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__trans,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__r__diff__Id,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__rtrancl__absorb,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__trancl__absorb,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_reflcl__trancl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__reflcl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__rtrancl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__unfold__left,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__unfold__right,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__Un__subset,axiom,
% 157.60/157.47 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_pair__in__Id__conv,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 157.60/157.47 <=> V_a_2 = V_b_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__eq__or__trancl,axiom,
% 157.60/157.47 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 <=> ( V_x_2 = V_y_2
% 157.60/157.47 | ( V_x_2 != V_y_2
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__into__trancl2,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtranclD,axiom,
% 157.60/157.47 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 => ( V_a_2 = V_b_2
% 157.60/157.47 | ( V_a_2 != V_b_2
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__into__trancl1,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__rtrancl__trancl,axiom,
% 157.60/157.47 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__trancl__trancl,axiom,
% 157.60/157.47 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Id,axiom,
% 157.60/157.47 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Id,axiom,
% 157.60/157.47 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__Id,axiom,
% 157.60/157.47 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_pair__leq__def,axiom,
% 157.60/157.47 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Not__Domain__rtrancl,axiom,
% 157.60/157.47 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 157.60/157.47 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 <=> V_x_2 = V_y_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acc__downwards__aux,axiom,
% 157.60/157.47 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acc__downwards,axiom,
% 157.60/157.47 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__insert,axiom,
% 157.60/157.47 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 157.60/157.47 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.47 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acyclic__insert,axiom,
% 157.60/157.47 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 157.60/157.47 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.47 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__reflcl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Id__def,axiom,
% 157.60/157.47 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_irrefl__diff__Id,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_pred__nat__trancl__eq__le,axiom,
% 157.60/157.47 ! [V_n_2,V_m_2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__subset__Sigma__aux,axiom,
% 157.60/157.47 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.47 => ( V_a_2 = V_b_2
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_irrefl__tranclI,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_b] :
% 157.60/157.47 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_sequence__trans,axiom,
% 157.60/157.47 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 157.60/157.47 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_total__on__diff__Id,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 157.60/157.47 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__Id,axiom,
% 157.60/157.47 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acyclic__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.47 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__rel__comp,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__Un,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__Id__on,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__Int,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_total__on__converse,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.47 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Field__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 157.60/157.47 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__inv__image,axiom,
% 157.60/157.47 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__UNION,axiom,
% 157.60/157.47 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__converse,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.47 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converseD,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converseI,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__iff,axiom,
% 157.60/157.47 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__converse__trancl,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_equiv__comp__eq,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.47 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_total__on__empty,axiom,
% 157.60/157.47 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__converseD,axiom,
% 157.60/157.47 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__converseI,axiom,
% 157.60/157.47 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__converseI,axiom,
% 157.60/157.47 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__converseD,axiom,
% 157.60/157.47 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__subset__eq,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_refl__on__comp__subset,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_comp__equivI,axiom,
% 157.60/157.47 ! [V_A_2,V_r_2,T_b] :
% 157.60/157.47 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
% 157.60/157.47 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 157.60/157.47 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__acyclic__wf__converse,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.60/157.47 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.47 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_total__on__def,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => ! [B_xa] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.60/157.47 => ( B_x != B_xa
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__def,axiom,
% 157.60/157.47 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 157.60/157.47 ! [V_R_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_acyclicI,axiom,
% 157.60/157.47 ! [V_r_2,T_b] :
% 157.60/157.47 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.60/157.47 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__Int__eq,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 157.60/157.47 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__subset,axiom,
% 157.60/157.47 ! [V_s_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.47 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 157.60/157.47 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__rel__comp,axiom,
% 157.60/157.47 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.60/157.47 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 157.60/157.47 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_comp__funpow,axiom,
% 157.60/157.47 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow__mult,axiom,
% 157.60/157.47 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow__swap1,axiom,
% 157.60/157.47 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_wf__exp,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,T_b] :
% 157.60/157.47 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
% 157.60/157.47 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__commute,axiom,
% 157.60/157.47 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__rel__pow,axiom,
% 157.60/157.47 ! [V_n_2,V_R_2,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 157.60/157.47 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__1,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__Id,axiom,
% 157.60/157.47 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__power,axiom,
% 157.60/157.47 ! [V_R_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__imp__rtrancl,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__Id__on,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_relpow_Osimps_I2_J,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__add,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_relpow_Osimps_I1_J,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__0__E,axiom,
% 157.60/157.47 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 157.60/157.47 => V_x_2 = V_y_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__0__I,axiom,
% 157.60/157.47 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__Suc__I,axiom,
% 157.60/157.47 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__Suc__I2,axiom,
% 157.60/157.47 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow_Osimps_I2_J,axiom,
% 157.60/157.47 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow__add,axiom,
% 157.60/157.47 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__def,axiom,
% 157.60/157.47 ! [V_r_2,T_c,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.60/157.47 <=> ! [B_x,B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 157.60/157.47 => ! [B_z] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 157.60/157.47 => B_y = B_z ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valuedD,axiom,
% 157.60/157.47 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 157.60/157.47 => V_y_2 = V_z_2 ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow_Osimps_I1_J,axiom,
% 157.60/157.47 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_trancl__power,axiom,
% 157.60/157.47 ! [V_R_2,V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 157.60/157.47 <=> ? [B_n] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_single__valued__confluent,axiom,
% 157.60/157.47 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.47 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_funpow__code__def,axiom,
% 157.60/157.47 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__E,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.47 => V_x_2 != V_z_2 )
% 157.60/157.47 => ~ ! [B_y,B_m] :
% 157.60/157.47 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__E2,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.47 => V_x_2 != V_z_2 )
% 157.60/157.47 => ~ ! [B_y,B_m] :
% 157.60/157.47 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 157.60/157.47 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 157.60/157.47 => ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Qa_2))
% 157.60/157.47 => B_y = B_x ) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rtrancl__Un__separatorE,axiom,
% 157.60/157.47 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 157.60/157.47 => ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Qa_2))
% 157.60/157.47 => B_x = B_y ) )
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__Suc__D2,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 157.60/157.47 => ? [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__Suc__E,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 157.60/157.47 => ~ ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_rel__pow__Suc__E2,axiom,
% 157.60/157.47 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 157.60/157.47 => ~ ! [B_y] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_tranclD,axiom,
% 157.60/157.47 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 157.60/157.47 => ? [B_z] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_tranclD2,axiom,
% 157.60/157.47 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 157.60/157.47 => ? [B_z] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_IdE,axiom,
% 157.60/157.47 ! [V_p_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 157.60/157.47 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__image__def,axiom,
% 157.60/157.47 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__empty,axiom,
% 157.60/157.47 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_folding_Oeq__fold,axiom,
% 157.60/157.47 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__def,axiom,
% 157.60/157.47 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_union__fold__insert,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__sup__insert,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Osemilattice__sup(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__inf__insert,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Osemilattice__inf(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_Ofold__inf__insert,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_Ofold__sup__insert,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 157.60/157.47 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 157.60/157.47 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_sup__SUPR__fold__sup,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_sup__le__fold__sup,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Osemilattice__sup(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold__inf__le__inf,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Osemilattice__inf(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold1__eq__fold__idem,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Olattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Olattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_minus__fold__remove,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_folding__one_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_SUPR__fold__sup,axiom,
% 157.60/157.47 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fold1__eq__fold,axiom,
% 157.60/157.47 ! [V_a_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Olattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Lattices_Olattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Min_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Max_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 157.60/157.47 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Orderings_Olinorder(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 157.60/157.47 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 157.60/157.47 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.60/157.47 => V_y_2 = V_x_2 ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.60/157.47 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 157.60/157.47 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 157.60/157.47 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 157.60/157.47 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 157.60/157.47 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 157.60/157.47 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 157.60/157.47 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 157.60/157.47 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 157.60/157.47 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => ? [B_y_H] :
% 157.60/157.47 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 157.60/157.47 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INFI__fold__inf,axiom,
% 157.60/157.47 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF1__D,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF1__E,axiom,
% 157.60/157.47 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__D,axiom,
% 157.60/157.47 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__E,axiom,
% 157.60/157.47 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF2__D,axiom,
% 157.60/157.47 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF2__E,axiom,
% 157.60/157.47 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 157.60/157.47 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 157.60/157.47 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__INT,axiom,
% 157.60/157.47 ! [V_A_2,T_c,V_I_2,T_b] :
% 157.60/157.47 ( ? [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.60/157.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__INT__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UN__simps_I7_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UN__extend__simps_I7_J,axiom,
% 157.60/157.47 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I9_J,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I9_J,axiom,
% 157.60/157.47 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__insert,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Collect__ball__eq,axiom,
% 157.60/157.47 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__Un,axiom,
% 157.60/157.47 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INFI__bool__eq,axiom,
% 157.60/157.47 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I5_J,axiom,
% 157.60/157.47 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I5_J,axiom,
% 157.60/157.47 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__Int__distrib,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Pow__INT__eq,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INFI__apply,axiom,
% 157.60/157.47 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__commute,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.47 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.47 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__INT__eq2,axiom,
% 157.60/157.47 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__iff,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_vimage__INT,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I10_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I10_J,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__less__iff,axiom,
% 157.60/157.47 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 & class_Orderings_Olinorder(T_b) )
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
% 157.60/157.47 <=> ? [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_le__INF__iff,axiom,
% 157.60/157.47 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__subset__iff,axiom,
% 157.60/157.47 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I1_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I2_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__constant,axiom,
% 157.60/157.47 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.60/157.47 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__empty,axiom,
% 157.60/157.47 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__const,axiom,
% 157.60/157.47 ! [V_M_2,T_b,V_A_2,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__absorb,axiom,
% 157.60/157.47 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__INT__eq,axiom,
% 157.60/157.47 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 157.60/157.47 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__lower,axiom,
% 157.60/157.47 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__insert__distrib,axiom,
% 157.60/157.47 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_converse__INTER,axiom,
% 157.60/157.47 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I7_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I6_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I7_J,axiom,
% 157.60/157.47 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Un__INT__distrib,axiom,
% 157.60/157.47 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I6_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Un__INT__distrib2,axiom,
% 157.60/157.47 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Compl__INT,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Compl__UN,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__subset,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INTER__def,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I1_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I2_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I3_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I3_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I4_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF__leI,axiom,
% 157.60/157.47 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__greaterThan__UNIV,axiom,
% 157.60/157.47 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I4_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.60/157.47 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 157.60/157.47 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Image__INT__eq,axiom,
% 157.60/157.47 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 157.60/157.47 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 157.60/157.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 157.60/157.47 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inf__INFI__fold__inf,axiom,
% 157.60/157.47 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__fold__inf,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__fold__sup,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__Inter,axiom,
% 157.60/157.47 ! [V_M_2,T_b] :
% 157.60/157.47 ( ? [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 157.60/157.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UnionI,axiom,
% 157.60/157.47 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_InterE,axiom,
% 157.60/157.47 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_InterD,axiom,
% 157.60/157.47 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF2__iff,axiom,
% 157.60/157.47 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INF1__iff,axiom,
% 157.60/157.47 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__extend__simps_I8_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INT__simps_I8_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_INTER__eq__Inter__image,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__image__eq,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Un__Inter,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__upper,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_le__Inf__iff,axiom,
% 157.60/157.47 ! [V_A_2,V_b_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__le__iff,axiom,
% 157.60/157.47 ! [V_b_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__less__iff,axiom,
% 157.60/157.47 ! [V_a_2,V_S_2,T_b] :
% 157.60/157.47 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 & class_Orderings_Olinorder(T_b) )
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 157.60/157.47 <=> ? [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_less__Sup__iff,axiom,
% 157.60/157.47 ! [V_S_2,V_a_2,T_b] :
% 157.60/157.47 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 & class_Orderings_Olinorder(T_b) )
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 157.60/157.47 <=> ? [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Field__Union,axiom,
% 157.60/157.47 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__Pow__eq,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__disjoint,axiom,
% 157.60/157.47 ! [V_A_2,V_C_2,T_b] :
% 157.60/157.47 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 <=> ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Domain__Union,axiom,
% 157.60/157.47 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_image__Union,axiom,
% 157.60/157.47 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Int__Union2,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Int__Union,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Range__Union,axiom,
% 157.60/157.47 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sigma__Union,axiom,
% 157.60/157.47 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UN__simps_I8_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UN__extend__simps_I8_J,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_vimage__Union,axiom,
% 157.60/157.47 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__Inf,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__Sup,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__lower,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__mono,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__quotient,axiom,
% 157.60/157.47 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.47 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__insert,axiom,
% 157.60/157.47 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__UnionD,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_subset__Pow__Union,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__anti__mono,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__empty,axiom,
% 157.60/157.47 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__eq,axiom,
% 157.60/157.47 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__UNIV,axiom,
% 157.60/157.47 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__Un__distrib,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__insert,axiom,
% 157.60/157.47 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_UNION__eq__Union__image,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__image__eq,axiom,
% 157.60/157.47 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__upper,axiom,
% 157.60/157.47 ! [V_A_2,V_x_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__UNIV,axiom,
% 157.60/157.47 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__lower,axiom,
% 157.60/157.47 ! [V_A_2,V_x_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__Un__distrib,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__empty,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__singleton,axiom,
% 157.60/157.47 ! [V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__insert,axiom,
% 157.60/157.47 ! [V_A_2,V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Int__Inter__image,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__UNIV,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__singleton,axiom,
% 157.60/157.47 ! [V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__empty,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__UNIV,axiom,
% 157.60/157.47 ! [T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__insert,axiom,
% 157.60/157.47 ! [V_A_2,V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Un__eq__Union,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Un__Union__image,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__Int__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Int__eq__Inter,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__Un__subset,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__binary,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__binary,axiom,
% 157.60/157.47 ! [V_b_2,V_a_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_sup__Sup__fold__sup,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Sup__fin__Sup,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_inf__Inf__fold__inf,axiom,
% 157.60/157.47 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inf__fin__Inf,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.47 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_image__INT,axiom,
% 157.60/157.47 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 157.60/157.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.60/157.47 => ( ! [B_x] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 157.60/157.47 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 157.60/157.47 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_card__partition,axiom,
% 157.60/157.47 ! [V_k_2,V_C_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 157.60/157.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 157.60/157.47 => ( ! [B_c] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 157.60/157.47 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 157.60/157.47 => ( ! [B_c1] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 157.60/157.47 => ! [B_c2] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 157.60/157.47 => ( B_c1 != B_c2
% 157.60/157.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 157.60/157.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Inter__def,axiom,
% 157.60/157.47 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_Union__def,axiom,
% 157.60/157.47 ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_finite__Union,axiom,
% 157.60/157.47 ! [V_A_2,T_b] :
% 157.60/157.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 157.60/157.47 => ( ! [B_M] :
% 157.60/157.47 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 157.60/157.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 157.60/157.47
% 157.60/157.47 fof(fact_insert__partition,axiom,
% 157.60/157.48 ! [V_F_2,V_x_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 157.60/157.48 => ! [B_xa] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 157.60/157.48 => ( B_x != B_xa
% 157.60/157.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 157.60/157.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__on__Inter,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b,V_S_2] :
% 157.60/157.48 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 157.60/157.48 => ( ! [B_A] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 157.60/157.48 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 157.60/157.48 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Inter__subset,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.48 ( ! [B_X] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 157.60/157.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__on__INTER,axiom,
% 157.60/157.48 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 157.60/157.48 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.48 => ( ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 157.60/157.48 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 157.60/157.48 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 157.60/157.48 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 157.60/157.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.48 => ~ ! [B_y] :
% 157.60/157.48 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 157.60/157.48 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 157.60/157.48 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 157.60/157.48 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_InterI,axiom,
% 157.60/157.48 ! [V_A_2,V_C_2,T_b] :
% 157.60/157.48 ( ! [B_X] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inf__le__fold__inf,axiom,
% 157.60/157.48 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Lattices_Osemilattice__inf(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fold__sup__le__sup,axiom,
% 157.60/157.48 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Lattices_Osemilattice__sup(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_mod__div__decomp,axiom,
% 157.60/157.48 ! [V_b,V_a,T_a] :
% 157.60/157.48 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.48 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_wf__eq__minimal,axiom,
% 157.60/157.48 ! [V_r_2,T_b] :
% 157.60/157.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.60/157.48 <=> ! [B_Q] :
% 157.60/157.48 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 157.60/157.48 => ? [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 157.60/157.48 & ! [B_y] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.60/157.48 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 157.60/157.48 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.60/157.48 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 157.60/157.48 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.60/157.48 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 157.60/157.48 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.60/157.48 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.48 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_transfer__nat__int__set__cong,axiom,
% 157.60/157.48 ! [V_P_H_2,V_Pa_2] :
% 157.60/157.48 ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.60/157.48 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.48 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 157.60/157.48 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Int__Collect__mono,axiom,
% 157.60/157.48 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.48 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_UnionE,axiom,
% 157.60/157.48 ! [V_C_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 157.60/157.48 => ~ ! [B_X] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_converseE,axiom,
% 157.60/157.48 ! [V_r_2,V_yx_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 157.60/157.48 => ~ ! [B_x,B_y] :
% 157.60/157.48 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rel__compE,axiom,
% 157.60/157.48 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 157.60/157.48 => ~ ! [B_x,B_y,B_z] :
% 157.60/157.48 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 157.60/157.48 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 157.60/157.48 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Oof__frac__def,axiom,
% 157.60/157.48 ! [V_q,T_a,T_b] :
% 157.60/157.48 ( ( class_Rings_Oinverse(T_b)
% 157.60/157.48 & class_Rings_Oring__1(T_b) )
% 157.60/157.48 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 157.60/157.48 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 157.60/157.48 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Oless__frac__def,axiom,
% 157.60/157.48 ! [V_r_2,V_q_2,T_b] :
% 157.60/157.48 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 157.60/157.48 ! [V_r_2,V_q_2,T_b] :
% 157.60/157.48 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Odenom__def,axiom,
% 157.60/157.48 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Onum__def,axiom,
% 157.60/157.48 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_setprod__pos,axiom,
% 157.60/157.48 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.48 ( class_Rings_Olinordered__semidom(T_c)
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_internal__split__def,axiom,
% 157.60/157.48 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_internal__split__conv,axiom,
% 157.60/157.48 ! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_setprod__nonneg,axiom,
% 157.60/157.48 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.48 ( class_Rings_Olinordered__semidom(T_c)
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_bool_Osize_I1_J,axiom,
% 157.60/157.48 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_bool_Osize_I2_J,axiom,
% 157.60/157.48 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_finite__less__ub,axiom,
% 157.60/157.48 ! [V_u_2,V_f_2] :
% 157.60/157.48 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 157.60/157.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lenlex__def,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexn__length,axiom,
% 157.60/157.48 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 157.60/157.48 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 157.60/157.48 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_neq__if__length__neq,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_a] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
% 157.60/157.48 => V_xs != V_ys ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lenlex__conv,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__sublist,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexn_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_impossible__Cons,axiom,
% 157.60/157.48 ! [V_x,V_ys,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 157.60/157.48 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Oinject,axiom,
% 157.60/157.48 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 157.60/157.48 <=> ( V_a_2 = V_a_H_2
% 157.60/157.48 & V_list_2 = V_list_H_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_not__Cons__self2,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_not__Cons__self,axiom,
% 157.60/157.48 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osize_I4_J,axiom,
% 157.60/157.48 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__in__lex,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 157.60/157.48 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.48 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 157.60/157.48 | ( V_x_2 = V_y_2
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__Cons__def,axiom,
% 157.60/157.48 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_pick_Osimps,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_i] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 157.60/157.48 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 157.60/157.48 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select__weight__cons__zero,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__cons__cons,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.48 | ( V_a_2 = V_b_2
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__lex,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osize_I2_J,axiom,
% 157.60/157.48 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__acc__listrel1I,axiom,
% 157.60/157.48 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__converse,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__mono,axiom,
% 157.60/157.48 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1I2,axiom,
% 157.60/157.48 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 157.60/157.48 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__eq__len,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__listrel1__converse,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1I1,axiom,
% 157.60/157.48 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__listrel1__Cons,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.48 & V_xs_2 = V_ys_2 )
% 157.60/157.48 | ( V_x_2 = V_y_2
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Cons,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__irreflexive,axiom,
% 157.60/157.48 ! [V_y_2,V_r_2,T_b] :
% 157.60/157.48 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__rtrancl__refl,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__mono,axiom,
% 157.60/157.48 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__eq__len,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__rtrancl__trans,axiom,
% 157.60/157.48 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__subset__listrel,axiom,
% 157.60/157.48 ! [V_r_H_2,V_r_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 157.60/157.48 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel_OCons,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrelp__listrel__eq,axiom,
% 157.60/157.48 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 157.60/157.48 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Cons2,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => ~ ! [B_x,B_xs] :
% 157.60/157.48 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrelp_Oequations_I2_J,axiom,
% 157.60/157.48 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 157.60/157.48 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 157.60/157.48 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrelp_OCons,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.60/157.48 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 157.60/157.48 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Cons1,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => ~ ! [B_y,B_ys] :
% 157.60/157.48 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__subset,axiom,
% 157.60/157.48 ! [V_A_2,V_r_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__UNIV,axiom,
% 157.60/157.48 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__mono,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_equiv__listrel,axiom,
% 157.60/157.48 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.48 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__refl__on,axiom,
% 157.60/157.48 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.48 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__in__lists__iff,axiom,
% 157.60/157.48 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__accI,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__accD,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__iff__nth,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 157.60/157.48 & ! [B_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__linear,axiom,
% 157.60/157.48 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.60/157.48 ( ! [B_a,B_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2))
% 157.60/157.48 | B_a = B_b
% 157.60/157.48 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) )
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 | V_x_2 = V_y_2
% 157.60/157.48 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_infinite__UNIV__listI,axiom,
% 157.60/157.48 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__eq__iff__nth__eq,axiom,
% 157.60/157.48 ! [T_b,V_ys_2,V_xs_2] :
% 157.60/157.48 ( V_xs_2 = V_ys_2
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 157.60/157.48 & ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__Cons__Suc,axiom,
% 157.60/157.48 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__Cons__0,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth_Osimps,axiom,
% 157.60/157.48 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__Cons_H,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_n] :
% 157.60/157.48 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 157.60/157.48 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__Cons__number__of,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_v] :
% 157.60/157.48 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x )
% 157.60/157.48 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__take__index__conv,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 157.60/157.48 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 157.60/157.48 | ? [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 157.60/157.48 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__sublist,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_finite__set,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__subset__Cons,axiom,
% 157.60/157.48 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__all,axiom,
% 157.60/157.48 ! [V_n,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__take__subset__set__take,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__take__subset,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__sublist__subset,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__take,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Suc__Cons,axiom,
% 157.60/157.48 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__ConsD,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 157.60/157.48 => ( V_y_2 = V_x_2
% 157.60/157.48 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__sublistD,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__takeD,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_notin__set__sublistI,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__take,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__take,axiom,
% 157.60/157.48 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__upt__eq__take,axiom,
% 157.60/157.48 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_card__length,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_all__set__conv__all__nth,axiom,
% 157.60/157.48 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.48 ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.48 <=> ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__size__estimation,axiom,
% 157.60/157.48 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__size__estimation_H,axiom,
% 157.60/157.48 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__lists__conv__set,axiom,
% 157.60/157.48 ! [V_A_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 <=> ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__pos__if__in__set,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__conv__nth,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 <=> ? [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__mem,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__eq__set,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__conv__nth,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_finite__lists__length__eq,axiom,
% 157.60/157.48 ! [V_n_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_finite__lists__length__le,axiom,
% 157.60/157.48 ! [V_n_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__iff__zip,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 157.60/157.48 & ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__zip,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__zip,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__zip,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__Cons__Cons,axiom,
% 157.60/157.48 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__eq__iff__zip__eq,axiom,
% 157.60/157.48 ! [T_b,V_ys_2,V_xs_2] :
% 157.60/157.48 ( V_xs_2 = V_ys_2
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 157.60/157.48 & ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__same,axiom,
% 157.60/157.48 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 & V_a_2 = V_b_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__zip__leftD,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__zip__rightD,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__zipE,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 157.60/157.48 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__zip,axiom,
% 157.60/157.48 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_greaterThanLessThan__upto,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__setsum__nth,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 157.60/157.48 ! [V_ns_2] :
% 157.60/157.48 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 <=> ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.60/157.48 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__upto,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_atLeastAtMost__upto,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_elem__le__listsum__nat,axiom,
% 157.60/157.48 ! [V_ns,V_k] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__simps_I2_J,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_a)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_atLeastLessThan__upto,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_greaterThanAtMost__upto,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__list__def,axiom,
% 157.60/157.48 ! [V_l_2] :
% 157.60/157.48 ( c_List_Onat__list(V_l_2)
% 157.60/157.48 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__size__pointwise,axiom,
% 157.60/157.48 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 157.60/157.48 ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__update__nat,axiom,
% 157.60/157.48 ! [V_n,V_ns,V_k] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__take,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__beyond,axiom,
% 157.60/157.48 ! [V_x,V_i,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__id,axiom,
% 157.60/157.48 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__list__update__neq,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a,V_j,V_i] :
% 157.60/157.48 ( V_i != V_j
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__list__update,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a,V_k] :
% 157.60/157.48 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) )
% 157.60/157.48 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__list__update,axiom,
% 157.60/157.48 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__update,axiom,
% 157.60/157.48 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_update__zip,axiom,
% 157.60/157.48 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__swap,axiom,
% 157.60/157.48 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 157.60/157.48 ( V_i != V_i_H
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__overwrite,axiom,
% 157.60/157.48 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__code_I3_J,axiom,
% 157.60/157.48 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__code_I2_J,axiom,
% 157.60/157.48 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__butlastD,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__update__subsetI,axiom,
% 157.60/157.48 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__update__subset__insert,axiom,
% 157.60/157.48 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__list__update__eq,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__same__conv,axiom,
% 157.60/157.48 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 157.60/157.48 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__list__update,axiom,
% 157.60/157.48 ! [V_x,V_j,V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => ( ( V_i = V_j
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x )
% 157.60/157.48 & ( V_i != V_j
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__butlast,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__butlast,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__update__memI,axiom,
% 157.60/157.48 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__conv__take,axiom,
% 157.60/157.48 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1__iff__update,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 <=> ? [B_y,B_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__list__update,axiom,
% 157.60/157.48 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__upto,axiom,
% 157.60/157.48 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__take,axiom,
% 157.60/157.48 ! [V_i,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__sublistI,axiom,
% 157.60/157.48 ! [V_I_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__zipI2,axiom,
% 157.60/157.48 ! [V_xs,T_b,V_ys,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__zipI1,axiom,
% 157.60/157.48 ! [V_ys,T_b,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 157.60/157.48 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_card__distinct,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__card,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__eq__iff__index__eq,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 157.60/157.48 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__conv__nth,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 <=> ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ! [B_j] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ( B_i != B_j
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Ocard_H__def,axiom,
% 157.60/157.48 ! [V_A_2,T_b] :
% 157.60/157.48 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__take__lemma,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_a,V_k] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 157.60/157.48 => ( ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__remove1__eq,axiom,
% 157.60/157.48 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Cons__number__of,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_v] :
% 157.60/157.48 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 157.60/157.48 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists_ONil,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Nil1,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Nil2,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 157.60/157.48 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__butlast,axiom,
% 157.60/157.48 ! [T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__remove1,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_x,T_a,V_xs] :
% 157.60/157.48 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 157.60/157.48 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_y,V_x] :
% 157.60/157.48 ( ( V_x = V_y
% 157.60/157.48 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 157.60/157.48 & ( V_x != V_y
% 157.60/157.48 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osimps_I3_J,axiom,
% 157.60/157.48 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upto__empty,axiom,
% 157.60/157.48 ! [V_i,V_j] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 157.60/157.48 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Nil,axiom,
% 157.60/157.48 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__0,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__eq__Nil,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__nil,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1__commute,axiom,
% 157.60/157.48 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrelp_ONil,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrelp_Oequations_I1_J,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osize_I1_J,axiom,
% 157.60/157.48 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__Nil,axiom,
% 157.60/157.48 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__simps_I1_J,axiom,
% 157.60/157.48 ! [T_a] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_a)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osize_I3_J,axiom,
% 157.60/157.48 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__0__conv,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__empty,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__empty2,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__nonempty,axiom,
% 157.60/157.48 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__code_I1_J,axiom,
% 157.60/157.48 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__remove1,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 157.60/157.48 ( V_a_2 != V_b_2
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_notin__set__remove1,axiom,
% 157.60/157.48 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1__idem,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__empty,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__remove1__subset,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__greater__0__conv,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__1__Cons,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_not__Nil__listrel1,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_not__listrel1__Nil,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel_ONil,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__Nil__right,axiom,
% 157.60/157.48 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nil__notin__lex,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nil2__notin__lex,axiom,
% 157.60/157.48 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Cons,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upto_Osimps,axiom,
% 157.60/157.48 ! [V_j,V_i] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.60/157.48 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.60/157.48 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__singleton,axiom,
% 157.60/157.48 ! [V_x_2,T_b,V_A_2] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 157.60/157.48 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 157.60/157.48 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__empty,axiom,
% 157.60/157.48 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Cons_H,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_n] :
% 157.60/157.48 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 157.60/157.48 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upto__rec__number__of,axiom,
% 157.60/157.48 ! [V_n,V_m] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 157.60/157.48 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 157.60/157.48 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel__Nil,axiom,
% 157.60/157.48 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__Cons__sing__Nil,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__remove1,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upto_Opsimps,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2] :
% 157.60/157.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
% 157.60/157.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 157.60/157.48 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 157.60/157.48 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select,axiom,
% 157.60/157.48 ! [V_s_2,T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listset_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__Cons1,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osimps_I5_J,axiom,
% 157.60/157.48 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list_Osimps_I4_J,axiom,
% 157.60/157.48 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listset_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__Cons,axiom,
% 157.60/157.48 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sorted__list__of__set__remove,axiom,
% 157.60/157.48 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upto_Opinduct,axiom,
% 157.60/157.48 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 157.60/157.48 => ( ! [B_i,B_j] :
% 157.60/157.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
% 157.60/157.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sorted__list__of__set__empty,axiom,
% 157.60/157.48 ! [T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_anamorph_Osimps,axiom,
% 157.60/157.48 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 157.60/157.48 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.48 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 157.60/157.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.48 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__Cons,axiom,
% 157.60/157.48 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append1__eq__conv,axiom,
% 157.60/157.48 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 157.60/157.48 <=> ( V_xs_2 = V_ys_2
% 157.60/157.48 & V_x_2 = V_y_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__eq__append__conv,axiom,
% 157.60/157.48 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 157.60/157.48 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 157.60/157.48 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 157.60/157.48 | ? [B_ys_H] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 157.60/157.48 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__eq__Cons__conv,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 157.60/157.48 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 157.60/157.48 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 157.60/157.48 | ? [B_ys_H] :
% 157.60/157.48 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 157.60/157.48 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Cons__eq__appendI,axiom,
% 157.60/157.48 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 157.60/157.48 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 157.60/157.48 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__Cons,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__in__lists__conv,axiom,
% 157.60/157.48 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__assoc,axiom,
% 157.60/157.48 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__eq__append__conv2,axiom,
% 157.60/157.48 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 157.60/157.48 <=> ? [B_us] :
% 157.60/157.48 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 157.60/157.48 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 157.60/157.48 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 157.60/157.48 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_same__append__eq,axiom,
% 157.60/157.48 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 157.60/157.48 <=> V_ys_2 = V_zs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__same__eq,axiom,
% 157.60/157.48 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 157.60/157.48 <=> V_ys_2 = V_zs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__eq__appendI,axiom,
% 157.60/157.48 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 157.60/157.48 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 157.60/157.48 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_a] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_a)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__append,axiom,
% 157.60/157.48 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 157.60/157.48 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
% 157.60/157.48 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_eq__Nil__appendI,axiom,
% 157.60/157.48 ! [T_a,V_ys,V_xs] :
% 157.60/157.48 ( V_xs = V_ys
% 157.60/157.48 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__self__conv2,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__self__conv,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 157.60/157.48 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__is__Nil__conv,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.60/157.48 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_self__append__conv2,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_ys_2] :
% 157.60/157.48 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_self__append__conv,axiom,
% 157.60/157.48 ! [V_ys_2,T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.60/157.48 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__Nil2,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nil__is__append__conv,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.60/157.48 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.60/157.48 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__Nil,axiom,
% 157.60/157.48 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__append,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_ys] :
% 157.60/157.48 ( ( V_ys = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 157.60/157.48 & ( V_ys != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__append__length,axiom,
% 157.60/157.48 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__append__length__plus,axiom,
% 157.60/157.48 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__append1,axiom,
% 157.60/157.48 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__length,axiom,
% 157.60/157.48 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__butlast__appendI,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 157.60/157.48 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__snoc,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__listrel1I,axiom,
% 157.60/157.48 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 & V_us_2 = V_vs_2 )
% 157.60/157.48 | ( V_xs_2 = V_ys_2
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__append__leftI,axiom,
% 157.60/157.48 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 157.60/157.48 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,T_a,V_n] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__update__append,axiom,
% 157.60/157.48 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublist__append,axiom,
% 157.60/157.48 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1I,axiom,
% 157.60/157.48 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 157.60/157.48 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
% 157.60/157.48 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__append__left__rightI,axiom,
% 157.60/157.48 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Suc__conv__app__nth,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 & V_x_2 = V_y_2 )
% 157.60/157.48 | ( V_xs_2 = V_ys_2
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listrel1E,axiom,
% 157.60/157.48 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 157.60/157.48 => ~ ! [B_x,B_y] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 157.60/157.48 => ! [B_us,B_vs] :
% 157.60/157.48 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 157.60/157.48 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__append__leftD,axiom,
% 157.60/157.48 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate1__def,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_upd__conv__take__nth__drop,axiom,
% 157.60/157.48 ! [V_a,V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__take__drop__id,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Suc__Cons,axiom,
% 157.60/157.48 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__1__Cons,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__via__drop,axiom,
% 157.60/157.48 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct1__rotate,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 157.60/157.48 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__drop,axiom,
% 157.60/157.48 ! [V_i,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__butlast,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_butlast__drop,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__drop,axiom,
% 157.60/157.48 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__take,axiom,
% 157.60/157.48 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__drop,axiom,
% 157.60/157.48 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__0,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__zip,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__rotate1,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__drop,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__rotate1,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__set__dropD,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__drop__subset,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate1__is__Nil__conv,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Nil,axiom,
% 157.60/157.48 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__drop__subset__set__drop,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__all,axiom,
% 157.60/157.48 ! [V_n,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 157.60/157.48 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__eq__Nil,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__eq__conv__conj,axiom,
% 157.60/157.48 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 157.60/157.48 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
% 157.60/157.48 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Cons,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Cons_H,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_n] :
% 157.60/157.48 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 157.60/157.48 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__drop,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_i,V_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__eq__append__conv__if,axiom,
% 157.60/157.48 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 157.60/157.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 157.60/157.48 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 157.60/157.48 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 157.60/157.48 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 157.60/157.48 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__drop_H,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__simps,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_b,T_a] :
% 157.60/157.48 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 157.60/157.48 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Cons__number__of,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a,V_v] :
% 157.60/157.48 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 157.60/157.48 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__add,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_j,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate1__length01,axiom,
% 157.60/157.48 ! [V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 157.60/157.48 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__append2,axiom,
% 157.60/157.48 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__append1,axiom,
% 157.60/157.48 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_id__take__nth__drop,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__hd__drop,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__drop__conv__nth,axiom,
% 157.60/157.48 ! [V_n,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd_Osimps,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__append,axiom,
% 157.60/157.48 ! [V_ys,T_a,V_xs] :
% 157.60/157.48 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) )
% 157.60/157.48 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__append2,axiom,
% 157.60/157.48 ! [V_ys,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__in__set,axiom,
% 157.60/157.48 ! [T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__conv__nth,axiom,
% 157.60/157.48 ! [T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate1__hd__tl,axiom,
% 157.60/157.48 ! [T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__rotate__conv__nth,axiom,
% 157.60/157.48 ! [V_n,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl__drop,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__tl,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__rotate,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 157.60/157.48 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__tl,axiom,
% 157.60/157.48 ! [V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__add,axiom,
% 157.60/157.48 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__rotate,axiom,
% 157.60/157.48 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate0,axiom,
% 157.60/157.48 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__rotate,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__rotate,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__is__Nil__conv,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] :
% 157.60/157.48 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate1__rotate__swap,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__def,axiom,
% 157.60/157.48 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl__append2,axiom,
% 157.60/157.48 ! [V_ys,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__tl,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__conv__mod,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__Suc,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__Suc,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__id,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n] :
% 157.60/157.48 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__length01,axiom,
% 157.60/157.48 ! [V_n,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 157.60/157.48 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__tl,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_tl__take,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__Suc,axiom,
% 157.60/157.48 ! [V_n,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__drop__take,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fold1__set,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.60/157.48 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sorted__list__of__set__insert,axiom,
% 157.60/157.48 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__not__Nil,axiom,
% 157.60/157.48 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__Nil,axiom,
% 157.60/157.48 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1__insort,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__insort,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__insort,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_start__le__sum,axiom,
% 157.60/157.48 ! [V_ns_2,V_n_2,V_m_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fun__left__comm__insort,axiom,
% 157.60/157.48 ! [T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__left__comm,axiom,
% 157.60/157.48 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__key__left__comm,axiom,
% 157.60/157.48 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__assoc,axiom,
% 157.60/157.48 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Groups_Osemigroup__add(T_b)
% 157.60/157.48 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__absorb0,axiom,
% 157.60/157.48 ! [V_zs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_b)
% 157.60/157.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__Cons,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__key_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__key_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_x_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__foldl,axiom,
% 157.60/157.48 ! [T_b] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_b)
% 157.60/157.48 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sum__eq__0__conv,axiom,
% 157.60/157.48 ! [V_ns_2,V_m_2] :
% 157.60/157.48 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 & ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.60/157.48 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__insort,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 157.60/157.48 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 157.60/157.48 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.60/157.48 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Sup__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.48 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Inf__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.48 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Sup__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Lattices_Olattice(T_b)
% 157.60/157.48 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Inf__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Lattices_Olattice(T_b)
% 157.60/157.48 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Min__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Max__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_SUPR__set__fold,axiom,
% 157.60/157.48 ! [V_f_2,V_xs_2,T_c,T_b] :
% 157.60/157.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.48 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_INFI__set__fold,axiom,
% 157.60/157.48 ! [V_f_2,V_xs_2,T_c,T_b] :
% 157.60/157.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.48 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_elem__le__sum,axiom,
% 157.60/157.48 ! [V_ns_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__insert__insort__key,axiom,
% 157.60/157.48 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 157.60/157.48 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__append__rightI,axiom,
% 157.60/157.48 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 157.60/157.48 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__insort__insert,axiom,
% 157.60/157.48 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_c)
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__insert__triv,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__insort__insert,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__insert__key__triv,axiom,
% 157.60/157.48 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 157.60/157.48 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_insort__insert__insort,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( class_Orderings_Olinorder(T_b)
% 157.60/157.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lexord__Nil__left,axiom,
% 157.60/157.48 ! [V_r_2,V_y_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.48 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__list__update,axiom,
% 157.60/157.48 ! [V_x,V_k,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 157.60/157.48 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__ConsL,axiom,
% 157.60/157.48 ! [V_x,T_a,V_xs] :
% 157.60/157.48 ( V_xs = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__ConsR,axiom,
% 157.60/157.48 ! [V_x,T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last_Osimps,axiom,
% 157.60/157.48 ! [V_x,T_a,V_xs] :
% 157.60/157.48 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 157.60/157.48 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__append,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_ys] :
% 157.60/157.48 ( ( V_ys = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 157.60/157.48 & ( V_ys != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__appendR,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_ys] :
% 157.60/157.48 ( V_ys != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__appendL,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_ys] :
% 157.60/157.48 ( V_ys = c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__in__set,axiom,
% 157.60/157.48 ! [T_b,V_as_2] :
% 157.60/157.48 ( V_as_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__snoc,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__drop,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_n] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.48 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__butlast__last__id,axiom,
% 157.60/157.48 ! [T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_snoc__eq__iff__butlast,axiom,
% 157.60/157.48 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 157.60/157.48 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 157.60/157.48 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__conv__nth,axiom,
% 157.60/157.48 ! [T_a,V_xs] :
% 157.60/157.48 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.48 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists_Osimps,axiom,
% 157.60/157.48 ! [V_A_2,V_a_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 157.60/157.48 | ? [B_a,B_l] :
% 157.60/157.48 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.60/157.48 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select__weigth__select,axiom,
% 157.60/157.48 ! [T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__mapI,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.48 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_last__map,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__size__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Omap_Oidentity,axiom,
% 157.60/157.48 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Omap_Oid,axiom,
% 157.60/157.48 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Omap_Ocompositionality,axiom,
% 157.60/157.48 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__comp__map,axiom,
% 157.60/157.48 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_List_Omap_Ocomp,axiom,
% 157.60/157.48 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_drop__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_hd__map,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b,V_xs_2] :
% 157.60/157.48 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.48 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__append,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__butlast,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_take__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__ident,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__map__eq__map,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.48 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 157.60/157.48 <=> V_xs_2 = V_ys_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__injective,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 157.60/157.48 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.48 => V_xs_2 = V_ys_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__addf,axiom,
% 157.60/157.48 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__subtractf,axiom,
% 157.60/157.48 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__0,axiom,
% 157.60/157.48 ! [V_xs_2,T_c,T_b] :
% 157.60/157.48 ( class_Groups_Omonoid__add(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__const__mult,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 157.60/157.48 ( class_Rings_Osemiring__0(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__mult__const,axiom,
% 157.60/157.48 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( class_Rings_Osemiring__0(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__eq__imp__length__eq,axiom,
% 157.60/157.48 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__eq__conv,axiom,
% 157.60/157.48 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 157.60/157.48 <=> ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 157.60/157.48 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__update,axiom,
% 157.60/157.48 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__is__Nil__conv,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nil__is__map__conv,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__same__conv__map,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__map__map,axiom,
% 157.60/157.48 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__map1,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__zip__map,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__zip__map2,axiom,
% 157.60/157.48 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__map2,axiom,
% 157.60/157.48 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_rotate__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__tl,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_foldl__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__inj__on,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.48 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 157.60/157.48 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 157.60/157.48 => V_xs_2 = V_ys_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__on__map__eq__map,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 157.60/157.48 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 157.60/157.48 <=> V_xs_2 = V_ys_2 ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nth__map,axiom,
% 157.60/157.48 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__fun__upd,axiom,
% 157.60/157.48 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 157.60/157.48 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__abs,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_uminus__listsum__map,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( class_Groups_Oab__group__add(T_b)
% 157.60/157.48 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__on__mapI,axiom,
% 157.60/157.48 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 157.60/157.48 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__mapD,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 157.60/157.48 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_inj__map,axiom,
% 157.60/157.48 ! [V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 157.60/157.48 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 157.60/157.48 ! [V_f_2,V_xs_2,T_b,T_c] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__triv,axiom,
% 157.60/157.48 ! [V_xs_2,V_r_2,T_c,T_b] :
% 157.60/157.48 ( class_Rings_Osemiring__1(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__map__remove1,axiom,
% 157.60/157.48 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 157.60/157.48 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.48 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 157.60/157.48 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.48 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_pick__same,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_l_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_one__code__numeral__def,axiom,
% 157.60/157.48 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zero__code__numeral__def,axiom,
% 157.60/157.48 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_times__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 157.60/157.48 ! [V_m_2,V_n_2] :
% 157.60/157.48 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 157.60/157.48 <=> V_n_2 = V_m_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 157.60/157.48 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_less__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 157.60/157.48 ! [V_y_2,V_x_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.48 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 157.60/157.48 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__fst__zip,axiom,
% 157.60/157.48 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__snd__zip,axiom,
% 157.60/157.48 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_number__of__code__numeral__def,axiom,
% 157.60/157.48 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__map__fst__snd,axiom,
% 157.60/157.48 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 157.60/157.48
% 157.60/157.48 fof(fact_plus__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_less__eq__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_pick__member,axiom,
% 157.60/157.48 ! [V_xs_2,T_b,V_i_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_zip__eq__conv,axiom,
% 157.60/157.48 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 157.60/157.48 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 157.60/157.48 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__size__conv__listsum,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_code__numeral__not__eq__zero,axiom,
% 157.60/157.48 ! [V_i_2] :
% 157.60/157.48 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 157.60/157.48 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.48 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 157.60/157.48 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 157.60/157.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select__weight__member,axiom,
% 157.60/157.48 ! [V_s_2,V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select__weight__def,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_select__def,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_subtract__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_times__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of__inverse,axiom,
% 157.60/157.48 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 157.60/157.48
% 157.60/157.48 fof(fact_of__nat__nat__of,axiom,
% 157.60/157.48 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of__of__nat,axiom,
% 157.60/157.48 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 157.60/157.48 ! [V_l_2,V_k_2] :
% 157.60/157.48 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 157.60/157.48 <=> V_k_2 = V_l_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_code__numeral_Onat__of__inject,axiom,
% 157.60/157.48 ! [V_y_2,V_x_2] :
% 157.60/157.48 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 157.60/157.48 <=> V_x_2 = V_y_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_type__definition__code__numeral,axiom,
% 157.60/157.48 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_less__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of,axiom,
% 157.60/157.48 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of__number,axiom,
% 157.60/157.48 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_int__of__def,axiom,
% 157.60/157.48 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_less__eq__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m_2,V_n_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of__code,axiom,
% 157.60/157.48 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_nat__of__aux__def,axiom,
% 157.60/157.48 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_Suc__code__numeral__def,axiom,
% 157.60/157.48 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_minus__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_of__nat__inverse,axiom,
% 157.60/157.48 ! [V_y_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.48 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_plus__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_div__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_subtract__code__numeral__def,axiom,
% 157.60/157.48 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_minus__code__numeral__code,axiom,
% 157.60/157.48 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_mod__code__numeral__def,axiom,
% 157.60/157.48 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_code__numeral__decr,axiom,
% 157.60/157.48 ! [V_k] :
% 157.60/157.48 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsum__mono,axiom,
% 157.60/157.48 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.60/157.48 ( ( class_Groups_Omonoid__add(T_c)
% 157.60/157.48 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 157.60/157.48 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_partition__set,axiom,
% 157.60/157.48 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 157.60/157.48 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 157.60/157.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__IntI,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 157.60/157.48 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp_ONil,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_append__in__listsp__conv,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 157.60/157.48 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp_Oequations_I2_J,axiom,
% 157.60/157.48 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 157.60/157.48 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 157.60/157.48 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp__infI,axiom,
% 157.60/157.48 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 157.60/157.48 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp__inf__eq,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp__conj__eq,axiom,
% 157.60/157.48 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
% 157.60/157.48 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 157.60/157.48 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_in__listsp__conv__set,axiom,
% 157.60/157.48 ! [V_xs_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 157.60/157.48 <=> ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp_Oequations_I1_J,axiom,
% 157.60/157.48 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp__mono,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_partition__P,axiom,
% 157.60/157.48 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 157.60/157.48 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 157.60/157.48 => ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 157.60/157.48 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.48 & ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 157.60/157.48 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_partition_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_listsp__lists__eq,axiom,
% 157.60/157.48 ! [V_x_2,V_A_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 157.60/157.48 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_partition_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_lists__Int__eq,axiom,
% 157.60/157.48 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_product_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__def,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 & ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__map1,axiom,
% 157.60/157.48 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 157.60/157.48 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__map2,axiom,
% 157.60/157.48 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 157.60/157.48 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__Nil,axiom,
% 157.60/157.48 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 157.60/157.48 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__Nil2,axiom,
% 157.60/157.48 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 157.60/157.48 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__lengthD,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__eq,axiom,
% 157.60/157.48 ! [T_b,V_ys_2,V_xs_2] :
% 157.60/157.48 ( V_xs_2 = V_ys_2
% 157.60/157.48 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__takeI,axiom,
% 157.60/157.48 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__Cons,axiom,
% 157.60/157.48 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 157.60/157.48 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.60/157.48 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__append,axiom,
% 157.60/157.48 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 157.60/157.48 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__appendI,axiom,
% 157.60/157.48 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 157.60/157.48 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__dropI,axiom,
% 157.60/157.48 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_product_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__conv__all__nth,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 157.60/157.48 & ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__nthD,axiom,
% 157.60/157.48 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__nthD2,axiom,
% 157.60/157.48 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 157.60/157.48 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__update__cong,axiom,
% 157.60/157.48 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2__update__cong2,axiom,
% 157.60/157.48 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.48 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__product,axiom,
% 157.60/157.48 ! [V_ys,T_b,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_product__list__set,axiom,
% 157.60/157.48 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublists__powset,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__sublists,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublists_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_sublists_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__set__sublists,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__n__lists,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_enum__the__def,axiom,
% 157.60/157.48 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__n__lists,axiom,
% 157.60/157.48 ! [V_n,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_n__lists__Nil,axiom,
% 157.60/157.48 ! [T_a,V_n] :
% 157.60/157.48 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) )
% 157.60/157.48 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.48 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_n__lists_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__n__lists,axiom,
% 157.60/157.48 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__n__lists__elem,axiom,
% 157.60/157.48 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
% 157.60/157.48 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_list__all2I,axiom,
% 157.60/157.48 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.48 ( ! [B_x] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
% 157.60/157.48 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 157.60/157.48 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 157.60/157.48 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_all__nth__imp__all__set,axiom,
% 157.60/157.48 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 157.60/157.48 ( ! [B_i] :
% 157.60/157.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 157.60/157.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 157.60/157.48 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.60/157.48 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_map__removeAll__inj__on,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.60/157.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__remdups,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__remdups__leq,axiom,
% 157.60/157.48 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__remdups__id,axiom,
% 157.60/157.48 ! [V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__removeAll,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups__id__iff__distinct,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 157.60/157.48 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_length__remdups__eq,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] :
% 157.60/157.48 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 157.60/157.48 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_set__remdups,axiom,
% 157.60/157.48 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups__remdups,axiom,
% 157.60/157.48 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_removeAll__append,axiom,
% 157.60/157.48 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_removeAll_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs,T_a,V_y,V_x] :
% 157.60/157.48 ( ( V_x = V_y
% 157.60/157.48 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) )
% 157.60/157.48 & ( V_x != V_y
% 157.60/157.48 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups__eq__nil__iff,axiom,
% 157.60/157.48 ! [V_x_2,T_b] :
% 157.60/157.48 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 157.60/157.48 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_removeAll_Osimps_I1_J,axiom,
% 157.60/157.48 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups__eq__nil__right__iff,axiom,
% 157.60/157.48 ! [V_x_2,T_b] :
% 157.60/157.48 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 157.60/157.48 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups_Osimps_I1_J,axiom,
% 157.60/157.48 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups__map__remdups,axiom,
% 157.60/157.48 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remove1__remdups,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_removeAll__id,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_distinct__remove1__removeAll,axiom,
% 157.60/157.48 ! [V_x,V_xs,T_a] :
% 157.60/157.48 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.48 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 157.60/157.48
% 157.60/157.48 fof(fact_remdups_Osimps_I2_J,axiom,
% 157.60/157.48 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.48 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.48 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__remdups__card__conv,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__removeAll__inj,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__removeAll,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__remdups__concat,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__conv__foldl,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldl__conv__concat,axiom,
% 157.60/157.49 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sort__key__simps_I1_J,axiom,
% 157.60/157.49 ! [V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__sort,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__sort,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__sort,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 157.60/157.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat_Osimps_I1_J,axiom,
% 157.60/157.49 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__eq__Nil__conv,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] :
% 157.60/157.49 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 157.60/157.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Nil__eq__concat__conv,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] :
% 157.60/157.49 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 157.60/157.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__concat,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__concat,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__concat,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sort__key__simps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__append,axiom,
% 157.60/157.49 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sort__foldl__insort,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__eq__concat__iff,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 157.60/157.49 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 157.60/157.49 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 157.60/157.49 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__injective,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 157.60/157.49 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 157.60/157.49 => V_xs_2 = V_ys_2 ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__map__singleton,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_n__lists_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Osimps_I3_J,axiom,
% 157.60/157.49 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__aux__filter__head,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__concat,axiom,
% 157.60/157.49 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__sort,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__filter,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sum__length__filter__compl,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__filter__le,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__id__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__is__subset,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_partition__filter1,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__remove1,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_remove1__filter__not,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Qa_2)),V_Pa_2)),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__insort__triv,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__append,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Osimps_I1_J,axiom,
% 157.60/157.49 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__empty__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_remdups__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_removeAll__filter__not,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_removeAll__filter__not__eq,axiom,
% 157.60/157.49 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_partition__filter2,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__transpose,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_i_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__map__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__filter__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__filter__less,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_partition__filter__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__minus__filter__out,axiom,
% 157.60/157.49 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__in__sublist,axiom,
% 157.60/157.49 ! [V_s_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__empty,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__filter__conv__card,axiom,
% 157.60/157.49 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__aux__filter__tail,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Opsimps_I3_J,axiom,
% 157.60/157.49 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 157.60/157.49 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Opsimps_I2_J,axiom,
% 157.60/157.49 ! [V_xss_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 157.60/157.49 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sublist__shift__lemma__Suc,axiom,
% 157.60/157.49 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pick__drop__zero,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_select__weigth__drop__zero,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose_Opsimps_I1_J,axiom,
% 157.60/157.49 ! [T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 157.60/157.49 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__max__length,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__aux__max,axiom,
% 157.60/157.49 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr__append,axiom,
% 157.60/157.49 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr__conv__foldl,axiom,
% 157.60/157.49 ! [V_a_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Groups_Oab__semigroup__add(T_b)
% 157.60/157.49 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr__map,axiom,
% 157.60/157.49 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldl__foldr1__lemma,axiom,
% 157.60/157.49 ! [V_xs_2,V_a_2,T_b] :
% 157.60/157.49 ( class_Groups_Omonoid__add(T_b)
% 157.60/157.49 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldl__foldr1,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( class_Groups_Omonoid__add(T_b)
% 157.60/157.49 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__transpose,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sublist__def,axiom,
% 157.60/157.49 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sublist__shift__lemma,axiom,
% 157.60/157.49 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__upt,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_atLeastLessThan__upt,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__0,axiom,
% 157.60/157.49 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__eq__Nil__conv,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2] :
% 157.60/157.49 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 157.60/157.49 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__conv__Nil,axiom,
% 157.60/157.49 ! [V_i,V_j] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 157.60/157.49 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__conv__Cons,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__rec,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__add__eq__append,axiom,
% 157.60/157.49 ! [V_k,V_j,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__Suc,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__Suc__append,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_drop__upt,axiom,
% 157.60/157.49 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_hd__upt,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__list__of__set__range,axiom,
% 157.60/157.49 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_take__upt,axiom,
% 157.60/157.49 ! [V_n,V_m,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 157.60/157.49 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__upt,axiom,
% 157.60/157.49 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__upt,axiom,
% 157.60/157.49 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__rec__number__of,axiom,
% 157.60/157.49 ! [V_n,V_m] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 157.60/157.49 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 157.60/157.49 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_upt__eq__Cons__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 157.60/157.49 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 157.60/157.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 157.60/157.49 & V_i_2 = V_x_2
% 157.60/157.49 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_last__upt,axiom,
% 157.60/157.49 ! [V_j,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__Suc__upt,axiom,
% 157.60/157.49 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_atLeastAtMost__upt,axiom,
% 157.60/157.49 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_atLeast__upt,axiom,
% 157.60/157.49 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__upt,axiom,
% 157.60/157.49 ! [V_j,V_k,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_greaterThanAtMost__upt,axiom,
% 157.60/157.49 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_greaterThanLessThan__upt,axiom,
% 157.60/157.49 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_atMost__upto,axiom,
% 157.60/157.49 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__nth,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 157.60/157.49 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.60/157.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.49 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 157.60/157.49 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.60/157.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.60/157.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__map__upt,axiom,
% 157.60/157.49 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__rectangle,axiom,
% 157.60/157.49 ! [V_n_2,T_b,V_xs_2] :
% 157.60/157.49 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.60/157.49 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.49 => ( ! [B_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 157.60/157.49 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_insort__key__remove1,axiom,
% 157.60/157.49 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 157.60/157.49 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 157.60/157.49 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted_ONil,axiom,
% 157.60/157.49 ! [T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__single,axiom,
% 157.60/157.49 ! [V_x,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__upt,axiom,
% 157.60/157.49 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__sort,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__insort__insert,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__tl,axiom,
% 157.60/157.49 ! [V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__remove1,axiom,
% 157.60/157.49 ! [V_a,V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__take,axiom,
% 157.60/157.49 ! [V_n,V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__upto,axiom,
% 157.60/157.49 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__drop,axiom,
% 157.60/157.49 ! [V_n,V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__insort,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 157.60/157.49 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__many__eq,axiom,
% 157.60/157.49 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 157.60/157.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__many,axiom,
% 157.60/157.49 ! [V_zs,V_y,V_x,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted_Oequations_I1_J,axiom,
% 157.60/157.49 ! [T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__butlast,axiom,
% 157.60/157.49 ! [V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__remdups,axiom,
% 157.60/157.49 ! [V_l,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__distinct__set__unique,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 157.60/157.49 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 157.60/157.49 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__sort__key,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__insort__insert__key,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__map__remove1,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__insort__key,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 157.60/157.49 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__filter,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__map__same,axiom,
% 157.60/157.49 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__same,axiom,
% 157.60/157.49 ! [V_xs_2,V_g_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__Cons,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.60/157.49 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 & ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__append,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.60/157.49 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 157.60/157.49 & ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ! [B_xa] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__insort,axiom,
% 157.60/157.49 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.60/157.49 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted_Oequations_I2_J,axiom,
% 157.60/157.49 ! [V_a1_2,V_a2_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 157.60/157.49 <=> ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__list__of__set,axiom,
% 157.60/157.49 ! [V_A_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.49 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 157.60/157.49 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_insort__remove1,axiom,
% 157.60/157.49 ! [V_xs_2,V_a_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__nth__mono,axiom,
% 157.60/157.49 ! [V_j,V_i,V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__equals__nth__mono,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 <=> ! [B_j] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ! [B_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__sorted__distinct__set__unique,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 157.60/157.49 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 157.60/157.49 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__column,axiom,
% 157.60/157.49 ! [V_i_2,V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__nth__transpose__sorted,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_inj__on__rev,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__rev,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 157.60/157.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__append,axiom,
% 157.60/157.49 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_singleton__rev__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 157.60/157.49 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__singleton__conv,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 157.60/157.49 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__is__Nil__conv,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Nil__is__rev__conv,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 157.60/157.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev_Osimps_I1_J,axiom,
% 157.60/157.49 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__concat,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_zip__rev,axiom,
% 157.60/157.49 ! [V_ys,T_b,V_xs,T_a] :
% 157.60/157.49 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
% 157.60/157.49 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__rev,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all2__rev,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.49 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 157.60/157.49 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all2__rev1,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.60/157.49 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 157.60/157.49 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__rev__ident,axiom,
% 157.60/157.49 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__swap,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 157.60/157.49 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__is__rev__conv,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 157.60/157.49 <=> V_xs_2 = V_ys_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_listsum__rev,axiom,
% 157.60/157.49 ! [V_xs,T_a] :
% 157.60/157.49 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.60/157.49 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__rev,axiom,
% 157.60/157.49 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr__foldl,axiom,
% 157.60/157.49 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldl__foldr,axiom,
% 157.60/157.49 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__eq__Cons__iff,axiom,
% 157.60/157.49 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 157.60/157.49 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_hd__rev,axiom,
% 157.60/157.49 ! [T_a,V_xs] :
% 157.60/157.49 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.49 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_last__rev,axiom,
% 157.60/157.49 ! [T_a,V_xs] :
% 157.60/157.49 ( V_xs != c_List_Olist_ONil(T_a)
% 157.60/157.49 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__transpose,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__foldl__cons,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__take,axiom,
% 157.60/157.49 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__drop,axiom,
% 157.60/157.49 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rotate__rev,axiom,
% 157.60/157.49 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__nth,axiom,
% 157.60/157.49 ! [V_xs,T_a,V_n] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__update,axiom,
% 157.60/157.49 ! [V_y,V_xs,T_a,V_k] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.49 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__rev__nth__mono,axiom,
% 157.60/157.49 ! [V_j,V_i,V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldr__max__sorted,axiom,
% 157.60/157.49 ! [V_y_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.60/157.49 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.60/157.49 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 157.60/157.49 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.49 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__transpose__sorted,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.60/157.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.60/157.49 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.60/157.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__column__length,axiom,
% 157.60/157.49 ! [V_i_2,V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpose__transpose,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 157.60/157.49 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 157.60/157.49 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__takeWhile,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__takeWhile__le,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__takeWhileD,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__eq__all__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_zip__takeWhile__fst,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_zip__takeWhile__snd,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__tail,axiom,
% 157.60/157.49 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__eq__take,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__takeWhile,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_return__list__def,axiom,
% 157.60/157.49 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__append1,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__nth,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__length__takeWhile,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__not__last,axiom,
% 157.60/157.49 ! [T_b,V_xs_2] :
% 157.60/157.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 157.60/157.49 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 157.60/157.49 ! [V_l] :
% 157.60/157.49 ( c_List_Onat__list(V_l)
% 157.60/157.49 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 157.60/157.49 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_embed__list__def,axiom,
% 157.60/157.49 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__neq__rev,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__neq__rev,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__dropWhile__id,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__dropWhile,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__dropWhile__le,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__dropWhile,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_hd__dropWhile,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__map,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__append1,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 157.60/157.49 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 157.60/157.49 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 157.60/157.49 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__eq__drop,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__nth,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_listsum__map__filter,axiom,
% 157.60/157.49 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 157.60/157.49 ( class_Groups_Omonoid__add(T_c)
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.49 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 157.60/157.49 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted__nth__monoI,axiom,
% 157.60/157.49 ! [V_xs,T_a] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_a)
% 157.60/157.49 => ( ! [B_i,B_j] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__eq__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 157.60/157.49 ( ! [B_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 157.60/157.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__takeWhile__less__P__nth,axiom,
% 157.60/157.49 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 157.60/157.49 ( ! [B_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted_Osimps,axiom,
% 157.60/157.49 ! [V_a_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 157.60/157.49 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 157.60/157.49 | ? [B_xs,B_x] :
% 157.60/157.49 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 157.60/157.49 & ! [B_xa] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_List_Oinsert__def,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_not__in__set__insert,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_insert__remdups,axiom,
% 157.60/157.49 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__insert,axiom,
% 157.60/157.49 ! [V_x,V_xs,T_a] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__insert,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_List_Oset__insert,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_insert__Nil,axiom,
% 157.60/157.49 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_maps__def,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__map__maps,axiom,
% 157.60/157.49 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_maps__simps_I2_J,axiom,
% 157.60/157.49 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_maps__simps_I1_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_distinct__concat,axiom,
% 157.60/157.49 ! [V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 157.60/157.49 => ( ! [B_ys] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 157.60/157.49 => ( ! [B_ys] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ! [B_zs] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ( B_ys != B_zs
% 157.60/157.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 157.60/157.49 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measures__lesseq,axiom,
% 157.60/157.49 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_wf__measures,axiom,
% 157.60/157.49 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__measures_I1_J,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measures__def,axiom,
% 157.60/157.49 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measures__less,axiom,
% 157.60/157.49 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__measures_I2_J,axiom,
% 157.60/157.49 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 157.60/157.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 157.60/157.49 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.60/157.49 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_foldl__apply,axiom,
% 157.60/157.49 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
% 157.60/157.49 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_order__fun_I2_J,axiom,
% 157.60/157.49 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( ( class_Orderings_Oorder(T_c)
% 157.60/157.49 & class_Enum_Oenum(T_b) )
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.60/157.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.60/157.49 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_enum__ex__prod__def,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b,T_c] :
% 157.60/157.49 ( ( class_Enum_Oenum(T_c)
% 157.60/157.49 & class_Enum_Oenum(T_b) )
% 157.60/157.49 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 157.60/157.49 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_enum__ex,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ( class_Enum_Oenum(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 157.60/157.49 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_exists__code,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ( class_Enum_Oenum(T_b)
% 157.60/157.49 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.49 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_zip__obtain__same__length,axiom,
% 157.60/157.49 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.60/157.49 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__not__random__dseq__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_dropWhile__append2,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all2__all__nthI,axiom,
% 157.60/157.49 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 157.60/157.49 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 157.60/157.49 => ( ! [B_n] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 157.60/157.49 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_finite__sorted__distinct__unique,axiom,
% 157.60/157.49 ! [V_A_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.49 => ? [B_x] :
% 157.60/157.49 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 157.60/157.49 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 157.60/157.49 & ! [B_y] :
% 157.60/157.49 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 157.60/157.49 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 157.60/157.49 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 157.60/157.49 => B_y = B_x ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_takeWhile__append2,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_insort__is__Cons,axiom,
% 157.60/157.49 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_c)
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 157.60/157.49 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Cons__eq__filter__iff,axiom,
% 157.60/157.49 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)
% 157.60/157.49 <=> ? [B_us,B_vs] :
% 157.60/157.49 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 157.60/157.49 & ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__eq__Cons__iff,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 157.60/157.49 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 157.60/157.49 <=> ? [B_us,B_vs] :
% 157.60/157.49 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 157.60/157.49 & ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 157.60/157.49 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_order__fun_I1_J,axiom,
% 157.60/157.49 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.60/157.49 ( ( class_Orderings_Oorder(T_c)
% 157.60/157.49 & class_Enum_Oenum(T_b) )
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.60/157.49 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_all__code,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ( class_Enum_Oenum(T_b)
% 157.60/157.49 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.60/157.49 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_enum__all,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ( class_Enum_Oenum(T_b)
% 157.60/157.49 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 157.60/157.49 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_enum__all__prod__def,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b,T_c] :
% 157.60/157.49 ( ( class_Enum_Oenum(T_c)
% 157.60/157.49 & class_Enum_Oenum(T_b) )
% 157.60/157.49 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 157.60/157.49 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ball__nth,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sorted_OCons,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( class_Orderings_Olinorder(T_b)
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 157.60/157.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.60/157.49 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__length,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ? [B_n] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__conv__decomp,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__simps_I2_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__append,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.60/157.49 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__iff,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__rev,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.60/157.49 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__simps_I1_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.60/157.49 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__conv__decomp__first,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 <=> ? [B_ys] :
% 157.60/157.49 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 157.60/157.49 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__conv__decomp__last,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 <=> ? [B_ys,B_zs] :
% 157.60/157.49 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 157.60/157.49 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__length,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ! [B_n] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_finite__induct,axiom,
% 157.60/157.49 ! [V_Pa_2,V_F_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.60/157.49 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.49 => ( ! [B_x,B_F] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 157.60/157.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 157.60/157.49 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__simps_I2_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__append,axiom,
% 157.60/157.49 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.60/157.49 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__iff,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__rev,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.60/157.49 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__simps_I1_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.60/157.49 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Ball__set__list__all,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__iff__raw,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex1__simps_I2_J,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.60/157.49 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measure__function__int,axiom,
% 157.60/157.49 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measure__fst,axiom,
% 157.60/157.49 ! [T_c,V_f_2,T_b] :
% 157.60/157.49 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 157.60/157.49 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measure__snd,axiom,
% 157.60/157.49 ! [T_c,V_f_2,T_b] :
% 157.60/157.49 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 157.60/157.49 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_is__measure_Ointros,axiom,
% 157.60/157.49 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_is__measure_Oequations,axiom,
% 157.60/157.49 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_is__measure_Osimps,axiom,
% 157.60/157.49 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_measure__size,axiom,
% 157.60/157.49 ! [T_b] :
% 157.60/157.49 ( class_Nat_Osize(T_b)
% 157.60/157.49 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex1__simps_I1_J,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex1__iff,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.49 & ! [B_y] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 157.60/157.49 => B_y = B_x ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transfer__morphism__int__nat,axiom,
% 157.60/157.49 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 157.60/157.49 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 157.60/157.49 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.49 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) )
% 157.60/157.49 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.49 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bool_Osize_I3_J,axiom,
% 157.60/157.49 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bool_Osize_I4_J,axiom,
% 157.60/157.49 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 157.60/157.49 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__empty__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 157.60/157.49 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__bind__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 157.60/157.49 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 157.60/157.49 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.49 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) )
% 157.60/157.49 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.60/157.49 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 157.60/157.49 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_neg__bind__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__map__def,axiom,
% 157.60/157.49 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__single__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_neg__map__def,axiom,
% 157.60/157.49 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Opos__single__def,axiom,
% 157.60/157.49 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_neg__single__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 157.60/157.49 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_,axiom,
% 157.60/157.49 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy__list_Osimps,axiom,
% 157.60/157.49 ! [V_d_2,T_b] :
% 157.60/157.49 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__splice,axiom,
% 157.60/157.49 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy__prod__def,axiom,
% 157.60/157.49 ! [V_d,T_b,T_a] :
% 157.60/157.49 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 157.60/157.49 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_splice_Osimps_I3_J,axiom,
% 157.60/157.49 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_splice_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 157.60/157.49
% 157.60/157.49 fof(fact_splice__Nil2,axiom,
% 157.60/157.49 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 157.60/157.49
% 157.60/157.49 fof(fact_splice_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_New__DSequence_Opos__union__def,axiom,
% 157.60/157.49 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_acyclicP__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
% 157.60/157.49 <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_converse__pred__comp,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep__noteq,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 157.60/157.49 <=> V_x_2 != V_y_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversepD,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep_Ointros,axiom,
% 157.60/157.49 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep_Oequations,axiom,
% 157.60/157.49 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep__iff,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep__conversep,axiom,
% 157.60/157.49 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep__eq,axiom,
% 157.60/157.49 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 157.60/157.49
% 157.60/157.49 fof(fact_converse__join,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_converse__meet,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_conversep__converse__eq,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pos__union__def,axiom,
% 157.60/157.49 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy_H_Osimps,axiom,
% 157.60/157.49 ! [V_i,V_d] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy__int__def,axiom,
% 157.60/157.49 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy_H_Opsimps,axiom,
% 157.60/157.49 ! [V_i_2,V_d_2] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
% 157.60/157.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 157.60/157.49 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_tl__replicate,axiom,
% 157.60/157.49 ! [V_x,T_a,V_n] :
% 157.60/157.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__replicate__const,axiom,
% 157.60/157.49 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_length__replicate,axiom,
% 157.60/157.49 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__length__filter,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__replicate,axiom,
% 157.60/157.49 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__empty,axiom,
% 157.60/157.49 ! [V_x_2,V_n_2,T_b] :
% 157.60/157.49 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 157.60/157.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_empty__replicate,axiom,
% 157.60/157.49 ! [V_x_2,V_n_2,T_b] :
% 157.60/157.49 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 157.60/157.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__0,axiom,
% 157.60/157.49 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_concat__replicate__trivial,axiom,
% 157.60/157.49 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_filter__replicate,axiom,
% 157.60/157.49 ! [V_n_2,T_b,V_x_2,V_Pa_2] :
% 157.60/157.49 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.60/157.49 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__add,axiom,
% 157.60/157.49 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_append__replicate__commute,axiom,
% 157.60/157.49 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nth__replicate,axiom,
% 157.60/157.49 ! [V_x,T_a,V_n,V_i] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 157.60/157.49 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__eq__replicate,axiom,
% 157.60/157.49 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 157.60/157.49 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 157.60/157.49 <=> ( V_m_2 = V_n_2
% 157.60/157.49 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => V_x_2 = V_y_2 ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Ball__set__replicate,axiom,
% 157.60/157.49 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.60/157.49 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Bex__set__replicate,axiom,
% 157.60/157.49 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 157.60/157.49 ( ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.60/157.49 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_zip__replicate,axiom,
% 157.60/157.49 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_last__replicate,axiom,
% 157.60/157.49 ! [V_x,T_a,V_n] :
% 157.60/157.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_drop__replicate,axiom,
% 157.60/157.49 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_hd__replicate,axiom,
% 157.60/157.49 ! [V_x,T_a,V_n] :
% 157.60/157.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_take__replicate,axiom,
% 157.60/157.49 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rev__replicate,axiom,
% 157.60/157.49 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__Suc,axiom,
% 157.60/157.49 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__app__Cons__same,axiom,
% 157.60/157.49 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__replicate,axiom,
% 157.60/157.49 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
% 157.60/157.49 <=> ( V_x_2 = V_y_2
% 157.60/157.49 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_replicate__append__same,axiom,
% 157.60/157.49 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_map__replicate__trivial,axiom,
% 157.60/157.49 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__replicate,axiom,
% 157.60/157.49 ! [V_x_2,T_b,V_n_2] :
% 157.60/157.49 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__replicate__conv__if,axiom,
% 157.60/157.49 ! [V_x_2,T_b,V_n_2] :
% 157.60/157.49 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 157.60/157.49 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.49 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_set__replicate__Suc,axiom,
% 157.60/157.49 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_small__lazy_H_Opinduct,axiom,
% 157.60/157.49 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 157.60/157.49 => ( ! [B_d,B_i] :
% 157.60/157.49 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
% 157.60/157.49 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_eq__comp__r,axiom,
% 157.60/157.49 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_field__le__epsilon,axiom,
% 157.60/157.49 ! [V_y,V_x,T_a] :
% 157.60/157.49 ( class_Fields_Olinordered__field(T_a)
% 157.60/157.49 => ( ! [B_e] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact__01,axiom,
% 157.60/157.49 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Oinject,axiom,
% 157.60/157.49 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 157.60/157.49 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
% 157.60/157.49 <=> ( V_a_2 = V_a_H_2
% 157.60/157.49 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_size__code,axiom,
% 157.60/157.49 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence__size__code,axiom,
% 157.60/157.49 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_seq__case,axiom,
% 157.60/157.49 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_yieldn__def,axiom,
% 157.60/157.49 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_refl__on__INTER,axiom,
% 157.60/157.49 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.49 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 157.60/157.49 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__set__member,axiom,
% 157.60/157.49 ! [V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_member__rec_I1_J,axiom,
% 157.60/157.49 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
% 157.60/157.49 <=> ( V_x_2 = V_y_2
% 157.60/157.49 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_member__set,axiom,
% 157.60/157.49 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_member__rec_I2_J,axiom,
% 157.60/157.49 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_List_Omember__def,axiom,
% 157.60/157.49 ! [V_x_2,V_xs_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pair__box_Osize_I1_J,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex1__iff__raw,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.49 & ! [B_y] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 157.60/157.49 => B_y = B_x ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pair__box_Oinject,axiom,
% 157.60/157.49 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.60/157.49 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 157.60/157.49 <=> ( V_a_2 = V_a_H_2
% 157.60/157.49 & V_b_2 = V_b_H_2 ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pair__box_Osize_I2_J,axiom,
% 157.60/157.49 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pair__box_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_pair__box_Orecs,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_THE__default__def,axiom,
% 157.60/157.49 ! [V_d_2,T_b,V_Pa_2] :
% 157.60/157.49 ( ( ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.49 & ! [B_y] :
% 157.60/157.49 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.60/157.49 => B_y = B_x ) )
% 157.60/157.49 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) )
% 157.60/157.49 & ( ~ ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.60/157.49 & ! [B_y] :
% 157.60/157.49 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.60/157.49 => B_y = B_x ) )
% 157.60/157.49 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_setsum__UNION__zero,axiom,
% 157.60/157.49 ! [V_f_2,V_S_2,T_b,T_c] :
% 157.60/157.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 157.60/157.49 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 157.60/157.49 => ( ! [B_T1] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 157.60/157.49 => ! [B_T2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 157.60/157.49 => ( B_T1 != B_T2
% 157.60/157.49 => ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 157.60/157.49 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 157.60/157.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_SUP2__E,axiom,
% 157.60/157.49 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 157.60/157.49 => ~ ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.49 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_INF2__I,axiom,
% 157.60/157.49 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_finite__maxlen,axiom,
% 157.60/157.49 ! [V_M_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 157.60/157.49 => ? [B_n] :
% 157.60/157.49 ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 157.60/157.49 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact__02,axiom,
% 157.60/157.49 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 157.60/157.49 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 157.60/157.49 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__all__iff__all__interval__int,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.49 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 157.60/157.49 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.49 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 157.60/157.49 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_all__interval__int__def,axiom,
% 157.60/157.49 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.49 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 157.60/157.49 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Random_Osimps,axiom,
% 157.60/157.49 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 157.60/157.49 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 157.60/157.49 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 157.60/157.49 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Random__Sequence_Oempty__def,axiom,
% 157.60/157.49 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Random__Sequence_Osingle__def,axiom,
% 157.60/157.49 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Random__Sequence_Omap__def,axiom,
% 157.60/157.49 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_exE__realizer,axiom,
% 157.60/157.49 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 157.60/157.49 => ( ! [B_x,B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 157.60/157.49 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 157.60/157.49 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Image__Collect__split,axiom,
% 157.60/157.49 ! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lexord__trans,axiom,
% 157.60/157.49 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
% 157.60/157.49 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__less__than,axiom,
% 157.60/157.49 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__lex__prod,axiom,
% 157.60/157.49 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_R1_2)
% 157.60/157.49 => ( c_Relation_Otrans(T_c,V_R2_2)
% 157.60/157.49 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__def,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 <=> ! [B_x,B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 157.60/157.49 => ! [B_z] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transD,axiom,
% 157.60/157.49 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Union__eq,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__reflclI,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__Int,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Otrans(T_b,V_s_2)
% 157.60/157.49 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bex__UNIV,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ( ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_finite__Collect__bex,axiom,
% 157.60/157.49 ! [V_Qa_2,T_c,V_A_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Qa_2)))))
% 157.60/157.49 <=> ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.49 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_x)))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bex__empty,axiom,
% 157.60/157.49 ! [V_Pa_2,T_b] :
% 157.60/157.49 ~ ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_listrel__trans,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.49 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lexord__transI,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__finite__psubset,axiom,
% 157.60/157.49 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__Id,axiom,
% 157.60/157.49 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__Id__on,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trancl__id,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__trancl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__rtrancl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_SUPR__bool__eq,axiom,
% 157.60/157.49 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__O__subset,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__inv__image,axiom,
% 157.60/157.49 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Bex__set__list__ex,axiom,
% 157.60/157.49 ! [V_Pa_2,V_xs_2,T_b] :
% 157.60/157.49 ( ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_list__ex__iff__raw,axiom,
% 157.60/157.49 ! [V_xs_2,V_Pa_2,T_b] :
% 157.60/157.49 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.60/157.49 <=> ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_UN__eq,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_INT__eq,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Sup__fun__def,axiom,
% 157.60/157.49 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.49 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Sup__apply,axiom,
% 157.60/157.49 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.49 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Inf__fun__def,axiom,
% 157.60/157.49 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.49 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Inf__apply,axiom,
% 157.60/157.49 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.60/157.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.60/157.49 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_max__extp_Ointros,axiom,
% 157.60/157.49 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 157.60/157.49 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 157.60/157.49 => ? [B_xa] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 157.60/157.49 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 157.60/157.49 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transp__def,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Predicate_Otransp(T_b,V_r_2)
% 157.60/157.49 <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_transpE,axiom,
% 157.60/157.49 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Predicate_Otransp(T_b,V_r_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivpE,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.60/157.49 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivpI,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.60/157.49 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 => ( c_Predicate_Otransp(T_b,V_R_2)
% 157.60/157.49 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sympE,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Predicate_Osymp(T_b,V_r_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivp__reflp__symp__transp,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.60/157.49 & c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_max__extp_Osimps,axiom,
% 157.60/157.49 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 157.60/157.49 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 157.60/157.49 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.60/157.49 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.60/157.49 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.49 & ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.60/157.49 => ? [B_xa] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.60/157.49 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_trans__diff__Id,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Oantisym(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__subset,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 157.60/157.49 => ( c_Relation_Oantisym(T_b,V_s_2)
% 157.60/157.49 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__Id,axiom,
% 157.60/157.49 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__Id__on,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__empty,axiom,
% 157.60/157.49 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.49 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisymD,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Oantisym(T_b,V_r_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
% 157.60/157.49 => V_a_2 = V_b_2 ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__def,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Oantisym(T_b,V_r_2)
% 157.60/157.49 <=> ! [B_x,B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 157.60/157.49 => B_x = B_y ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_antisym__reflcl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 157.60/157.49 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_fun__lub__def,axiom,
% 157.60/157.49 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__trans__comp__subset,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__def,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 <=> ! [B_x,B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_symD,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Int__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Un__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Int,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Osym(T_b,V_s_2)
% 157.60/157.49 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_listrel__sym,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__conv__converse__eq,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__converse,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.60/157.49 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Id,axiom,
% 157.60/157.49 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Un,axiom,
% 157.60/157.49 ! [V_s_2,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Osym(T_b,V_s_2)
% 157.60/157.49 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__Id__on,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__trancl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__rtrancl,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_sym__inv__image,axiom,
% 157.60/157.49 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.60/157.49 ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equiv__def,axiom,
% 157.60/157.49 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.49 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.49 & c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivI,axiom,
% 157.60/157.49 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.49 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.49 => ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.60/157.49 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivE,axiom,
% 157.60/157.49 ! [V_r_2,V_A_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.60/157.49 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.60/157.49 => ( c_Relation_Osym(T_b,V_r_2)
% 157.60/157.49 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_symp__def,axiom,
% 157.60/157.49 ! [V_r_2,T_b] :
% 157.60/157.49 ( c_Predicate_Osymp(T_b,V_r_2)
% 157.60/157.49 <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivpI,axiom,
% 157.60/157.49 ! [T_b,V_R_2] :
% 157.60/157.49 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.60/157.49 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 => ( c_Predicate_Otransp(T_b,V_R_2)
% 157.60/157.49 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivp__refl__symp__transp,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.60/157.49 & c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_equivp__implies__part__equivp,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivp__transp,axiom,
% 157.60/157.49 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivp__symp,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivp__def,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.60/157.49 & ! [B_x,B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 157.60/157.49 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.60/157.49 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 157.60/157.49 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivpE,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.60/157.49 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.60/157.49 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_part__equivp__typedef,axiom,
% 157.60/157.49 ! [V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.60/157.49 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_fold__image__UN__disjoint,axiom,
% 157.60/157.49 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 157.60/157.49 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.60/157.49 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.60/157.49 => ! [B_xa] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 157.60/157.49 => ( B_x != B_xa
% 157.60/157.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
% 157.60/157.49 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nat__of__induct,axiom,
% 157.60/157.49 ! [V_Pa_2,V_y_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.49 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_nat__of__cases,axiom,
% 157.60/157.49 ! [V_y_2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.49 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_of__nat__induct,axiom,
% 157.60/157.49 ! [V_x_2,V_Pa_2] :
% 157.60/157.49 ( ! [B_y] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_of__nat__cases,axiom,
% 157.60/157.49 ! [V_x_2] :
% 157.60/157.49 ~ ! [B_y] :
% 157.60/157.49 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 157.60/157.49 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 157.60/157.49 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 157.60/157.49 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_beyond__def,axiom,
% 157.60/157.49 ! [V_l,V_k] :
% 157.60/157.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.60/157.49 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 157.60/157.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.60/157.49 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__image__Collect__eq,axiom,
% 157.60/157.49 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__id,axiom,
% 157.60/157.49 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__image__INT,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_o__inv__distrib,axiom,
% 157.60/157.49 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.49 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__comp__iff2,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
% 157.60/157.49 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 157.60/157.49 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__comp,axiom,
% 157.60/157.49 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__trans,axiom,
% 157.60/157.49 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__comp__iff,axiom,
% 157.60/157.49 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.60/157.49 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 157.60/157.49 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__is__inj,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__imp__inj__on,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_inj__on__imp__bij__betw,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__def,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.60/157.49 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__is__surj,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__imp__surj,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__subset,axiom,
% 157.60/157.49 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.49 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__id,axiom,
% 157.60/157.49 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__id__iff,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 157.60/157.49 <=> V_A_2 = V_B_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__finite,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.49 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_BIJ,axiom,
% 157.60/157.49 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.60/157.49 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 157.60/157.49 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__empty2,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__empty1,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 157.60/157.49 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__same__card,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_beyond__zero,axiom,
% 157.60/157.49 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__inv__into,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__the__inv__into,axiom,
% 157.60/157.49 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_inv__into__inv__into__eq,axiom,
% 157.60/157.49 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.60/157.49 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_inv__inv__eq,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__imp__bij__inv,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__Disj__Un,axiom,
% 157.60/157.49 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 157.60/157.49 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 157.60/157.49 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.60/157.49 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__betw__combine,axiom,
% 157.60/157.49 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.60/157.49 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 157.60/157.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__def,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.49 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bijI,axiom,
% 157.60/157.49 ! [V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.60/157.49 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 157.60/157.49 => c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__image__Compl__eq,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_finite__vimage__iff,axiom,
% 157.60/157.49 ! [V_F_2,V_h_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 157.60/157.49 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vimage__subset__eq,axiom,
% 157.60/157.49 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bij__vimage__eq__inv__image,axiom,
% 157.60/157.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.60/157.49 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 157.60/157.49 ! [V_M_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.60/157.49 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Cantor__Bernstein,axiom,
% 157.60/157.49 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 157.60/157.49 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 157.60/157.49 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_ex__bij__betw__nat__finite,axiom,
% 157.60/157.49 ! [V_M_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.60/157.49 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_ex__bij__betw__finite__nat,axiom,
% 157.60/157.49 ! [V_M_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.60/157.49 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curry__def,axiom,
% 157.60/157.49 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_refl__on__UNION,axiom,
% 157.60/157.49 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.60/157.49 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 157.60/157.49 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curryI,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 157.60/157.49 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curry__split,axiom,
% 157.60/157.49 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_split__curry,axiom,
% 157.60/157.49 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curry__conv,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curryD,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 157.60/157.49 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_curryE,axiom,
% 157.60/157.49 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 157.60/157.49 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bex__reg__eqv,axiom,
% 157.60/157.49 ! [V_Pa_2,V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 => ( ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_hoare__derivs_OLocal,axiom,
% 157.60/157.49 ! [V_a_2,V_s_H_2,V_X_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 157.60/157.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Qa_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),c_Natural_Ogetlocs(V_s_H_2,V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 157.60/157.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I2_J,axiom,
% 157.60/157.49 ! [V_loc_H_2,V_loc_2] :
% 157.60/157.49 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 157.60/157.49 <=> V_loc_2 = V_loc_H_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_in__respects,axiom,
% 157.60/157.49 ! [V_R_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Respects__def,axiom,
% 157.60/157.49 ! [V_x_2,V_R_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 157.60/157.49 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osize_I4_J,axiom,
% 157.60/157.49 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osize_I2_J,axiom,
% 157.60/157.49 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_bex__reg__right,axiom,
% 157.60/157.49 ! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(V_Qa_2,B_x))
% 157.60/157.49 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.60/157.49 => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1))
% 157.60/157.49 => ? [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 157.60/157.49 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osize_I3_J,axiom,
% 157.60/157.49 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osize_I1_J,axiom,
% 157.60/157.49 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I1_J,axiom,
% 157.60/157.49 ! [V_glb_H_2,V_glb_2] :
% 157.60/157.49 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 157.60/157.49 <=> V_glb_2 = V_glb_H_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I4_J,axiom,
% 157.60/157.49 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I3_J,axiom,
% 157.60/157.49 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Orecs_I1_J,axiom,
% 157.60/157.49 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I5_J,axiom,
% 157.60/157.49 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Osimps_I6_J,axiom,
% 157.60/157.49 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_vname_Orecs_I2_J,axiom,
% 157.60/157.49 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_babs__reg__eqv,axiom,
% 157.60/157.49 ! [V_Pa_2,T_c,V_R_2,T_b] :
% 157.60/157.49 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.60/157.49 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_wf__weak__decr__stable,axiom,
% 157.60/157.49 ! [V_r_2,V_f_2,T_b] :
% 157.60/157.49 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 157.60/157.49 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 157.60/157.49 => ? [B_i] :
% 157.60/157.49 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_Babs__def,axiom,
% 157.60/157.49 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 157.60/157.49 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_INT__greatest,axiom,
% 157.60/157.49 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 157.60/157.49 ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_INT__anti__mono,axiom,
% 157.60/157.49 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.60/157.49 => ( ! [B_x] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_converse__rtranclE2,axiom,
% 157.60/157.49 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 157.60/157.49 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
% 157.60/157.49 => ~ ! [B_a,B_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
% 157.60/157.49 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_converse__rtrancl__induct2,axiom,
% 157.60/157.49 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
% 157.60/157.49 => ( ! [B_a,B_b,B_aa,B_ba] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_rtrancl__induct2,axiom,
% 157.60/157.49 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
% 157.60/157.49 => ( ! [B_a,B_b] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 157.60/157.49 => ! [B_aa,B_ba] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 157.60/157.49 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
% 157.60/157.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_congruentI,axiom,
% 157.60/157.49 ! [T_c,V_f_2,V_r_2,T_b] :
% 157.60/157.49 ( ! [B_y,B_z] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 157.60/157.49 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 157.60/157.49 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 157.60/157.49
% 157.60/157.49 fof(fact_congruent2I_H,axiom,
% 157.60/157.49 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 157.60/157.49 ( ! [B_y1,B_z1] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
% 157.60/157.49 => ! [B_y2,B_z2] :
% 157.60/157.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
% 157.60/157.49 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 157.60/157.50 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact__03,axiom,
% 157.60/157.50 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ).
% 157.60/157.50
% 157.60/157.50 fof(fact__04,axiom,
% 157.60/157.50 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 157.60/157.50
% 157.60/157.50 fof(fact__05,axiom,
% 157.60/157.50 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_all__interval__nat__def,axiom,
% 157.60/157.50 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.50 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
% 157.60/157.50 <=> ! [B_x] :
% 157.60/157.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
% 157.60/157.50 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact__06,axiom,
% 157.60/157.50 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ).
% 157.60/157.50
% 157.60/157.50 fof(fact__07,axiom,
% 157.60/157.50 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_list__all__iff__all__interval__nat,axiom,
% 157.60/157.50 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.50 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 157.60/157.50 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 157.60/157.50 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.60/157.50 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 157.60/157.50 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_New__DSequence_Opos__map__def,axiom,
% 157.60/157.50 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_folding__image_Ocong,axiom,
% 157.60/157.50 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.60/157.50 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.60/157.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.60/157.50 => ( ! [B_x] :
% 157.60/157.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.60/157.50 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 157.60/157.50 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_power__dvd__imp__le,axiom,
% 157.60/157.50 ! [V_n,V_m,V_i] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 157.60/157.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 157.60/157.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_finite__nonempty__imp__fold1Set,axiom,
% 157.60/157.50 ! [V_f_2,V_A_2,T_b] :
% 157.60/157.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.60/157.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.60/157.50 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd_Oorder__refl,axiom,
% 157.60/157.50 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__0__right,axiom,
% 157.60/157.50 ! [V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__1__left,axiom,
% 157.60/157.50 ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__imp__le,axiom,
% 157.60/157.50 ! [V_n,V_k] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 157.60/157.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.60/157.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__div__eq__mult,axiom,
% 157.60/157.50 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_b)
% 157.60/157.50 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)
% 157.60/157.50 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2
% 157.60/157.50 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__div__div__eq__mult,axiom,
% 157.60/157.50 ! [V_d_2,V_b_2,V_ca_2,V_a_2,T_b] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_b)
% 157.60/157.50 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.50 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,V_ca_2,V_d_2)
% 157.60/157.50 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2)
% 157.60/157.50 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_inf__period_I3_J,axiom,
% 157.60/157.50 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 157.60/157.50 ( ( class_Rings_Ocomm__ring(T_b)
% 157.60/157.50 & class_Rings_Odvd(T_b) )
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)
% 157.60/157.50 => ! [B_x,B_k] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))
% 157.60/157.50 <=> c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_inf__period_I4_J,axiom,
% 157.60/157.50 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 157.60/157.50 ( ( class_Rings_Ocomm__ring(T_b)
% 157.60/157.50 & class_Rings_Odvd(T_b) )
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)
% 157.60/157.50 => ! [B_x,B_k] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))
% 157.60/157.50 <=> c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult__div__cancel,axiom,
% 157.60/157.50 ! [V_b,V_a,T_a] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 157.60/157.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_div__mult__swap,axiom,
% 157.60/157.50 ! [V_a,V_b,V_c,T_a] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)
% 157.60/157.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__div__mult__self,axiom,
% 157.60/157.50 ! [V_b,V_a,T_a] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 157.60/157.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__div__mult,axiom,
% 157.60/157.50 ! [V_c,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 157.60/157.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_div__mult__div__if__dvd,axiom,
% 157.60/157.50 ! [V_w,V_z,V_x,V_y,T_a] :
% 157.60/157.50 ( class_Divides_Osemiring__div(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)
% 157.60/157.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult__cancel__right,axiom,
% 157.60/157.50 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.60/157.50 ( class_Rings_Oidom(T_b)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))
% 157.60/157.50 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.50 | c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult__cancel__left,axiom,
% 157.60/157.50 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.60/157.50 ( class_Rings_Oidom(T_b)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))
% 157.60/157.50 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.60/157.50 | c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__triv__left,axiom,
% 157.60/157.50 ! [V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__triv__right,axiom,
% 157.60/157.50 ! [V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult2,axiom,
% 157.60/157.50 ! [V_c,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult,axiom,
% 157.60/157.50 ! [V_b,V_c,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_mult__dvd__mono,axiom,
% 157.60/157.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvdI,axiom,
% 157.60/157.50 ! [V_k,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Odvd(T_a)
% 157.60/157.50 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult__left,axiom,
% 157.60/157.50 ! [V_c,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__mult__right,axiom,
% 157.60/157.50 ! [V_c,V_b,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 157.60/157.50 ! [V_n_2,V_m_2,V_k_2] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 157.60/157.50 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.60/157.50 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_unity__coeff__ex,axiom,
% 157.60/157.50 ! [V_l_2,V_Pa_2,T_b] :
% 157.60/157.50 ( ( class_Rings_Odvd(T_b)
% 157.60/157.50 & class_Rings_Osemiring__0(T_b) )
% 157.60/157.50 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 157.60/157.50 <=> ? [B_x] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(T_b,V_l_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))
% 157.60/157.50 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__diffD,axiom,
% 157.60/157.50 ! [V_n,V_m,V_k] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 157.60/157.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_dvd__diffD1,axiom,
% 157.60/157.50 ! [V_n,V_m,V_k] :
% 157.60/157.50 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 157.60/157.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 fof(fact_power__le__dvd,axiom,
% 157.60/157.50 ! [V_m,V_b,V_n,V_a,T_a] :
% 157.60/157.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.60/157.50 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
% 157.60/157.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.60/157.50 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 %----Arity declarations (223)
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 157.60/157.50 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Obounded__lattice(T_1)
% 157.60/157.50 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 157.60/157.50 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Obounded__lattice(T_1)
% 157.60/157.50 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Obounded__lattice(T_1)
% 157.60/157.50 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Olattice(T_1)
% 157.60/157.50 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Olattice(T_1)
% 157.60/157.50 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Odistrib__lattice(T_1)
% 157.60/157.50 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Oboolean__algebra(T_1)
% 157.60/157.50 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Orderings_Opreorder,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Orderings_Opreorder(T_1)
% 157.60/157.50 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Finite__Set_Ofinite(T_2)
% 157.60/157.50 & class_Finite__Set_Ofinite(T_1) )
% 157.60/157.50 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Lattices_Olattice,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Lattices_Olattice(T_1)
% 157.60/157.50 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Orderings_Oorder,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Orderings_Oorder(T_1)
% 157.60/157.50 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Orderings_Otop,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Orderings_Otop(T_1)
% 157.60/157.50 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Orderings_Oord,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Orderings_Oord(T_1)
% 157.60/157.50 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Orderings_Obot,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Orderings_Obot(T_1)
% 157.60/157.50 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Groups_Ouminus,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Groups_Ouminus(T_1)
% 157.60/157.50 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Groups_Ominus,axiom,
% 157.60/157.50 ! [T_2,T_1] :
% 157.60/157.50 ( class_Groups_Ominus(T_1)
% 157.60/157.50 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_fun__Enum_Oenum,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Enum_Oenum(T_2)
% 157.60/157.50 & class_Enum_Oenum(T_1) )
% 157.60/157.50 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Com_Ocom) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 157.60/157.50 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 157.60/157.50 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 157.60/157.50 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 157.60/157.50 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 157.60/157.50 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 157.60/157.50 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 157.60/157.50 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 157.60/157.50 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 157.60/157.50 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 157.60/157.50 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 157.60/157.50 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 157.60/157.50 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 157.60/157.50 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 157.60/157.50 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 157.60/157.50 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 157.60/157.50 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 157.60/157.50 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 157.60/157.50 class_Orderings_Opreorder(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 157.60/157.50 class_Orderings_Olinorder(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 157.60/157.50 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 157.60/157.50 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 157.60/157.50 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 157.60/157.50 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 157.60/157.50 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 157.60/157.50 class_Lattices_Olattice(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 157.60/157.50 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 157.60/157.50 class_Divides_Oring__div(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 157.60/157.50 class_Rings_Omult__zero(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 157.60/157.50 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 157.60/157.50 class_Orderings_Oorder(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 157.60/157.50 class_Int_Oring__char__0(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 157.60/157.50 class_Int_Onumber__ring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 157.60/157.50 class_Rings_Osemiring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 157.60/157.50 class_Orderings_Oord(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 157.60/157.50 class_Groups_Ouminus(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 157.60/157.50 class_Groups_Osgn__if(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 157.60/157.50 class_Groups_Oabs__if(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 157.60/157.50 class_Rings_Oring__1(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 157.60/157.50 class_Groups_Ominus(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Power_Opower,axiom,
% 157.60/157.50 class_Power_Opower(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 157.60/157.50 class_Groups_Ozero(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oring,axiom,
% 157.60/157.50 class_Rings_Oring(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 157.60/157.50 class_Rings_Oidom(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Int_Onumber,axiom,
% 157.60/157.50 class_Int_Onumber(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Groups_Oone,axiom,
% 157.60/157.50 class_Groups_Oone(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 157.60/157.50 class_Rings_Odvd(tc_Int_Oint) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 157.60/157.50 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 157.60/157.50 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 157.60/157.50 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 157.60/157.50 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 157.60/157.50 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 157.60/157.50 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 157.60/157.50 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 157.60/157.50 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 157.60/157.50 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 157.60/157.50 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 157.60/157.50 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 157.60/157.50 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 157.60/157.50 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 157.60/157.50 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 157.60/157.50 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 157.60/157.50 class_Lattices_Olattice(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 157.60/157.50 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 157.60/157.50 class_Orderings_Oorder(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 157.60/157.50 class_Rings_Osemiring(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 157.60/157.50 class_Orderings_Oord(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 157.60/157.50 class_Orderings_Obot(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 157.60/157.50 class_Groups_Ominus(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Power_Opower,axiom,
% 157.60/157.50 class_Power_Opower(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 157.60/157.50 class_Groups_Ozero(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 157.60/157.50 class_Int_Onumber(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 157.60/157.50 class_Groups_Oone(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 157.60/157.50 class_Rings_Odvd(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Nat_Onat) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 157.60/157.50 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 157.60/157.50 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 157.60/157.50 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 157.60/157.50 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 157.60/157.50 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 157.60/157.50 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 157.60/157.50 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 157.60/157.50 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 157.60/157.50 class_Lattices_Olattice(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 157.60/157.50 class_Orderings_Oorder(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 157.60/157.50 class_Orderings_Otop(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 157.60/157.50 class_Orderings_Oord(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 157.60/157.50 class_Orderings_Obot(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 157.60/157.50 class_Groups_Ouminus(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 157.60/157.50 class_Groups_Ominus(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 157.60/157.50 class_Enum_Oenum(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_HOL_Obool) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Com_Ostate) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Com__Ovname__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Com_Ovname) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 157.60/157.50 ! [T_1] :
% 157.60/157.50 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 157.60/157.50 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_List__Olist__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Finite__Set_Ofinite(T_2)
% 157.60/157.50 & class_Finite__Set_Ofinite(T_1) )
% 157.60/157.50 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_sum__Enum_Oenum,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Enum_Oenum(T_2)
% 157.60/157.50 & class_Enum_Oenum(T_1) )
% 157.60/157.50 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_sum__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 157.60/157.50 ! [T_1] :
% 157.60/157.50 ( class_Finite__Set_Ofinite(T_1)
% 157.60/157.50 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 157.60/157.50 ! [T_1] :
% 157.60/157.50 ( class_Enum_Oenum(T_1)
% 157.60/157.50 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 157.60/157.50 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 157.60/157.50 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Finite__Set_Ofinite(T_2)
% 157.60/157.50 & class_Finite__Set_Ofinite(T_1) )
% 157.60/157.50 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_prod__Enum_Oenum,axiom,
% 157.60/157.50 ! [T_1,T_2] :
% 157.60/157.50 ( ( class_Enum_Oenum(T_2)
% 157.60/157.50 & class_Enum_Oenum(T_1) )
% 157.60/157.50 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_prod__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 157.60/157.50 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 157.60/157.50 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 157.60/157.50 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 157.60/157.50 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 157.60/157.50 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 157.60/157.50 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 157.60/157.50 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 157.60/157.50 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 157.60/157.50 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 157.60/157.50 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 157.60/157.50 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 157.60/157.50 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 157.60/157.50 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 157.60/157.50 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 157.60/157.50 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 157.60/157.50 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 157.60/157.50 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 157.60/157.50 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 157.60/157.50 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 157.60/157.50 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 157.60/157.50 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 157.60/157.50 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 157.60/157.50 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 157.60/157.50 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 157.60/157.50 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 157.60/157.50 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 157.60/157.50 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 157.60/157.50 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 157.60/157.50 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 157.60/157.50 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 157.60/157.50 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 157.60/157.50
% 157.60/157.50 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 157.60/157.50 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 157.60/157.50
% 157.60/157.50 %----Helper facts (20)
% 157.60/157.50 fof(help_c__COMBI__1,axiom,
% 157.60/157.50 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__COMBK__1,axiom,
% 157.60/157.50 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__COMBB__1,axiom,
% 157.60/157.50 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__COMBC__1,axiom,
% 157.60/157.50 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__COMBS__1,axiom,
% 157.60/157.50 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fequal__1,axiom,
% 157.60/157.50 ! [V_y_2,V_x_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 157.60/157.50 | V_x_2 = V_y_2 ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fequal__2,axiom,
% 157.60/157.50 ! [V_y_2,V_x_2] :
% 157.60/157.50 ( V_x_2 != V_y_2
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fFalse__1,axiom,
% 157.60/157.50 ~ hBOOL(c_fFalse) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fTrue__1,axiom,
% 157.60/157.50 hBOOL(c_fTrue) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fNot__1,axiom,
% 157.60/157.50 ! [V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 157.60/157.50 | ~ hBOOL(V_Pa_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fNot__2,axiom,
% 157.60/157.50 ! [V_Pa_2] :
% 157.60/157.50 ( ~ ~ hBOOL(V_Pa_2)
% 157.60/157.50 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fconj__1,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(V_Pa_2)
% 157.60/157.50 | ~ hBOOL(V_Qa_2)
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fconj__2,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 157.60/157.50 | hBOOL(V_Pa_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fconj__3,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 157.60/157.50 | hBOOL(V_Qa_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fdisj__1,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(V_Pa_2)
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fdisj__2,axiom,
% 157.60/157.50 ! [V_Pa_2,V_Qa_2] :
% 157.60/157.50 ( ~ hBOOL(V_Qa_2)
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fdisj__3,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 157.60/157.50 | hBOOL(V_Pa_2)
% 157.60/157.50 | hBOOL(V_Qa_2) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fimplies__1,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( hBOOL(V_Pa_2)
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fimplies__2,axiom,
% 157.60/157.50 ! [V_Pa_2,V_Qa_2] :
% 157.60/157.50 ( ~ hBOOL(V_Qa_2)
% 157.60/157.50 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 157.60/157.50
% 157.60/157.50 fof(help_c__fimplies__3,axiom,
% 157.60/157.50 ! [V_Qa_2,V_Pa_2] :
% 157.60/157.50 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 157.60/157.50 | ~ hBOOL(V_Pa_2)
% 157.60/157.50 | hBOOL(V_Qa_2) ) ).
% 157.60/157.50
% 157.60/157.50 %----Conjectures (2)
% 157.60/157.50 fof(conj_0,hypothesis,
% 157.60/157.50 ! [B_Z,B_s] :
% 157.60/157.50 ( v_P(B_Z,B_s)
% 157.60/157.50 => c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ).
% 157.60/157.50
% 157.60/157.50 fof(conj_1,conjecture,
% 157.60/157.50 ! [B_Z,B_s] :
% 157.60/157.50 ( v_P(B_Z,B_s)
% 157.60/157.50 => ? [B_P_H,B_Q_H] :
% 157.60/157.50 ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,B_P_H,v_c,B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
% 157.60/157.50 & ! [B_s_H] :
% 157.60/157.50 ( ! [B_Z_H] :
% 157.60/157.50 ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
% 157.60/157.50 => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
% 157.60/157.50 => hBOOL(hAPP(v_Q(B_Z),B_s_H)) ) ) ) ).
% 157.60/157.50
% 157.60/157.50 %------------------------------------------------------------------------------
% 157.60/157.50 %-------------------------------------------
% 157.60/157.50 % Proof found
% 157.60/157.50 % SZS status Theorem for theBenchmark
% 157.60/157.50 % SZS output start Proof
% 157.60/157.50 %ClaNum:10490(EqnAxiom:3146)
% 157.60/157.50 %VarNum:70988(SingletonVarNum:20581)
% 157.60/157.50 %MaxLitNum:8
% 157.60/157.50 %MaxfuncDepth:13
% 157.60/157.50 %SharedTerms:1008
% 157.60/157.50 %goalClause: 3359 9484 9507
% 157.60/157.50 %singleGoalClaCount:1
% 157.60/157.50 [3150]P1(a925)
% 157.60/157.50 [3151]P1(a930)
% 157.60/157.50 [3152]P107(a194)
% 157.60/157.50 [3153]P108(a925)
% 157.60/157.50 [3154]P108(a930)
% 157.60/157.50 [3155]P108(a1)
% 157.60/157.50 [3156]P108(a106)
% 157.60/157.50 [3157]P109(a925)
% 157.60/157.50 [3158]P109(a930)
% 157.60/157.50 [3159]P109(a1)
% 157.60/157.50 [3160]P109(a106)
% 157.60/157.50 [3161]P110(a930)
% 157.60/157.50 [3162]P110(a1)
% 157.60/157.50 [3163]P110(a106)
% 157.60/157.50 [3164]P111(a925)
% 157.60/157.50 [3165]P111(a930)
% 157.60/157.50 [3166]P111(a1)
% 157.60/157.50 [3167]P111(a106)
% 157.60/157.50 [3168]P2(a925)
% 157.60/157.50 [3169]P2(a930)
% 157.60/157.50 [3170]P2(a1)
% 157.60/157.50 [3171]P2(a106)
% 157.60/157.50 [3172]P79(a1)
% 157.60/157.50 [3173]P3(a1)
% 157.60/157.50 [3174]P69(a930)
% 157.60/157.50 [3175]P69(a1)
% 157.60/157.50 [3176]P69(a106)
% 157.60/157.50 [3177]P112(a925)
% 157.60/157.50 [3178]P83(a925)
% 157.60/157.50 [3179]P83(a930)
% 157.60/157.50 [3180]P83(a1)
% 157.60/157.50 [3181]P102(a925)
% 157.60/157.50 [3182]P102(a930)
% 157.60/157.50 [3183]P102(a1)
% 157.60/157.50 [3184]P84(a925)
% 157.60/157.50 [3185]P4(a925)
% 157.60/157.50 [3186]P4(a933)
% 157.60/157.50 [3187]P85(a925)
% 157.60/157.50 [3188]P5(a925)
% 157.60/157.50 [3189]P80(a930)
% 157.60/157.50 [3190]P80(a1)
% 157.60/157.50 [3191]P80(a106)
% 157.60/157.50 [3192]P71(a930)
% 157.60/157.50 [3193]P71(a1)
% 157.60/157.50 [3194]P71(a106)
% 157.60/157.50 [3195]P81(a930)
% 157.60/157.50 [3196]P81(a1)
% 157.60/157.50 [3197]P81(a106)
% 157.60/157.50 [3198]P113(a930)
% 157.60/157.50 [3199]P113(a1)
% 157.60/157.50 [3200]P113(a106)
% 157.60/157.50 [3201]P114(a930)
% 157.60/157.50 [3202]P114(a1)
% 157.60/157.50 [3203]P114(a106)
% 157.60/157.50 [3204]P129(a930)
% 157.60/157.50 [3205]P129(a1)
% 157.60/157.50 [3206]P129(a106)
% 157.60/157.50 [3207]P134(a1)
% 157.60/157.50 [3208]P135(a930)
% 157.60/157.50 [3209]P135(a1)
% 157.60/157.50 [3210]P135(a106)
% 157.60/157.50 [3211]P86(a930)
% 157.60/157.50 [3212]P86(a1)
% 157.60/157.50 [3213]P86(a106)
% 157.60/157.50 [3214]P76(a1)
% 157.60/157.50 [3215]P82(a930)
% 157.60/157.50 [3216]P82(a1)
% 157.60/157.50 [3217]P82(a106)
% 157.60/157.50 [3218]P72(a930)
% 157.60/157.50 [3219]P72(a1)
% 157.60/157.50 [3220]P72(a106)
% 157.60/157.50 [3221]P91(a930)
% 157.60/157.50 [3222]P91(a1)
% 157.60/157.50 [3223]P91(a106)
% 157.60/157.50 [3224]P70(a930)
% 157.60/157.50 [3225]P70(a1)
% 157.60/157.50 [3226]P70(a106)
% 157.60/157.50 [3227]P73(a930)
% 157.60/157.50 [3228]P73(a1)
% 157.60/157.50 [3229]P73(a106)
% 157.60/157.50 [3230]P74(a930)
% 157.60/157.50 [3231]P74(a1)
% 157.60/157.50 [3232]P74(a106)
% 157.60/157.50 [3233]P144(a930)
% 157.60/157.50 [3234]P144(a1)
% 157.60/157.50 [3235]P145(a930)
% 157.60/157.50 [3236]P145(a1)
% 157.60/157.50 [3237]P145(a106)
% 157.60/157.50 [3238]P115(a930)
% 157.60/157.50 [3239]P115(a1)
% 157.60/157.50 [3240]P115(a106)
% 157.60/157.50 [3241]P120(a1)
% 157.60/157.50 [3242]P146(a930)
% 157.60/157.50 [3243]P146(a1)
% 157.60/157.50 [3244]P146(a106)
% 157.60/157.50 [3245]P121(a1)
% 157.60/157.50 [3246]P130(a1)
% 157.60/157.50 [3247]P87(a930)
% 157.60/157.50 [3248]P87(a1)
% 157.60/157.50 [3249]P87(a106)
% 157.60/157.50 [3250]P88(a930)
% 157.60/157.50 [3251]P88(a1)
% 157.60/157.50 [3252]P88(a106)
% 157.60/157.50 [3253]P90(a930)
% 157.60/157.50 [3254]P90(a1)
% 157.60/157.50 [3255]P90(a106)
% 157.60/157.50 [3256]P77(a1)
% 157.60/157.50 [3257]P136(a1)
% 157.60/157.50 [3258]P137(a930)
% 157.60/157.50 [3259]P137(a1)
% 157.60/157.50 [3260]P137(a106)
% 157.60/157.50 [3261]P138(a1)
% 157.60/157.50 [3262]P140(a930)
% 157.60/157.50 [3263]P140(a1)
% 157.60/157.50 [3264]P140(a106)
% 157.60/157.50 [3265]P139(a930)
% 157.60/157.50 [3266]P139(a1)
% 157.60/157.50 [3267]P139(a106)
% 157.60/157.50 [3268]P122(a930)
% 157.60/157.50 [3269]P122(a1)
% 157.60/157.50 [3270]P122(a106)
% 157.60/157.50 [3271]P132(a930)
% 157.60/157.50 [3272]P132(a1)
% 157.60/157.50 [3273]P132(a106)
% 157.60/157.50 [3274]P133(a1)
% 157.60/157.50 [3275]P131(a930)
% 157.60/157.50 [3276]P131(a1)
% 157.60/157.50 [3277]P131(a106)
% 157.60/157.50 [3278]P128(a1)
% 157.60/157.50 [3279]P142(a1)
% 157.60/157.50 [3280]P95(a1)
% 157.60/157.50 [3281]P143(a1)
% 157.60/157.50 [3282]P116(a930)
% 157.60/157.50 [3283]P116(a1)
% 157.60/157.50 [3284]P116(a106)
% 157.60/157.50 [3285]P147(a930)
% 157.60/157.50 [3286]P147(a1)
% 157.60/157.50 [3287]P147(a106)
% 157.60/157.50 [3288]P103(a925)
% 157.60/157.50 [3289]P103(a930)
% 157.60/157.50 [3290]P103(a1)
% 157.60/157.50 [3291]P101(a925)
% 157.60/157.50 [3292]P101(a930)
% 157.60/157.50 [3293]P101(a1)
% 157.60/157.50 [3294]P78(a930)
% 157.60/157.50 [3295]P78(a1)
% 157.60/157.50 [3296]P78(a106)
% 157.60/157.50 [3297]P62(a930)
% 157.60/157.50 [3298]P62(a1)
% 157.60/157.50 [3299]P62(a106)
% 157.60/157.50 [3300]P63(a1)
% 157.60/157.50 [3301]P104(a930)
% 157.60/157.50 [3302]P104(a1)
% 157.60/157.50 [3303]P104(a106)
% 157.60/157.50 [3304]P148(a930)
% 157.60/157.50 [3305]P148(a1)
% 157.60/157.50 [3306]P148(a106)
% 157.60/157.50 [3307]P89(a1)
% 157.60/157.50 [3308]P141(a1)
% 157.60/157.50 [3309]P98(a925)
% 157.60/157.50 [3310]P123(a1)
% 157.60/157.50 [3311]P92(a925)
% 157.60/157.50 [3312]P92(a1)
% 157.60/157.50 [3313]P118(a1)
% 157.60/157.50 [3314]P75(a1)
% 157.60/157.50 [3315]P93(a1)
% 157.60/157.50 [3316]P96(a1)
% 157.60/157.50 [3317]P97(a930)
% 157.60/157.50 [3318]P97(a1)
% 157.60/157.50 [3319]P97(a106)
% 157.60/157.50 [3320]P117(a930)
% 157.60/157.50 [3321]P94(a930)
% 157.60/157.50 [3322]P94(a1)
% 157.60/157.50 [3323]P94(a106)
% 157.60/157.50 [3324]P64(a925)
% 157.60/157.50 [3325]P64(a933)
% 157.60/157.50 [3326]P106(a925)
% 157.60/157.50 [3327]P106(a926)
% 157.60/157.50 [3328]P106(a930)
% 157.60/157.50 [3329]P106(a928)
% 157.60/157.50 [3330]P106(a933)
% 157.60/157.50 [3331]P106(a927)
% 157.60/157.50 [3332]P106(a106)
% 157.60/157.50 [3333]P106(a330)
% 157.60/157.50 [3334]P105(a933)
% 157.60/157.50 [3335]P105(a1)
% 157.60/157.50 [3336]P119(a1)
% 157.60/157.50 [3337]P124(a930)
% 157.60/157.50 [3338]P124(a1)
% 157.60/157.50 [3339]P124(a106)
% 157.60/157.50 [3340]P100(a925)
% 157.60/157.50 [3356]P37(a930,a248)
% 157.60/157.50 [3357]P37(a930,a324)
% 157.60/157.50 [3358]P38(a930,a248)
% 157.60/157.50 [3359]P151(a331,a865)
% 157.60/157.50 [4710]~E(a104,a89)
% 157.60/157.50 [4711]~P107(a247)
% 157.60/157.50 [3147]E(f2(a1),a89)
% 157.60/157.50 [3148]E(f107(a106),a3)
% 157.60/157.50 [3149]E(f23(a106),a24)
% 157.60/157.50 [3341]E(f195(a930),f2(a930))
% 157.60/157.50 [3342]E(f29(a25),f2(a930))
% 157.60/157.50 [3343]E(f108(a930),f241(a930))
% 157.60/157.50 [3344]E(f117(a930),f242(a930))
% 157.60/157.50 [3345]E(f109(a1),f32(a1))
% 157.60/157.50 [3346]E(f90(a247),f2(a930))
% 157.60/157.50 [3347]E(f90(a194),f2(a930))
% 157.60/157.50 [3348]P6(f84(a1))
% 157.60/157.50 [3349]P6(f2(a1))
% 157.60/157.50 [3411]P37(f936(a930,a930),a38)
% 157.60/157.50 [3757]E(f326(a930,a930,a248,a248),a38)
% 157.60/157.50 [4712]~E(f84(a1),f2(a1))
% 157.60/157.50 [3350]E(f4(f2(a106)),f2(a930))
% 157.60/157.50 [3351]E(f118(f2(a930)),f2(a930))
% 157.60/157.50 [3363]E(f866(f85(a1),a89),a89)
% 157.60/157.50 [3366]E(f866(a119,f2(a930)),f84(a930))
% 157.60/157.50 [3367]E(f866(a111,f84(a1)),f84(a930))
% 157.60/157.50 [3368]E(f866(a3,f84(a930)),f84(a106))
% 157.60/157.50 [3370]E(f866(a3,f2(a930)),f2(a106))
% 157.60/157.50 [3372]E(f866(f110(a1),a89),f2(a1))
% 157.60/157.50 [3373]E(f866(f110(a106),a89),f2(a106))
% 157.60/157.50 [3374]E(f866(a111,f2(a1)),f2(a930))
% 157.60/157.50 [3375]E(f866(f196(a925),a247),f2(a930))
% 157.60/157.50 [3376]E(f866(f196(a925),a194),f2(a930))
% 157.60/157.50 [3377]E(f866(f196(a927),a25),f2(a930))
% 157.60/157.50 [3378]E(f866(f110(a930),a89),f2(a930))
% 157.60/157.50 [3384]E(f866(f85(a1),f84(a1)),a104)
% 157.60/157.50 [3392]E(f866(f196(a106),f2(a106)),f2(a930))
% 157.60/157.50 [3393]E(f866(f107(a1),f84(a930)),f84(a1))
% 157.60/157.50 [3394]E(f866(f107(a1),f2(a930)),f2(a1))
% 157.60/157.50 [3395]E(f866(f85(a1),f2(a1)),f2(a1))
% 157.60/157.50 [3407]E(f866(a111,f84(a1)),f866(a119,f2(a930)))
% 157.60/157.50 [3409]E(f325(f936(a930,a930),a38),a39)
% 157.60/157.50 [3410]E(f327(f936(a930,a930),a38),a74)
% 157.60/157.50 [3437]E(f866(f290(a930),f2(a930)),f195(f937(a930,a925)))
% 157.60/157.50 [3438]E(f866(f291(a930),f2(a930)),f250(f937(a930,a925)))
% 157.60/157.50 [3447]P40(f195(f937(a1,a925)))
% 157.60/157.50 [3482]E(f866(f866(f23(a106),f2(a106)),f84(a106)),f2(a106))
% 157.60/157.50 [3557]P107(f866(f866(f244(a1),a104),f2(a1)))
% 157.60/157.50 [3581]P107(f866(f866(f243(a1),f2(a1)),f84(a1)))
% 157.60/157.50 [3583]P107(f866(f866(f244(a1),f2(a1)),f84(a1)))
% 157.60/157.50 [3788]E(f866(f866(f296(a930,a930,a930),a324),f314(a930,a324)),a248)
% 157.60/157.50 [3830]P41(a1,a930,a111,f866(f243(a1),f2(a1)))
% 157.60/157.50 [3834]E(f866(f866(f44(a930,f937(a930,a925)),f250(f937(a930,a925))),f290(a930)),f250(f937(a930,a925)))
% 157.60/157.50 [3835]E(f866(f866(f44(a930,f937(a930,a925)),f250(f937(a930,a925))),f308(a930)),f250(f937(a930,a925)))
% 157.60/157.50 [3836]E(f866(f866(f44(a930,f937(a930,a925)),f250(f937(a930,a925))),f291(a930)),f250(f937(a930,a925)))
% 157.60/157.50 [3837]E(f866(f866(f45(a930,f937(a930,a925)),f250(f937(a930,a925))),f311(a930)),f195(f937(a930,a925)))
% 157.60/157.50 [3852]P25(a930,a1,f107(a1),f250(f937(a930,a925)))
% 157.60/157.50 [3866]P41(a930,a1,f107(a1),f866(f16(a925,a930),a194))
% 157.60/157.50 [4002]E(f866(f78(a930,a106,a1,a3),a111),f110(a106))
% 157.60/157.50 [4227]P58(a106,a930,a20,a3,f250(f937(a930,a925)))
% 157.60/157.50 [4232]P58(a1,f937(f936(a930,a930),a925),a114,a95,a105)
% 157.60/157.50 [4488]E(f266(a1,a1,a1,a1,f32(a1),f85(a1)),a56)
% 157.60/157.50 [4735]~E(f866(f110(a1),a104),f866(f110(a1),a89))
% 157.60/157.50 [4736]~P107(f866(a200,f84(a1)))
% 157.60/157.50 [4737]~P107(f866(a200,f2(a1)))
% 157.60/157.50 [4778]~P107(f866(f866(f244(a1),a89),f2(a1)))
% 157.60/157.50 [3429]E(f866(f866(f23(a1),a104),a104),a89)
% 157.60/157.50 [3445]E(f866(f107(a1),f866(a119,f2(a930))),f84(a1))
% 157.60/157.50 [3511]E(f866(f40(a933),f250(f937(a933,a925))),f84(a930))
% 157.60/157.50 [3532]P107(f866(a200,f866(f110(a1),a104)))
% 157.60/157.50 [3534]P107(f866(f866(f243(a1),a104),a89))
% 157.60/157.50 [3536]P107(f866(f866(f244(a1),a104),a89))
% 157.60/157.50 [3592]E(f866(f866(f316(a930),f2(a930)),f195(f937(a930,a925))),f866(f308(a930),f2(a930)))
% 157.60/157.50 [3647]P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),a89)))
% 157.60/157.50 [3659]E(f866(f317(a930,a930,a119),f250(f937(a930,a925))),f866(f311(a930),f2(a930)))
% 157.60/157.50 [3696]P8(f936(a930,a930),f250(f937(f936(a930,a930),a925)),a115)
% 157.60/157.50 [4009]E(f866(f78(a930,a1,a106,f107(a1)),a20),a22)
% 157.60/157.50 [4070]P37(a930,f866(f270(f936(a930,a930)),f866(f265(a930,a930,a925),f244(a930))))
% 157.60/157.50 [4769]~P107(f866(a200,f866(f110(a1),a89)))
% 157.60/157.50 [4770]~P107(f866(f866(f243(a1),a89),a104))
% 157.60/157.50 [4771]~P107(f866(f866(f244(a1),a89),a89))
% 157.60/157.50 [4772]~P107(f866(f866(f244(a1),a89),a104))
% 157.60/157.50 [4773]~P107(f866(f866(f244(a1),a104),a104))
% 157.60/157.50 [4784]~P107(f866(f66(a930),f250(f937(a930,a925))))
% 157.60/157.50 [4785]~P107(f866(f66(a1),f250(f937(a1,a925))))
% 157.60/157.50 [4654]E(f866(f265(a1,a1,a925),f866(f866(f8(f937(a1,a925),f937(a1,a925),a1),f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f244(a1),f2(a1))))),f866(f866(f7(a1,a1,f937(a1,a925)),f866(f866(f8(f937(a1,f937(a1,a925)),f937(a1,f937(a1,a925)),a1),f7(a1,a1,a925)),f866(f866(f8(f937(a1,a1),f937(a1,f937(a1,a925)),a1),f866(f8(a1,f937(a1,a925),a1),a332)),a226))),f84(a1)))),a222)
% 157.60/157.50 [3732]E(f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104),f866(f85(a1),a104))
% 157.60/157.50 [3770]E(f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104),f866(f866(f23(a1),a89),a104))
% 157.60/157.50 [3935]E(f866(f866(f65(f936(a930,a930)),f250(f937(f936(a930,a930),a925))),a115),a105)
% 157.60/157.50 [3964]E(f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f84(a1))
% 157.60/157.50 [3965]E(f866(f110(a106),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f84(a106))
% 157.60/157.50 [3966]E(f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f84(a930))
% 157.60/157.50 [3970]E(f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(a119,f2(a930)))
% 157.60/157.50 [4354]E(f866(f866(f117(f937(f936(f936(a930,a930),f936(a930,a930)),a925)),a38),f314(f936(a930,a930),f195(f937(f936(f936(a930,a930),f936(a930,a930)),a925)))),a76)
% 157.60/157.50 [4422]E(f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),f84(a930)),f2(a930))),f195(f937(f936(a930,a930),a925))))),f84(a1))
% 157.60/157.50 [4423]E(f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),f2(a930)),f2(a930))),f195(f937(f936(a930,a930),a925))))),f2(a1))
% 157.60/157.50 [4436]E(f866(f270(f936(a930,a930)),f866(f265(a930,a930,a925),f866(f866(f8(a930,f937(a930,a925),a930),f866(f7(a930,a930,a925),a332)),a119))),a324)
% 157.60/157.50 [4408]E(f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),f866(a119,f866(a119,f2(a930))))
% 157.60/157.50 [4411]E(f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),f866(f866(f86(a930),f84(a930)),f84(a930)))
% 157.60/157.50 [4412]E(f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),f866(f40(a925),f250(f937(a925,a925))))
% 157.60/157.50 [4475]P6(f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))
% 157.60/157.50 [4544]P27(f937(f936(a930,a930),a925),f866(f866(f260(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925),f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)),a39),a75))
% 157.60/157.50 [4545]P27(f937(f936(a930,a930),a925),f866(f866(f260(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925),f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)),a74),a77))
% 157.60/157.50 [4585]E(f866(f866(f117(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)),f327(f936(a930,a930),a76)),f866(f866(f316(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f195(f937(f936(a930,a930),a925))),f195(f937(f936(a930,a930),a925)))),f195(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)))),a77)
% 157.60/157.50 [4586]E(f866(f866(f117(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)),f325(f936(a930,a930),a76)),f866(f866(f316(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f195(f937(f936(a930,a930),a925))),f195(f937(f936(a930,a930),a925)))),f195(f937(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a925)))),a75)
% 157.60/157.50 [4477]E(f866(a111,f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(a119,f866(a119,f2(a930))))
% 157.60/157.50 [4522]E(f866(f107(a1),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))
% 157.60/157.50 [4555]P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.50 [4556]E(f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104)),f866(a119,f866(a119,f866(a119,f2(a930)))))
% 157.60/157.50 [4600]P6(f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104)))
% 157.60/157.50 [4626]E(f866(f107(a1),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104)))
% 157.60/157.50 [4639]P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))))
% 157.60/157.50 [3360]P7(x33601,a332)
% 157.60/157.50 [3460]P57(a930,x34601,x34601)
% 157.60/157.50 [3758]P25(a930,a930,a119,x37581)
% 157.60/157.50 [3352]P106(f929(x33521))
% 157.60/157.50 [3353]P106(f934(x33531))
% 157.60/157.50 [3354]P106(f931(x33541))
% 157.60/157.50 [3355]P106(f932(x33551))
% 157.60/157.50 [3379]P37(a1,f112(x33791))
% 157.60/157.50 [3380]P37(a1,f113(x33801))
% 157.60/157.50 [3433]P37(f937(x34331,a925),f321(x34331))
% 157.60/157.50 [3434]P38(f937(x34341,a925),f321(x34341))
% 157.60/157.50 [3459]E(f251(x34591,x34591,a332),a332)
% 157.60/157.50 [3475]E(f50(a1,x34751,x34751),f2(a1))
% 157.60/157.50 [3529]P14(x35291,f937(x35291,a925),f316(x35291))
% 157.60/157.50 [4716]~E(f866(a119,x47161),x47161)
% 157.60/157.50 [4728]~E(f866(a119,x47281),f2(a930))
% 157.60/157.50 [3361]E(f35(f33(x33611)),f2(a930))
% 157.60/157.50 [3362]E(f35(f34(x33621)),f2(a930))
% 157.60/157.50 [3364]E(f866(f196(a930),x33641),x33641)
% 157.60/157.50 [3365]E(f866(f110(a1),x33651),x33651)
% 157.60/157.50 [3381]E(f866(a95,f335(x33811)),x33811)
% 157.60/157.50 [3382]E(f866(a3,f552(x33821)),x33821)
% 157.60/157.50 [3383]E(f249(x33831,f2(a106)),f2(a106))
% 157.60/157.50 [3396]E(f121(x33961,f120(x33961)),f120(x33961))
% 157.60/157.50 [3397]E(f159(x33971,f120(x33971)),f120(x33971))
% 157.60/157.50 [3399]E(f866(f196(a928),f33(x33991)),f2(a930))
% 157.60/157.50 [3400]E(f866(f196(a928),f34(x34001)),f2(a930))
% 157.60/157.50 [3404]E(f866(f174(x34041),f120(x34041)),f120(x34041))
% 157.60/157.50 [3405]E(f866(f178(x34051),f120(x34051)),f120(x34051))
% 157.60/157.50 [3406]E(f866(f175(x34061),f120(x34061)),f120(x34061))
% 157.60/157.50 [3412]E(f866(f110(a1),x34121),f866(f109(a1),x34121))
% 157.60/157.50 [3413]E(f866(a95,f866(a114,x34131)),x34131)
% 157.60/157.50 [3415]E(f866(a3,f866(a20,x34151)),x34151)
% 157.60/157.50 [3416]E(f866(a20,f866(a3,x34161)),x34161)
% 157.60/157.50 [3418]P6(f866(f107(a1),x34181))
% 157.60/157.50 [3427]E(f866(f196(f931(x34271)),f120(x34271)),f2(a930))
% 157.60/157.50 [3428]E(f866(f196(f932(x34281)),f126(x34281)),f2(a930))
% 157.60/157.50 [3450]E(f866(f866(f23(a930),x34501),f2(a930)),x34501)
% 157.60/157.50 [3451]E(f866(f866(f87(a930),x34511),f84(a930)),x34511)
% 157.60/157.50 [3452]E(f866(f866(f87(a1),x34521),f84(a1)),x34521)
% 157.60/157.50 [3453]E(f866(f866(f86(a930),x34531),f2(a930)),x34531)
% 157.60/157.50 [3454]E(f866(f866(f86(a1),x34541),f2(a1)),x34541)
% 157.60/157.50 [3455]E(f866(f866(f242(a930),x34551),f2(a930)),x34551)
% 157.60/157.50 [3456]E(f866(f866(f87(a930),x34561),f2(a930)),f2(a930))
% 157.60/157.50 [3457]E(f866(f866(f41(a1),x34571),f2(a1)),f2(a1))
% 157.60/157.50 [3458]E(f866(f866(f241(a930),x34581),f2(a930)),f2(a930))
% 157.60/157.50 [3466]E(f866(f179(x34661),f120(x34661)),f195(f937(x34661,a925)))
% 157.60/157.50 [3470]P107(f866(f144(x34701),f120(x34701)))
% 157.60/157.50 [3476]E(f866(f161(x34761,x34761),f5(x34761)),f32(f931(x34761)))
% 157.60/157.50 [3477]E(f866(f161(x34771,x34771),f32(x34771)),f32(f931(x34771)))
% 157.60/157.50 [3478]E(f50(a1,x34781,f2(a1)),x34781)
% 157.60/157.50 [3479]E(f866(f243(a930),f866(a119,x34791)),f866(f244(a930),x34791))
% 157.60/157.50 [3480]E(f866(f290(a930),f866(a119,x34801)),f866(f308(a930),x34801))
% 157.60/157.50 [3481]E(f866(f291(a930),f866(a119,x34811)),f866(f311(a930),x34811))
% 157.60/157.50 [3483]E(f50(a1,f2(a1),x34831),f2(a1))
% 157.60/157.50 [3496]E(f866(f866(f86(a930),x34961),f84(a930)),f866(a119,x34961))
% 157.60/157.50 [3505]E(f866(f309(a930,x35051),f2(a930)),f195(f937(a930,a925)))
% 157.60/157.50 [3517]E(f310(a930,f2(a930),x35171),f866(f308(a930),x35171))
% 157.60/157.50 [3526]P57(a930,f866(a119,f2(a930)),x35261)
% 157.60/157.50 [3560]E(f866(f866(f23(a930),f866(a119,x35601)),f84(a930)),x35601)
% 157.60/157.50 [3572]E(f52(f2(a1),x35721),f866(f866(f260(a1,a1),f2(a1)),f2(a1)))
% 157.60/157.50 [3622]P107(f866(f866(f244(a930),x36221),f866(a119,x36221)))
% 157.60/157.50 [3634]P107(f866(f866(f244(a930),f2(a930)),f866(a119,x36341)))
% 157.60/157.50 [3865]E(f97(x38651,x38651,f250(f937(x38651,a925)),f32(x38651)),f32(x38651))
% 157.60/157.50 [3922]E(f866(f866(f23(a106),f866(a3,f866(a119,f866(a20,x39221)))),f84(a106)),x39221)
% 157.60/157.50 [3993]P107(f866(f866(f243(a1),f866(f85(a1),f866(f107(a1),x39931))),f2(a1)))
% 157.60/157.50 [4142]P107(f866(f866(f244(a1),f866(f85(a1),f866(f107(a1),f866(a119,x41421)))),f2(a1)))
% 157.60/157.50 [4742]~E(f250(f937(x47421,a925)),f195(f937(x47421,a925)))
% 157.60/157.50 [4781]~P107(f866(f866(f244(a930),x47811),f2(a930)))
% 157.60/157.50 [4794]~P107(f866(f866(f244(a1),f866(f107(a1),x47941)),f2(a1)))
% 157.60/157.50 [3417]E(f127(x34171,f126(f932(x34171))),f126(x34171))
% 157.60/157.50 [3432]E(f186(x34321,f120(f931(x34321))),f120(f931(x34321)))
% 157.60/157.50 [3435]E(f866(f866(f87(a1),a89),x34351),a89)
% 157.60/157.50 [3436]E(f866(f866(f86(a1),a89),x34361),x34361)
% 157.60/157.50 [3439]E(f866(a111,f866(f107(a1),x34391)),x34391)
% 157.60/157.50 [3440]E(f866(f866(f23(a1),x34401),a89),x34401)
% 157.60/157.50 [3441]E(f866(f866(f86(a1),x34411),a89),x34411)
% 157.60/157.50 [3444]E(f866(f866(f23(a930),x34441),x34441),f2(a930))
% 157.60/157.50 [3448]E(f866(f40(a930),f866(f290(a930),x34481)),x34481)
% 157.60/157.50 [3449]E(f866(f85(a1),f866(f85(a1),x34491)),x34491)
% 157.60/157.50 [3461]E(f866(f866(f87(a930),f84(a930)),x34611),x34611)
% 157.60/157.50 [3462]E(f866(f866(f87(a1),f84(a1)),x34621),x34621)
% 157.60/157.50 [3463]E(f866(f866(f86(a930),f2(a930)),x34631),x34631)
% 157.60/157.50 [3464]E(f866(f866(f86(a1),f2(a1)),x34641),x34641)
% 157.60/157.50 [3465]E(f866(f866(f242(a930),f2(a930)),x34651),x34651)
% 157.60/157.50 [3471]E(f866(f866(f23(a930),f2(a930)),x34711),f2(a930))
% 157.60/157.50 [3472]E(f866(f866(f87(a930),f2(a930)),x34721),f2(a930))
% 157.60/157.50 [3473]E(f866(f866(f41(a1),f2(a1)),x34731),f2(a1))
% 157.60/157.50 [3474]E(f866(f866(f241(a930),f2(a930)),x34741),f2(a930))
% 157.60/157.50 [3484]E(f135(x34841,f866(f85(a1),x34841)),f139(a1,x34841))
% 157.60/157.50 [3489]E(f866(f309(a930,f2(a930)),x34891),f866(f290(a930),x34891))
% 157.60/157.50 [3490]E(f866(f866(f87(a1),a104),x34901),f866(f85(a1),x34901))
% 157.60/157.50 [3498]E(f866(a111,f866(f110(a1),x34981)),f866(f110(a930),x34981))
% 157.60/157.50 [3499]E(f866(a20,f866(f110(a106),x34991)),f866(f110(a930),x34991))
% 157.60/157.50 [3500]E(f866(f40(a930),f866(f308(a930),x35001)),f866(a119,x35001))
% 157.60/157.50 [3509]E(f866(f866(f86(a930),f84(a930)),x35091),f866(a119,x35091))
% 157.60/157.50 [3513]E(f866(f81(a1),f866(f107(a1),x35131)),f866(f107(a1),x35131))
% 157.60/157.50 [3514]E(f866(f109(a1),f866(f107(a1),x35141)),f866(f107(a1),x35141))
% 157.60/157.50 [3518]E(f866(f40(x35181),f195(f937(x35181,a925))),f2(a930))
% 157.60/157.50 [3520]E(f866(f866(f41(a930),x35201),f866(a119,f2(a930))),x35201)
% 157.60/157.50 [3530]E(f50(a930,x35301,f866(a119,f2(a930))),f2(a930))
% 157.60/157.50 [3531]E(f50(a1,x35311,f866(f110(a1),a104)),f2(a1))
% 157.60/157.50 [3545]E(f866(f866(f41(a1),x35451),f866(f110(a1),a104)),f866(f85(a1),x35451))
% 157.60/157.50 [3549]E(f146(a930,f866(f309(a930,x35491),f2(a930))),f120(a930))
% 157.60/157.50 [3550]E(f866(f866(f86(a1),x35501),f84(a1)),f866(f866(f23(a1),x35501),a104))
% 157.60/157.50 [3551]E(f866(f866(f23(a1),x35511),f84(a1)),f866(f866(f86(a1),x35511),a104))
% 157.60/157.50 [3555]P107(f866(f866(f243(a930),x35551),x35551))
% 157.60/157.50 [3556]P107(f866(f866(f243(a1),x35561),x35561))
% 157.60/157.50 [3561]E(f866(f85(a1),f866(f110(a1),x35611)),f866(f110(a1),f866(f85(a1),x35611)))
% 157.60/157.50 [3562]P107(f866(f66(a930),f866(f290(a930),x35621)))
% 157.60/157.50 [3563]P107(f866(f66(a930),f866(f308(a930),x35631)))
% 157.60/157.50 [3570]E(f168(x35701,f250(f937(x35701,a925))),f250(f937(f931(x35701),a925)))
% 157.60/157.50 [3575]P107(f866(f866(f243(a930),f2(a930)),x35751))
% 157.60/157.50 [3585]E(f866(f866(f86(a930),f118(x35851)),f866(a119,f2(a930))),f118(f866(a119,x35851)))
% 157.60/157.50 [3586]E(f866(f270(x35861),f866(f16(a925,x35861),a247)),f195(f937(x35861,a925)))
% 157.60/157.50 [3587]E(f866(f270(x35871),f866(f16(a925,x35871),a194)),f250(f937(x35871,a925)))
% 157.60/157.50 [3591]E(f866(f866(f316(a930),x35911),f866(f290(a930),x35911)),f866(f290(a930),f866(a119,x35911)))
% 157.60/157.50 [3603]E(f866(f866(f86(a1),f84(a1)),f866(f107(a1),x36031)),f866(f107(a1),f866(a119,x36031)))
% 157.60/157.50 [3605]E(f866(f866(f158(f931(x36051)),f120(x36051)),f120(f931(x36051))),f59(x36051,f120(x36051)))
% 157.60/157.50 [3625]E(f195(f937(f936(x36251,x36251),a925)),f271(x36251,f195(f937(x36251,a925))))
% 157.60/157.50 [3626]E(f866(f315(x36261),f250(f937(x36261,a925))),f250(f937(f937(x36261,a925),a925)))
% 157.60/157.50 [3627]E(f866(f85(f937(x36271,a925)),f195(f937(x36271,a925))),f250(f937(x36271,a925)))
% 157.60/157.50 [3628]E(f866(f85(f937(x36281,a925)),f250(f937(x36281,a925))),f195(f937(x36281,a925)))
% 157.60/157.50 [3630]P107(f866(f66(x36301),f195(f937(x36301,a925))))
% 157.60/157.50 [3632]E(f866(f309(a930,x36321),f866(a119,x36321)),f866(f866(f316(a930),x36321),f195(f937(a930,a925))))
% 157.60/157.50 [3633]E(f91(f936(a930,a930),f53(x36331,f2(a930))),f866(f866(f260(a930,a930),f2(a930)),x36331))
% 157.60/157.50 [3646]E(f866(f866(f316(a930),f866(a119,x36461)),f866(f308(a930),x36461)),f866(f308(a930),f866(a119,x36461)))
% 157.60/157.50 [3650]P37(x36501,f195(f937(f936(x36501,x36501),a925)))
% 157.60/157.50 [3651]P39(x36511,f195(f937(f936(x36511,x36511),a925)))
% 157.60/157.50 [3654]P107(f866(f866(f243(a1),f2(a1)),f866(f107(a1),x36541)))
% 157.60/157.50 [3661]E(f866(f866(f86(a930),f866(f196(a930),x36611)),f866(a119,f2(a930))),f866(f196(a930),f866(a119,x36611)))
% 157.60/157.50 [3765]P40(f866(f317(a930,a1,f107(a1)),x37651))
% 157.60/157.50 [3803]P53(x38031,f195(f937(x38031,a925)),f195(f937(f936(x38031,x38031),a925)))
% 157.60/157.50 [3826]E(f866(f866(f260(a1,a1),f866(f110(a1),a104)),f866(f866(f23(a1),x38261),f84(a1))),f55(f866(f110(a1),a104),x38261))
% 157.60/157.50 [3878]P61(x38781,f866(f16(f937(x38781,a925),x38781),f866(f16(a925,x38781),a247)))
% 157.60/157.50 [4082]P107(f866(f866(f336(f937(f936(a930,a930),a925)),f335(x40821)),a105))
% 157.60/157.50 [4108]P107(f866(f866(f336(f937(f936(a930,a930),a925)),f866(a114,x41081)),a105))
% 157.60/157.50 [4241]P25(x42411,f937(x42411,a925),f866(f866(f7(x42411,f937(x42411,a925),f937(x42411,a925)),f316(x42411)),f195(f937(x42411,a925))),f250(f937(x42411,a925)))
% 157.60/157.50 [4739]~E(f866(f866(f86(a1),x47391),x47391),a104)
% 157.60/157.50 [4768]~E(f866(a3,f866(a119,f866(a20,x47681))),f2(a106))
% 157.60/157.50 [4774]~P107(f866(a200,f866(f107(a1),x47741)))
% 157.60/157.50 [4777]~P107(f866(f866(f244(a930),x47771),x47771))
% 157.60/157.50 [4787]~P107(f866(f866(f243(a930),f866(a119,x47871)),x47871))
% 157.60/157.50 [3577]E(f866(a111,f866(f85(a1),f866(f107(a1),x35771))),f2(a930))
% 157.60/157.50 [3580]E(f866(f866(f86(a1),f866(f85(a1),x35801)),x35801),f2(a1))
% 157.60/157.50 [3584]E(f866(f40(a1),f866(f309(a1,f2(a1)),x35841)),f866(a111,x35841))
% 157.60/157.50 [3596]E(f866(f866(f252(a930),f866(a119,f2(a930))),x35961),f866(a119,f2(a930)))
% 157.60/157.50 [3693]E(f866(f289(x36931),f195(f937(f936(x36931,x36931),a925))),f195(f937(x36931,a925)))
% 157.60/157.50 [3701]E(f43(f937(x37011,a925),f195(f937(f937(x37011,a925),a925))),f250(f937(x37011,a925)))
% 157.60/157.50 [3702]E(f43(f937(x37021,a925),f250(f937(f937(x37021,a925),a925))),f195(f937(x37021,a925)))
% 157.60/157.50 [3703]E(f42(f937(x37031,a925),f195(f937(f937(x37031,a925),a925))),f195(f937(x37031,a925)))
% 157.60/157.50 [3704]E(f42(f937(x37041,a925),f250(f937(f937(x37041,a925),a925))),f250(f937(x37041,a925)))
% 157.60/157.50 [3748]E(f866(f866(f316(f931(x37481)),f120(x37481)),f195(f937(f931(x37481),a925))),f168(x37481,f195(f937(x37481,a925))))
% 157.60/157.50 [3749]E(f866(f866(f316(f931(x37491)),f120(x37491)),f195(f937(f931(x37491),a925))),f169(x37491,f120(f937(x37491,a925))))
% 157.60/157.50 [3787]E(f866(f866(f86(a930),f4(x37871)),f866(a119,f2(a930))),f4(f866(a3,f866(a119,f866(a20,x37871)))))
% 157.60/157.50 [3817]E(f866(f40(a1),f866(f317(a930,a1,f107(a1)),x38171)),f866(f40(a930),x38171))
% 157.60/157.50 [3818]P107(f866(f866(f243(a930),x38181),f866(f866(f87(a930),x38181),x38181)))
% 157.60/157.50 [3856]E(f866(f317(a1,a930,a111),f310(a1,f2(a1),f866(f107(a1),x38561))),f866(f308(a930),x38561))
% 157.60/157.50 [3873]E(f866(f866(f41(a930),f866(a119,f2(a930))),f866(f110(a930),x38731)),f866(a111,f866(f866(f41(a1),f84(a1)),f866(f110(a1),x38731))))
% 157.60/157.50 [3875]E(f866(f179(a930),f146(a930,f866(f309(a930,f2(a930)),f866(a119,x38751)))),f866(f308(a930),x38751))
% 157.60/157.50 [3876]E(f866(f866(f86(a930),f866(f196(a106),x38761)),f866(a119,f2(a930))),f866(f196(a106),f866(a3,f866(a119,f866(a20,x38761)))))
% 157.60/157.50 [3895]P39(x38951,f314(x38951,f195(f937(f936(x38951,x38951),a925))))
% 157.60/157.50 [3896]P52(x38961,f314(x38961,f195(f937(f936(x38961,x38961),a925))))
% 157.60/157.50 [3897]E(f866(f317(a1,a930,a111),f866(f317(a930,a1,f107(a1)),x38971)),x38971)
% 157.60/157.50 [3928]E(f866(f866(f316(a930),f2(a930)),f866(f317(a930,a930,a119),f866(f290(a930),x39281))),f866(f290(a930),f866(a119,x39281)))
% 157.60/157.50 [3934]P55(x39341,x39341,f314(x39341,f195(f937(f936(x39341,x39341),a925))))
% 157.60/157.50 [3940]P107(f866(a200,f866(f85(a1),f866(f107(a1),f866(a119,x39401)))))
% 157.60/157.50 [3950]E(f866(f866(f23(f937(a930,a925)),f866(f291(a930),x39501)),f866(f866(f316(a930),x39501),f195(f937(a930,a925)))),f866(f291(a930),f866(a119,x39501)))
% 157.60/157.50 [3967]E(f866(f866(f86(a1),f866(f866(f23(a1),a89),x39671)),f866(f866(f23(a1),a89),x39671)),f866(f866(f23(a1),a89),f866(f866(f86(a1),x39671),x39671)))
% 157.60/157.50 [3982]E(f866(f866(f316(f937(x39821,a925)),f195(f937(x39821,a925))),f195(f937(f937(x39821,a925),a925))),f866(f315(x39821),f195(f937(x39821,a925))))
% 157.60/157.50 [4010]E(f866(f866(f23(f937(a930,a925)),f866(f311(a930),x40101)),f866(f866(f316(a930),f866(a119,x40101)),f195(f937(a930,a925)))),f866(f311(a930),f866(a119,x40101)))
% 157.60/157.50 [4120]E(f866(f110(a930),f866(f866(f86(a1),x41201),x41201)),f866(f866(f92(a930,a930),f866(f110(a930),x41201)),f866(f866(f18(a930,a930,a930),f86(a930)),f5(a930))))
% 157.60/157.50 [4497]P14(x44971,f937(x44971,a925),f866(f866(f8(f937(x44971,a925),f937(f937(x44971,a925),f937(x44971,a925)),x44971),f866(f7(f937(x44971,a925),f937(x44971,a925),f937(x44971,a925)),f23(f937(x44971,a925)))),f866(f866(f7(x44971,f937(x44971,a925),f937(x44971,a925)),f316(x44971)),f195(f937(x44971,a925)))))
% 157.60/157.50 [4584]E(f866(f270(f936(a1,a1)),f866(f265(a1,a1,a925),f866(f866(f8(f937(a1,a925),f937(a1,a925),a1),f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),x45841)))),f244(a1)))),f112(x45841))
% 157.60/157.50 [4617]E(f866(f270(f936(a1,a1)),f866(f265(a1,a1,a925),f866(f866(f18(a1,f937(a1,a925),f937(a1,a925)),f866(f866(f8(f937(a925,a925),f937(f937(a1,a925),f937(a1,a925)),a1),f8(a925,a925,a1)),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),x46171)))),f244(a1)))),f113(x46171))
% 157.60/157.50 [4670]E(f866(f270(f936(f937(x46701,a925),f937(x46701,a925))),f866(f265(f937(x46701,a925),f937(x46701,a925),a925),f866(f866(f7(f937(x46701,a925),f937(f937(x46701,a925),a925),f937(f937(x46701,a925),a925)),f866(f866(f8(f937(f937(x46701,a925),f937(a925,a925)),f937(f937(f937(x46701,a925),a925),f937(f937(x46701,a925),a925)),f937(x46701,a925)),f18(f937(x46701,a925),a925,a925)),f866(f866(f8(f937(f937(x46701,a925),a925),f937(f937(x46701,a925),f937(a925,a925)),f937(x46701,a925)),f866(f8(a925,f937(a925,a925),f937(x46701,a925)),a333)),f244(f937(x46701,a925))))),f66(x46701)))),f321(x46701))
% 157.60/157.50 [4791]~P107(f866(f66(f931(x47911)),f250(f937(f931(x47911),a925))))
% 157.60/157.50 [4803]~P107(f866(f866(f243(a1),f2(a1)),f866(f85(a1),f866(f107(a1),f866(a119,x48031)))))
% 157.60/157.50 [3727]E(f866(f866(f23(a1),f866(f866(f86(a1),x37271),a104)),a104),x37271)
% 157.60/157.50 [3741]E(f866(f179(a930),f146(a930,f866(f309(a930,f2(a930)),x37411))),f866(f290(a930),x37411))
% 157.60/157.50 [3989]E(f866(f866(f86(a1),f866(f866(f86(a1),f84(a1)),x39891)),x39891),f866(f866(f23(a1),f866(f866(f86(a1),x39891),x39891)),a104))
% 157.60/157.50 [4038]E(f866(f294(x40381,x40381),f314(x40381,f195(f937(f936(x40381,x40381),a925)))),f314(x40381,f195(f937(f936(x40381,x40381),a925))))
% 157.60/157.50 [4085]P107(f866(f866(f243(a930),x40851),f866(f866(f87(a930),x40851),f866(f866(f87(a930),x40851),x40851))))
% 157.60/157.50 [4358]P107(f866(f66(a930),f866(f270(a930),f866(f866(f7(a930,a930,a925),f243(a930)),x43581))))
% 157.60/157.50 [4359]P107(f866(f66(a930),f866(f270(a930),f866(f866(f7(a930,a930,a925),f244(a930)),x43591))))
% 157.60/157.50 [4633]E(f866(f270(f936(x46331,x46331)),f866(f866(f8(f937(x46331,a925),a925,f936(x46331,x46331)),f93(x46331)),f866(f866(f7(f936(x46331,x46331),f937(x46331,f936(x46331,x46331)),f937(x46331,a925)),f866(f866(f8(f937(f936(x46331,x46331),a925),f937(f937(x46331,f936(x46331,x46331)),f937(x46331,a925)),f936(x46331,x46331)),f8(f936(x46331,x46331),a925,x46331)),a332)),f866(f866(f18(x46331,x46331,f936(x46331,x46331)),f260(x46331,x46331)),f5(x46331))))),f314(x46331,f195(f937(f936(x46331,x46331),a925))))
% 157.60/157.50 [4793]~E(f866(f866(f23(a1),f866(f866(f86(a1),x47931),x47931)),a104),a89)
% 157.60/157.50 [4795]~E(f866(f866(f86(a1),f866(f866(f86(a1),f84(a1)),x47951)),x47951),f2(a1))
% 157.60/157.50 [4131]E(f866(f866(f86(a1),f866(f866(f23(a1),a104),x41311)),f866(f866(f23(a1),a104),x41311)),f866(f866(f23(a1),a104),f866(f866(f23(a1),f866(f866(f86(a1),x41311),x41311)),a104)))
% 157.60/157.50 [4249]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),a104),x42491)),f866(f866(f23(a1),a104),x42491))),a104),f866(f866(f23(a1),a104),f866(f866(f86(a1),x42491),x42491)))
% 157.60/157.50 [4281]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f86(a1),x42811),a104)),f866(f866(f86(a1),x42811),a104))),a104),f866(f866(f86(a1),f866(f866(f86(a1),x42811),x42811)),a104))
% 157.60/157.50 [4319]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),a104),x43191)),f866(f866(f23(a1),a104),x43191))),a104),f866(f866(f23(a1),a89),f866(f866(f23(a1),f866(f866(f86(a1),x43191),x43191)),a104)))
% 157.60/157.50 [4418]E(f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x44181),f2(a930))),f195(f937(f936(a930,a930),a925))))),f866(f107(a1),x44181))
% 157.60/157.50 [4428]E(f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),f339(x44281)),f514(x44281))),f195(f937(f936(a930,a930),a925))))),x44281)
% 157.60/157.50 [4461]E(f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x44611)),f866(f317(a930,a1,f107(a1)),f866(f270(a930),f866(f866(f8(a1,a925,a930),x44611),f107(a1)))))
% 157.60/157.50 [4505]P40(f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x45051)))
% 157.60/157.50 [4525]P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x45251),f195(f937(f936(a930,a930),a925)))),a77))
% 157.60/157.50 [4530]E(f866(f317(a1,a930,a111),f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),f866(f866(f8(a930,a925,a1),x45301),a111)))),f866(f270(a930),x45301))
% 157.60/157.50 [4687]E(f319(a930,f866(f866(f44(f936(a930,a930),f937(a930,a925)),f866(a114,x46871)),f866(f265(a930,a930,f937(a930,a925)),f866(f866(f7(a930,f937(a930,a925),f937(a930,f937(a930,a925))),f866(f866(f8(f937(a930,f937(f937(a930,a925),f937(a930,a925))),f937(f937(a930,a925),f937(a930,f937(a930,a925))),a930),f7(a930,f937(a930,a925),f937(a930,a925))),f866(f866(f8(f937(a930,a930),f937(a930,f937(f937(a930,a925),f937(a930,a925))),a930),f866(f8(a930,f937(f937(a930,a925),f937(a930,a925)),a930),f316(a930))),f23(a930)))),f195(f937(a930,a925)))))),f866(a111,x46871))
% 157.60/157.50 [4178]E(f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),x41781),x41781)),a104)),a104),f866(f866(f86(a1),x41781),x41781))
% 157.60/157.50 [4228]E(f866(f866(f23(a1),f866(f866(f23(a1),f866(f866(f86(a1),x42281),x42281)),a104)),a104),f866(f866(f86(a1),f866(f866(f23(a1),x42281),a104)),f866(f866(f23(a1),x42281),a104)))
% 157.60/157.50 [4434]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f86(a1),f866(f85(a1),x44341)),a104)),f866(f866(f86(a1),f866(f85(a1),x44341)),a104))),a104),f866(f85(a1),f866(f866(f23(a1),f866(f866(f86(a1),x44341),x44341)),a104)))
% 157.60/157.50 [4478]E(f866(f866(f86(a930),x44781),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(a119,f866(a119,x44781)))
% 157.60/157.50 [4479]E(f866(f866(f87(a930),x44791),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f86(a930),x44791),x44791))
% 157.60/157.50 [4480]E(f866(f866(f41(a930),f866(f866(f86(a930),x44801),x44801)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x44801)
% 157.60/157.50 [4558]E(f50(a930,f866(a119,f866(a119,x45581)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a930,x45581,f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.50 [4701]E(f866(a95,f866(f866(f44(f936(a930,a930),f937(f936(a930,a930),a925)),f866(a114,x47011)),f866(f265(a930,a930,f937(f936(a930,a930),a925)),f866(f866(f8(f937(a930,f937(f936(a930,a930),a925)),f937(a930,f937(f936(a930,a930),a925)),a930),f866(f8(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925),a930),f293(f936(a930,a930),f936(a930,a930),a115))),f866(f866(f7(a930,f937(f936(a930,a930),a925),f937(a930,f937(f936(a930,a930),a925))),f866(f866(f8(f937(a930,f937(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f937(f937(f936(a930,a930),a925),f937(a930,f937(f936(a930,a930),a925))),a930),f7(a930,f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f8(f937(a930,f936(a930,a930)),f937(a930,f937(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),a930),f866(f8(f936(a930,a930),f937(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),a930),f316(f936(a930,a930)))),f866(f7(a930,a930,f936(a930,a930)),f260(a930,a930))))),f195(f937(f936(a930,a930),a925))))))),f866(f85(a1),x47011))
% 157.60/157.50 [4553]E(f866(f866(f86(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x45531),f866(a119,f866(a119,x45531)))
% 157.60/157.50 [4554]E(f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x45541),f866(f866(f86(a930),x45541),x45541))
% 157.60/157.50 [4590]E(f866(f866(f41(a930),f866(a119,f866(a119,x45901))),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(a119,f866(f866(f41(a930),x45901),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.50 [4640]E(f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46401),f866(a119,f866(a119,f866(a119,x46401))))
% 157.60/157.50 [4708]E(f866(f265(a1,a1,f936(a1,a1)),f866(f866(f18(a1,f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f937(f936(a1,a1),f936(a1,a1))),f937(f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),a1),f18(a1,f936(a1,a1),f936(a1,a1))),f866(f866(f8(f937(a1,f936(a1,a1)),f937(a1,f937(f936(a1,a1),f936(a1,a1))),a1),f866(f18(a1,f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),f866(f866(f8(a925,f937(f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),a1),f103(f936(a1,a1))),f866(f866(f8(a1,a925,a1),f866(f243(a1),f2(a1))),f866(f866(f7(a1,a1,a1),f23(a1)),x47081))))),f866(f866(f7(a1,f937(a1,a1),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f936(a1,a1)),f937(f937(a1,a1),f937(a1,f936(a1,a1))),a1),f8(a1,f936(a1,a1),a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f866(f866(f7(a1,a1,a1),f866(f866(f8(a1,f937(a1,a1),a1),f86(a1)),f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f84(a1))))),f866(f866(f7(a1,a1,a1),f23(a1)),x47081))))),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))),f48(x47081))
% 157.60/157.50 [3401]P106(f936(x34011,x34012))
% 157.60/157.50 [3402]P106(f938(x34021,x34022))
% 157.60/157.50 [3403]P106(f935(x34031,x34032))
% 157.60/157.50 [3421]P13(a1,f185(x34211,x34212))
% 157.60/157.50 [3422]P37(x34221,f160(x34221,x34222))
% 157.60/157.50 [3423]P38(x34231,f271(x34231,x34232))
% 157.60/157.50 [3424]P38(x34241,f314(x34241,x34242))
% 157.60/157.50 [3425]P39(x34251,f271(x34251,x34252))
% 157.60/157.50 [3426]P52(x34261,f271(x34261,x34262))
% 157.60/157.50 [3491]P31(x34911,x34912,f120(x34911))
% 157.60/157.50 [3524]P53(x35241,x35242,f271(x35241,x35242))
% 157.60/157.50 [3525]P55(x35251,x35251,f271(x35251,x35252))
% 157.60/157.50 [3790]P25(x37901,x37901,f5(x37901),x37902)
% 157.60/157.50 [3791]P25(x37911,x37911,f32(x37911),x37912)
% 157.60/157.50 [3799]P32(x37991,x37992,f120(x37991),f120(x37991))
% 157.60/157.50 [3807]P25(f931(x38071),f931(x38071),f175(x38071),x38072)
% 157.60/157.50 [4218]P26(x42181,x42181,f32(x42181),x42182,x42182)
% 157.60/157.50 [4714]~E(f34(x47141),f33(x47142))
% 157.60/157.50 [4720]~E(f31(x47201,x47202),a25)
% 157.60/157.50 [4721]~E(f26(x47211,x47212),a25)
% 157.60/157.50 [4722]~E(f30(x47221,x47222),a25)
% 157.60/157.50 [4751]~P33(x47511,x47512,f120(x47511))
% 157.60/157.50 [4752]~P35(x47521,x47522,f120(x47521))
% 157.60/157.50 [3385]E(f866(f270(x33851),x33852),x33852)
% 157.60/157.50 [3386]E(f866(f5(x33861),x33862),x33862)
% 157.60/157.50 [3388]E(f866(f32(x33881),x33882),x33882)
% 157.60/157.50 [3398]E(f866(f198(x33981),x33982),f122(x33981))
% 157.60/157.50 [3408]E(f29(f26(x34081,x34082)),f2(a930))
% 157.60/157.50 [3419]E(f91(x34191,f866(a332,x34192)),x34192)
% 157.60/157.50 [3420]E(f96(x34201,f866(a332,x34202)),x34202)
% 157.60/157.50 [3442]E(f866(f196(a927),f26(x34421,x34422)),f2(a930))
% 157.60/157.50 [3443]E(f866(f132(x34431,x34432),f126(x34431)),f2(a930))
% 157.60/157.50 [3446]E(f866(f143(x34461,x34462),f120(x34461)),f120(x34461))
% 157.60/157.50 [3467]E(f314(x34671,f314(x34671,x34672)),f314(x34671,x34672))
% 157.60/157.50 [3468]E(f159(x34681,f159(x34681,x34682)),f159(x34681,x34682))
% 157.60/157.50 [3486]E(f866(f866(f141(x34861),x34862),f120(x34861)),x34862)
% 157.60/157.50 [3492]E(f180(x34921,x34922,f120(x34921)),x34922)
% 157.60/157.50 [3493]E(f123(x34931,f126(x34931),x34932),x34932)
% 157.60/157.50 [3494]E(f180(x34941,f120(x34941),x34942),x34942)
% 157.60/157.50 [3495]E(f176(x34951,f2(a930),x34952),f120(x34951))
% 157.60/157.50 [3501]E(f866(f866(f182(x35011),x35012),f120(x35011)),f120(x35011))
% 157.60/157.50 [3502]E(f866(f866(f145(x35021),x35022),f120(x35021)),f120(x35021))
% 157.60/157.50 [3504]E(f162(x35041,x35042,f120(x35041)),f2(a930))
% 157.60/157.50 [3506]E(f177(x35061,x35062,f120(x35061)),f120(x35061))
% 157.60/157.50 [3507]E(f184(x35071,x35072,f120(x35071)),f120(x35071))
% 157.60/157.50 [3508]E(f183(x35081,f120(x35081),x35082),f120(x35081))
% 157.60/157.50 [3512]E(f866(f179(x35121),f159(x35121,x35122)),f866(f179(x35121),x35122))
% 157.60/157.50 [3515]E(f866(f292(x35151,x35151),f271(x35151,x35152)),x35152)
% 157.60/157.50 [3516]E(f866(f272(x35161,x35161),f271(x35161,x35162)),x35162)
% 157.60/157.50 [3523]E(f866(f294(x35231,x35231),f271(x35231,x35232)),f271(x35231,x35232))
% 157.60/157.50 [3537]E(f314(f931(x35371),f164(x35371,x35372)),f165(x35371,f314(x35371,x35372)))
% 157.60/157.50 [3539]P107(f866(f144(a1),f185(x35391,x35392)))
% 157.60/157.50 [3547]E(f866(f292(x35471,x35471),f314(x35471,x35472)),f250(f937(x35471,a925)))
% 157.60/157.50 [3548]E(f866(f272(x35481,x35481),f314(x35481,x35482)),f250(f937(x35481,a925)))
% 157.60/157.50 [3552]P107(f866(f144(x35521),f159(x35521,x35522)))
% 157.60/157.50 [3554]P107(f866(f167(x35541,x35542),f120(x35541)))
% 157.60/157.50 [3559]E(f866(f179(a1),f185(x35591,x35592)),f310(a1,x35591,x35592))
% 157.60/157.50 [3573]P56(x35731,f195(f937(x35731,a925)),x35732)
% 157.60/157.50 [3578]E(f866(f264(a1,a1),f51(x35781,x35782)),f50(a1,x35781,x35782))
% 157.60/157.50 [3579]E(f866(f309(a930,x35791),f866(a119,x35792)),f310(a930,x35791,x35792))
% 157.60/157.50 [3595]E(f866(f866(f158(x35951),x35952),f120(x35951)),f147(x35951,x35952,f120(x35951)))
% 157.60/157.50 [3607]E(f310(a930,f866(a119,x36071),x36072),f312(a930,x36071,x36072))
% 157.60/157.50 [3610]P53(x36101,f250(f937(x36101,a925)),f314(x36101,x36102))
% 157.60/157.50 [3673]E(f866(f866(f23(a930),x36731),f866(a119,x36732)),f866(f40(a930),f313(a930,x36732,x36731)))
% 157.60/157.50 [3728]E(f173(x37281,x37282,f120(x37281)),f866(f866(f260(f931(x37281),f931(x37281)),f120(x37281)),f120(x37281)))
% 157.60/157.50 [3746]E(f866(f265(x37461,x37462,f936(x37461,x37462)),f260(x37461,x37462)),f32(f936(x37461,x37462)))
% 157.60/157.50 [3750]P107(f866(f866(f336(f931(x37501)),f120(x37501)),f168(x37501,x37502)))
% 157.60/157.50 [3751]E(f866(f196(f931(x37511)),f121(x37511,x37512)),f866(f866(f23(a930),f866(f196(f931(x37511)),x37512)),f84(a930)))
% 157.60/157.50 [3759]P107(f866(f66(a930),f313(a930,x37591,x37592)))
% 157.60/157.50 [3760]P107(f866(f66(a930),f310(a930,x37601,x37602)))
% 157.60/157.50 [3761]P107(f866(f66(a930),f312(a930,x37611,x37612)))
% 157.60/157.50 [3762]P107(f866(f66(a1),f313(a1,x37621,x37622)))
% 157.60/157.50 [3763]P107(f866(f66(a1),f310(a1,x37631,x37632)))
% 157.60/157.50 [3764]P107(f866(f66(a1),f312(a1,x37641,x37642)))
% 157.60/157.50 [3872]E(f866(f317(a930,a930,a119),f310(a930,x38721,x38722)),f310(a930,f866(a119,x38721),f866(a119,x38722)))
% 157.60/157.50 [3891]E(f866(f866(f296(x38911,x38911,x38911),f314(x38911,x38912)),f314(x38911,x38912)),f314(x38911,x38912))
% 157.60/157.50 [3926]E(f866(f866(f260(a1,a1),f866(f866(f41(a1),x39261),x39262)),f50(a1,x39261,x39262)),f51(x39261,x39262))
% 157.60/157.50 [3927]E(f866(f866(f260(a106,a106),f866(f866(f41(a106),x39271),x39272)),f50(a106,x39271,x39272)),f21(x39271,x39272))
% 157.60/157.50 [3954]E(f866(f866(f260(a930,a930),f866(f866(f41(a930),x39541),x39542)),f50(a930,x39541,x39542)),f91(f936(a930,a930),f53(x39541,x39542)))
% 157.60/157.50 [4006]P107(f866(f866(f244(a930),f866(f866(f23(a930),x40061),x40062)),f866(a119,x40061)))
% 157.60/157.50 [4056]P38(x40561,f866(f866(f296(x40561,x40561,x40561),x40562),f314(x40561,x40562)))
% 157.60/157.50 [4107]E(f866(f866(f86(a1),f866(f866(f87(a1),x41071),f866(f866(f41(a1),x41072),x41071))),f50(a1,x41072,x41071)),x41072)
% 157.60/157.50 [4111]E(f866(f866(f44(a930,f937(f936(f931(x41111),f931(x41111)),a925)),f250(f937(a930,a925))),f150(x41111,x41112)),f152(x41111,x41112))
% 157.60/157.50 [4335]P107(f866(f866(f336(f936(f931(x43351),f931(x43351))),f866(f866(f260(f931(x43351),f931(x43351)),f120(x43351)),f120(x43351))),f165(x43351,x43352)))
% 157.60/157.50 [4446]E(f261(x44461,x44461,x44461,a332,f261(x44461,x44461,x44461,x44462,a332)),x44462)
% 157.60/157.50 [4490]E(f266(x44901,x44901,x44902,x44902,f5(x44901),f5(x44902)),f32(f936(x44901,x44902)))
% 157.60/157.50 [4492]E(f266(x44921,x44921,x44922,x44922,f32(x44921),f32(x44922)),f32(f936(x44921,x44922)))
% 157.60/157.50 [3485]E(f866(f175(x34851),f866(f175(x34851),x34852)),x34852)
% 157.60/157.50 [3487]E(f866(f866(f145(x34871),f2(a930)),x34872),x34872)
% 157.60/157.50 [3503]E(f866(f866(f182(x35031),f2(a930)),x35032),f120(x35031))
% 157.60/157.50 [3510]E(f866(f866(f141(x35101),f120(x35101)),x35102),x35102)
% 157.60/157.50 [3519]E(f42(f937(x35191,a925),f866(f315(x35191),x35192)),x35192)
% 157.60/157.50 [3521]E(f866(f179(x35211),f866(f174(x35211),x35212)),f866(f179(x35211),x35212))
% 157.60/157.50 [3522]E(f866(f179(x35221),f866(f175(x35221),x35222)),f866(f179(x35221),x35222))
% 157.60/157.50 [3528]E(f866(f866(f23(a106),x35281),x35282),f866(f866(a24,x35281),x35282))
% 157.60/157.50 [3541]E(f866(f866(f87(a930),x35411),x35412),f866(f866(f87(a930),x35412),x35411))
% 157.60/157.50 [3542]E(f866(f866(f87(a1),x35421),x35422),f866(f866(f87(a1),x35422),x35421))
% 157.60/157.50 [3543]E(f866(f866(f86(a930),x35431),x35432),f866(f866(f86(a930),x35432),x35431))
% 157.60/157.50 [3544]E(f866(f866(f86(a1),x35441),x35442),f866(f866(f86(a1),x35442),x35441))
% 157.60/157.50 [3565]E(f866(f866(f190(x35651,x35651),f2(a930)),x35652),f32(x35651))
% 157.60/157.50 [3566]E(f866(f196(f931(x35661)),f866(f174(x35661),x35662)),f866(f196(f931(x35661)),x35662))
% 157.60/157.50 [3567]E(f866(f196(f931(x35671)),f866(f175(x35671),x35672)),f866(f196(f931(x35671)),x35672))
% 157.60/157.50 [3568]E(f183(x35681,x35682,f195(f937(a930,a925))),f120(x35681))
% 157.60/157.50 [3569]E(f866(f866(f161(x35691,x35691),f5(x35691)),x35692),x35692)
% 157.60/157.50 [3571]E(f866(f259(a1,a1),f51(x35711,x35712)),f866(f866(f41(a1),x35711),x35712))
% 157.60/157.50 [3588]E(f866(f196(f931(x35881)),f159(x35881,x35882)),f866(f40(x35881),f866(f179(x35881),x35882)))
% 157.60/157.50 [3589]E(f29(f30(x35891,x35892)),f866(f866(f86(a930),f29(x35892)),f866(a119,f2(a930))))
% 157.60/157.50 [3590]E(f866(f289(x35901),f866(f294(x35901,x35901),x35902)),f866(f289(x35901),x35902))
% 157.60/157.50 [3594]P107(f866(f66(x35941),f866(f179(x35941),x35942)))
% 157.60/157.50 [3602]E(f866(f866(f86(a1),x36021),f866(f85(a1),x36022)),f866(f866(f23(a1),x36021),x36022))
% 157.60/157.50 [3609]P24(x36091,x36092,f195(f937(f929(x36091),a925)))
% 157.60/157.50 [3611]E(f866(f317(x36111,x36111,f5(x36111)),x36112),x36112)
% 157.60/157.50 [3612]E(f866(f317(x36121,x36121,f32(x36121)),x36122),x36122)
% 157.60/157.50 [3613]E(f866(f318(x36131,x36131,f5(x36131)),x36132),x36132)
% 157.60/157.50 [3614]E(f866(f318(x36141,x36141,f32(x36141)),x36142),x36142)
% 157.60/157.50 [3615]P107(f866(f250(f937(x36151,a925)),x36152))
% 157.60/157.50 [3617]E(f866(f40(a930),f866(f309(a930,x36171),x36172)),f866(f866(f23(a930),x36172),x36171))
% 157.60/157.50 [3618]E(f866(f309(a930,f866(a119,x36181)),x36182),f313(a930,x36181,x36182))
% 157.60/157.50 [3631]E(f866(f866(f316(x36311),x36312),f195(f937(x36311,a925))),f866(f270(x36311),f866(a332,x36312)))
% 157.60/157.50 [3636]E(f314(x36361,f866(f294(x36361,x36361),x36362)),f866(f294(x36361,x36361),f314(x36361,x36362)))
% 157.60/157.50 [3641]E(f866(f866(f86(a930),f866(a119,x36411)),x36412),f866(f866(f86(a930),x36411),f866(a119,x36412)))
% 157.60/157.50 [3642]E(f866(f866(f23(a930),f866(a119,x36421)),f866(a119,x36422)),f866(f866(f23(a930),x36421),x36422))
% 157.60/157.50 [3648]E(f60(x36481,f2(a930),x36482),f866(f866(f158(f931(x36481)),f120(x36481)),f120(f931(x36481))))
% 157.60/157.50 [3649]E(f866(f40(a930),f312(a930,x36491,x36492)),f866(f866(f23(a930),x36492),x36491))
% 157.60/157.50 [3658]P37(x36581,f866(f866(f295(a930,x36581),a248),x36582))
% 157.60/157.50 [3660]P13(a930,f146(a930,f866(f309(a930,x36601),x36602)))
% 157.60/157.50 [3662]P107(f866(f66(a930),f866(f309(a930,x36621),x36622)))
% 157.60/157.50 [3663]P107(f866(f66(a1),f866(f309(a1,x36631),x36632)))
% 157.60/157.50 [3666]E(f866(f294(f931(x36661),f931(x36661)),f164(x36661,x36662)),f164(x36661,f866(f294(x36661,x36661),x36662)))
% 157.60/157.50 [3667]E(f866(f196(a927),f30(x36671,x36672)),f866(f866(f86(a930),f866(f196(a927),x36672)),f866(a119,f2(a930))))
% 157.60/157.50 [3669]E(f866(f309(a1,x36691),f866(f866(f86(a1),x36692),f84(a1))),f310(a1,x36691,x36692))
% 157.60/157.50 [3672]E(f866(f866(f41(a1),f866(f85(a1),x36721)),f866(f85(a1),x36722)),f866(f866(f41(a1),x36721),x36722))
% 157.60/157.50 [3680]E(f866(f866(f190(f936(x36801,x36801),a925),f84(a930)),x36802),x36802)
% 157.60/157.50 [3682]E(f866(f866(f23(f937(x36821,a925)),x36822),f195(f937(x36821,a925))),x36822)
% 157.60/157.50 [3683]E(f866(f866(f117(f937(x36831,a925)),x36832),f195(f937(x36831,a925))),x36832)
% 157.60/157.50 [3684]E(f866(f866(f108(f937(x36841,a925)),x36842),f250(f937(x36841,a925))),x36842)
% 157.60/157.50 [3685]E(f866(f259(a930,a930),f91(f936(a930,a930),f53(x36851,x36852))),f866(f866(f41(a930),x36851),x36852))
% 157.60/157.50 [3692]E(f310(a1,f866(f866(f86(a1),x36921),f84(a1)),x36922),f312(a1,x36921,x36922))
% 157.60/157.50 [3697]E(f866(f264(a930,a930),f91(f936(a930,a930),f53(x36971,x36972))),f50(a930,x36971,x36972))
% 157.60/157.50 [3707]P107(f866(f866(f336(x37071),x37072),f250(f937(x37071,a925))))
% 157.60/157.50 [3711]E(f866(f866(f23(a930),f866(a119,x37111)),x37112),f866(f40(a930),f310(a930,x37112,x37111)))
% 157.60/157.50 [3737]E(f866(f866(f23(f937(x37371,a925)),x37372),f250(f937(x37371,a925))),f195(f937(x37371,a925)))
% 157.60/157.50 [3738]E(f866(f866(f117(f937(x37381,a925)),x37382),f250(f937(x37381,a925))),f250(f937(x37381,a925)))
% 157.60/157.50 [3739]E(f866(f866(f108(f937(x37391,a925)),x37392),f195(f937(x37391,a925))),f195(f937(x37391,a925)))
% 157.60/157.50 [3754]E(f50(a1,f866(f107(a1),x37541),f866(f107(a1),x37542)),f866(f107(a1),f50(a930,x37541,x37542)))
% 157.60/157.50 [3755]E(f50(a1,f866(f85(a1),x37551),f866(f85(a1),x37552)),f866(f85(a1),f50(a1,x37551,x37552)))
% 157.60/157.50 [3766]E(f866(f196(f931(x37661)),f866(f178(x37661),x37662)),f866(f866(f23(a930),f866(f196(f931(x37661)),x37662)),f84(a930)))
% 157.60/157.50 [3792]E(f866(f866(f41(a1),f50(a1,x37921,x37922)),x37922),f2(a1))
% 157.60/157.50 [3801]E(f866(a3,f50(a930,f866(a20,x38011),f866(a20,x38012))),f50(a106,x38011,x38012))
% 157.60/157.50 [3839]E(f866(a3,f866(f866(f23(a930),f866(a20,x38391)),f866(a20,x38392))),f866(f866(f23(a106),x38391),x38392))
% 157.60/157.50 [3840]E(f866(a3,f866(f866(f87(a930),f866(a20,x38401)),f866(a20,x38402))),f866(f866(f87(a106),x38401),x38402))
% 157.60/157.50 [3841]E(f866(a3,f866(f866(f86(a930),f866(a20,x38411)),f866(a20,x38412))),f866(f866(f86(a106),x38411),x38412))
% 157.60/157.50 [3842]E(f866(a3,f866(f866(f41(a930),f866(a20,x38421)),f866(a20,x38422))),f866(f866(f41(a106),x38421),x38422))
% 157.60/157.50 [3850]E(f866(f317(a930,a930,a119),f866(f309(a930,x38501),x38502)),f866(f309(a930,f866(a119,x38501)),f866(a119,x38502)))
% 157.60/157.50 [3877]P107(f866(f53(x38771,x38772),f91(f936(a930,a930),f53(x38771,x38772))))
% 157.60/157.50 [3900]E(f866(f866(f86(a930),f866(f866(f86(a930),f29(x39001)),f29(x39002))),f866(a119,f2(a930))),f29(f31(x39001,x39002)))
% 157.60/157.50 [3901]E(f50(a930,f866(a119,f50(a930,x39011,x39012)),x39012),f50(a930,f866(a119,x39011),x39012))
% 157.60/157.50 [3913]E(f866(f866(f45(f937(x39131,a925),f937(x39131,a925)),x39132),f5(f937(x39131,a925))),f43(f937(x39131,a925),x39132))
% 157.60/157.50 [3914]E(f866(f866(f44(f937(x39141,a925),f937(x39141,a925)),x39142),f5(f937(x39141,a925))),f42(f937(x39141,a925),x39142))
% 157.60/157.50 [3915]E(f866(f317(f931(x39151),f937(x39151,a925),f179(x39151)),f866(f179(f931(x39151)),f59(x39151,x39152))),f866(f315(x39151),f866(f179(x39151),x39152)))
% 157.60/157.50 [3919]P107(f866(f866(f336(f937(x39191,a925)),x39192),f866(f315(x39191),x39192)))
% 157.60/157.50 [3925]E(f50(a1,f866(f85(a1),f50(a1,x39251,x39252)),x39252),f50(a1,f866(f85(a1),x39251),x39252))
% 157.60/157.50 [3936]P107(f866(f866(f243(f937(x39361,a925)),x39362),f250(f937(x39361,a925))))
% 157.60/157.50 [3938]E(f866(f866(f296(x39381,x39381,x39381),f314(x39381,x39382)),f314(x39381,f314(x39381,x39382))),f314(x39381,x39382))
% 157.60/157.50 [3939]E(f866(f866(f117(f937(x39391,a925)),f866(f272(x39391,x39391),x39392)),f866(f292(x39391,x39391),x39392)),f866(f289(x39391),x39392))
% 157.60/157.50 [3960]E(f320(x39601,x39602,f250(f937(x39601,a925)),f250(f937(x39602,a925))),f250(f937(f938(x39601,x39602),a925)))
% 157.60/157.50 [4011]P107(f866(f866(f243(a930),f50(a930,x40111,x40112)),x40111))
% 157.60/157.50 [4036]P107(f866(f866(f243(a1),f866(f85(a1),f866(f107(a1),x40361))),f866(f107(a1),x40362)))
% 157.60/157.50 [4061]P107(f866(f866(f336(f937(x40611,a925)),f195(f937(x40611,a925))),f866(f315(x40611),x40612)))
% 157.60/157.50 [4066]E(f314(x40661,f866(f866(f296(x40661,x40661,x40661),x40662),f314(x40661,x40662))),f314(x40661,x40662))
% 157.60/157.50 [4069]E(f866(f866(f296(x40691,x40691,x40691),f314(x40691,x40692)),x40692),f866(f866(f296(x40691,x40691,x40691),x40692),f314(x40691,x40692)))
% 157.60/157.50 [4071]E(f866(a111,f866(f866(f86(a1),f866(f866(f23(a1),x40711),x40712)),f84(a1))),f866(f40(a1),f310(a1,x40712,x40711)))
% 157.60/157.50 [4086]E(f866(f292(x40861,x40861),f866(f866(f296(x40861,x40861,x40861),x40862),f314(x40861,x40862))),f866(f292(x40861,x40861),x40862))
% 157.60/157.50 [4087]E(f866(f272(x40871,x40871),f866(f866(f296(x40871,x40871,x40871),x40872),f314(x40871,x40872))),f866(f272(x40871,x40871),x40872))
% 157.60/157.50 [4103]E(f866(f866(f86(a930),f866(f866(f86(a930),f866(f196(a927),x41031)),f866(f196(a927),x41032))),f866(a119,f2(a930))),f866(f196(a927),f31(x41031,x41032)))
% 157.60/157.50 [4106]E(f866(f149(f931(x41061),f931(x41061),f141(x41061),f120(x41061)),f176(f931(x41061),x41062,f120(x41061))),f120(x41061))
% 157.60/157.50 [4115]P25(a930,a930,f866(f866(f7(a930,a930,a930),f86(a930)),x41151),x41152)
% 157.60/157.50 [4117]P13(a930,f866(f175(a930),f866(f866(f161(f931(x41171),a930),f196(f931(x41171))),f186(x41171,x41172))))
% 157.60/157.50 [4150]P52(x41501,f866(f866(f117(f937(f936(x41501,x41501),a925)),x41502),f866(f294(x41501,x41501),x41502)))
% 157.60/157.50 [4151]P52(x41511,f866(f866(f108(f937(f936(x41511,x41511),a925)),x41512),f866(f294(x41511,x41511),x41512)))
% 157.60/157.50 [4162]P107(f866(f866(f244(a1),f866(f85(a1),f866(f107(a1),f866(a119,x41621)))),f866(f107(a1),x41622)))
% 157.60/157.50 [4207]E(f866(f149(f931(x42071),x42071,f866(f7(x42071,f931(x42071),f931(x42071)),f158(x42071)),f120(x42071)),x42072),f866(f175(x42071),x42072))
% 157.60/157.50 [4256]P107(f866(f866(f243(f937(f936(f931(x42561),f931(x42561)),a925)),f165(x42561,x42562)),f314(f931(x42561),f164(x42561,x42562))))
% 157.60/157.50 [4285]P107(f866(f53(x42851,x42852),f866(f866(f260(a930,a930),f866(f866(f41(a930),x42851),x42852)),f50(a930,x42851,x42852))))
% 157.60/157.50 [4297]P107(f866(f866(f243(f937(f936(f931(x42971),f931(x42971)),a925)),f164(x42971,f314(x42971,x42972))),f314(f931(x42971),f164(x42971,x42972))))
% 157.60/157.50 [4515]E(f866(f866(f267(f936(a106,a106),a106,f936(a106,a106),f936(x45151,f936(a106,a106))),f275(f866(f172(a106),f866(f866(f161(f936(a106,x45151),a106),f259(a106,x45151)),x45152)))),f866(f866(f8(x45151,f937(f936(a106,a106),f936(x45151,f936(a106,a106))),a106),f260(x45151,f936(a106,a106))),f276(x45151,x45152))),f274(x45151,x45152))
% 157.60/157.50 [4592]E(f232(a930,f936(x45921,f932(x45921)),f2(a930),f866(f265(x45921,f932(x45921),a930),f866(f16(f937(f932(x45921),a930),x45921),f866(f866(f7(f932(x45921),a930,a930),f866(f866(f8(a930,f937(a930,a930),f932(x45921)),f86(a930)),f196(f932(x45921)))),f84(a930)))),f866(f142(x45921),x45922)),f866(f196(f932(x45921)),x45922))
% 157.60/157.50 [4700]E(f866(f265(f937(f936(x47001,x47001),a925),f937(f936(x47001,x47001),a925),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f866(f866(f7(f937(f936(x47001,x47001),a925),f937(f937(f936(x47001,x47001),a925),f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925))),f937(f937(f936(x47001,x47001),a925),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925))))),f866(f866(f8(f937(f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925)),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f937(f937(f937(f936(x47001,x47001),a925),f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925))),f937(f937(f936(x47001,x47001),a925),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925))))),f937(f936(x47001,x47001),a925)),f8(f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925)),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925))),f937(f936(x47001,x47001),a925))),f866(f866(f8(f937(f937(x47002,x47001),f937(f937(f936(x47002,x47002),a925),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f937(f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925)),f937(f937(x47002,x47001),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f937(f936(x47001,x47001),a925)),f18(f937(x47002,x47001),f937(f936(x47002,x47002),a925),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f866(f866(f8(f937(f937(x47002,x47001),f937(f936(x47002,x47002),a925)),f937(f937(x47002,x47001),f937(f937(f936(x47002,x47002),a925),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f937(f936(x47001,x47001),a925)),f866(f8(f937(f936(x47002,x47002),a925),f937(f937(f936(x47002,x47002),a925),f936(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925))),f937(x47002,x47001)),f260(f937(f936(x47002,x47002),a925),f937(f936(x47002,x47002),a925)))),f295(x47001,x47002))))),f295(x47001,x47002))),f79(x47001,x47002))
% 157.60/157.50 [4775]~E(f866(f315(x47751),x47752),f195(f937(f937(x47751,a925),a925)))
% 157.60/157.50 [4786]~P107(f866(f866(f179(x47861),f120(x47861)),x47862))
% 157.60/157.50 [4790]~P107(f866(f866(f336(x47901),x47902),f195(f937(x47901,a925))))
% 157.60/157.50 [4798]~P107(f866(f866(f244(f937(x47981,a925)),x47982),f195(f937(x47981,a925))))
% 157.60/157.50 [3620]E(f866(f866(f23(a930),x36201),f866(f866(f86(a930),x36201),x36202)),f2(a930))
% 157.60/157.50 [3623]E(f866(f866(f117(f937(x36231,a925)),x36232),x36232),x36232)
% 157.60/157.50 [3624]E(f866(f866(f108(f937(x36241,a925)),x36242),x36242),x36242)
% 157.60/157.50 [3652]E(f866(f866(f23(f937(x36521,a925)),x36522),x36522),f195(f937(x36521,a925)))
% 157.60/157.50 [3655]E(f866(f150(x36551,x36552),f2(a930)),f195(f937(f936(f931(x36551),f931(x36551)),a925)))
% 157.60/157.50 [3656]E(f866(f866(f86(a930),x36561),f866(a119,x36562)),f866(a119,f866(f866(f86(a930),x36561),x36562)))
% 157.60/157.50 [3668]E(f201(f866(f107(a1),x36681),f866(f107(a1),x36682)),f866(f107(a1),f866(f866(f23(a930),x36681),x36682)))
% 157.60/157.50 [3671]E(f866(f866(f41(a1),f866(f85(a1),x36711)),x36712),f866(f866(f41(a1),x36711),f866(f85(a1),x36712)))
% 157.60/157.50 [3675]E(f866(f40(a1),f866(f309(a1,x36751),x36752)),f866(a111,f866(f866(f23(a1),x36752),x36751)))
% 157.60/157.50 [3678]E(f866(f866(f86(a930),f866(a119,x36781)),x36782),f866(a119,f866(f866(f86(a930),x36781),x36782)))
% 157.60/157.50 [3681]E(f866(f85(f937(x36811,a925)),f866(f85(f937(x36811,a925)),x36812)),x36812)
% 157.60/157.50 [3694]E(f186(x36941,f866(f866(f158(f931(x36941)),f120(x36941)),x36942)),f186(x36941,x36942))
% 157.60/157.50 [3698]E(f866(f866(f86(a930),x36981),f866(f866(f87(a930),x36981),x36982)),f866(f866(f87(a930),x36981),f866(a119,x36982)))
% 157.60/157.50 [3705]E(f866(f866(a24,f866(a3,x37051)),f866(a3,x37052)),f866(a3,f866(f866(f23(a930),x37051),x37052)))
% 157.60/157.50 [3719]E(f866(f866(f87(a1),f866(f85(a1),x37191)),x37192),f866(f85(a1),f866(f866(f87(a1),x37191),x37192)))
% 157.60/157.50 [3721]E(f866(f866(f252(a1),f866(f107(a1),x37211)),x37212),f866(f107(a1),f866(f866(f252(a930),x37211),x37212)))
% 157.60/157.50 [3722]E(f866(f866(f87(a106),f866(a3,x37221)),f866(a3,x37222)),f866(a3,f866(f866(f87(a930),x37221),x37222)))
% 157.60/157.50 [3723]E(f866(f866(f86(a106),f866(a3,x37231)),f866(a3,x37232)),f866(a3,f866(f866(f86(a930),x37231),x37232)))
% 157.60/157.50 [3724]E(f866(f866(f241(a930),f866(a119,x37241)),f866(a119,x37242)),f866(a119,f866(f866(f241(a930),x37241),x37242)))
% 157.60/157.50 [3725]E(f866(f866(f242(a930),f866(a119,x37251)),f866(a119,x37252)),f866(a119,f866(f866(f242(a930),x37251),x37252)))
% 157.60/157.50 [3730]E(f866(f179(a930),f146(a930,f866(f309(a930,x37301),x37302))),f866(f309(a930,x37301),x37302))
% 157.60/157.50 [3731]E(f319(x37311,f866(f866(f316(x37311),x37312),f195(f937(x37311,a925)))),x37312)
% 157.60/157.50 [3735]E(f866(f292(x37351,x37352),f195(f937(f936(x37351,x37352),a925))),f195(f937(x37352,a925)))
% 157.60/157.50 [3736]E(f866(f272(x37361,x37362),f195(f937(f936(x37361,x37362),a925))),f195(f937(x37361,a925)))
% 157.60/157.50 [3740]E(f866(a111,f866(f866(f23(a1),x37401),x37402)),f866(f40(a1),f312(a1,x37402,x37401)))
% 157.60/157.50 [3745]E(f866(f866(f86(a930),x37451),f866(f866(f87(a930),x37452),x37451)),f866(f866(f87(a930),f866(a119,x37452)),x37451))
% 157.60/157.50 [3747]E(f866(f866(f65(x37471),f195(f937(x37471,a925))),x37472),f195(f937(f937(x37471,a925),a925)))
% 157.60/157.50 [3756]E(f866(f196(f931(a930)),f146(a930,f866(f309(a930,x37561),x37562))),f866(f866(f23(a930),x37562),x37561))
% 157.60/157.50 [3771]E(f866(f866(f117(f937(x37711,a925)),f195(f937(x37711,a925))),x37712),x37712)
% 157.60/157.50 [3772]E(f866(f866(f108(f937(x37721,a925)),f250(f937(x37721,a925))),x37722),x37722)
% 157.60/157.50 [3775]E(f866(f866(f86(a1),f866(f85(a1),x37751)),f866(f85(a1),x37752)),f866(f85(a1),f866(f866(f86(a1),x37751),x37752)))
% 157.60/157.50 [3778]E(f866(f866(f87(a1),f866(f107(a1),x37781)),f866(f107(a1),x37782)),f866(f107(a1),f866(f866(f87(a930),x37781),x37782)))
% 157.60/157.50 [3779]E(f866(f866(f87(a1),f866(f110(a1),x37791)),f866(f110(a1),x37792)),f866(f110(a1),f866(f866(f87(a1),x37791),x37792)))
% 157.60/157.50 [3781]E(f866(f866(f86(a1),f866(f107(a1),x37811)),f866(f107(a1),x37812)),f866(f107(a1),f866(f866(f86(a930),x37811),x37812)))
% 157.60/157.50 [3782]E(f866(f866(f86(a1),f866(f110(a1),x37821)),f866(f110(a1),x37822)),f866(f110(a1),f866(f866(f86(a1),x37821),x37822)))
% 157.60/157.50 [3783]E(f866(f866(f41(a1),f866(f107(a1),x37831)),f866(f107(a1),x37832)),f866(f107(a1),f866(f866(f41(a930),x37831),x37832)))
% 157.60/157.50 [3802]E(f866(f866(f6(x38021,a930),f866(f16(a930,x38021),f84(a930))),x38022),f866(f40(x38021),x38022))
% 157.60/157.50 [3812]E(f866(f85(a1),f50(a1,f866(f85(a1),x38121),x38122)),f50(a1,x38121,f866(f85(a1),x38122)))
% 157.60/157.50 [3814]E(f866(f179(a1),f185(x38141,f866(f866(f23(a1),x38142),f84(a1)))),f866(f309(a1,x38141),x38142))
% 157.60/157.50 [3819]P107(f866(f866(f243(a930),x38191),f866(f866(f86(a930),x38192),x38191)))
% 157.60/157.50 [3820]P107(f866(f866(f243(a930),x38201),f866(f866(f86(a930),x38201),x38202)))
% 157.60/157.50 [3822]E(f866(f866(f23(f937(x38221,a925)),f195(f937(x38221,a925))),x38222),f195(f937(x38221,a925)))
% 157.60/157.50 [3823]E(f866(f866(f117(f937(x38231,a925)),f250(f937(x38231,a925))),x38232),f250(f937(x38231,a925)))
% 157.60/157.50 [3824]E(f866(f866(f108(f937(x38241,a925)),f195(f937(x38241,a925))),x38242),f195(f937(x38241,a925)))
% 157.60/157.50 [3831]E(f866(f866(f260(a1,a1),x38311),f866(f85(a1),x38312)),f866(a56,f866(f866(f260(a1,a1),x38311),x38312)))
% 157.60/157.50 [3832]E(f866(f309(a1,f866(f866(f86(a1),x38321),f84(a1))),x38322),f313(a1,x38321,x38322))
% 157.60/157.50 [3843]E(f866(f866(f87(a930),x38431),f866(f866(f41(a930),x38432),x38431)),f866(f866(f23(a930),x38432),f50(a930,x38432,x38431)))
% 157.60/157.50 [3844]E(f866(f866(f87(a1),x38441),f866(f866(f41(a1),x38442),x38441)),f866(f866(f23(a1),x38442),f50(a1,x38442,x38441)))
% 157.60/157.50 [3847]E(f866(f179(a1),f185(f866(f866(f86(a1),x38471),f84(a1)),x38472)),f312(a1,x38471,x38472))
% 157.60/157.50 [3851]P107(f866(f866(f243(f937(x38511,a925)),x38512),x38512))
% 157.60/157.50 [3854]E(f866(f866(f117(f937(x38541,a925)),x38542),f866(f85(f937(x38541,a925)),x38542)),f250(f937(x38541,a925)))
% 157.60/157.50 [3855]E(f866(f866(f108(f937(x38551,a925)),x38552),f866(f85(f937(x38551,a925)),x38552)),f195(f937(x38551,a925)))
% 157.60/157.50 [3863]E(f866(f866(f23(a930),f866(f866(f23(a930),x38631),f84(a930))),x38632),f866(f866(f23(a930),x38631),f866(a119,x38632)))
% 157.60/157.50 [3869]E(f866(f866(f23(f937(x38691,a925)),f250(f937(x38691,a925))),x38692),f866(f85(f937(x38691,a925)),x38692))
% 157.60/157.50 [3870]E(f866(f866(f23(a1),f866(f110(a1),x38701)),f866(f110(a1),x38702)),f866(f110(a1),f866(f866(f86(a1),x38701),f866(f85(a1),x38702))))
% 157.60/157.50 [3883]E(f866(f179(a930),f146(a930,f866(f309(a930,x38831),f866(a119,x38832)))),f310(a930,x38831,x38832))
% 157.60/157.50 [3898]E(f866(f196(f931(f931(x38981))),f59(x38981,x38982)),f866(f866(f252(a930),f866(a119,f866(a119,f2(a930)))),f866(f196(f931(x38981)),x38982)))
% 157.60/157.50 [3917]E(f866(f866(f190(f936(x39171,x39171),a925),f2(a930)),x39172),f314(x39171,f195(f937(f936(x39171,x39171),a925))))
% 157.60/157.50 [3921]P107(f866(f144(a930),f146(a930,f866(f309(a930,x39211),x39212))))
% 157.60/157.50 [3937]E(f866(f317(a1,a930,a111),f310(a1,f866(f107(a1),x39371),f866(f107(a1),x39372))),f310(a930,x39371,x39372))
% 157.60/157.50 [3946]E(f192(a930,f2(a930),f5(a930),f866(f866(f23(a930),x39461),x39462)),f866(f866(f23(a930),x39461),f866(a119,x39462)))
% 157.60/157.50 [3947]E(f866(a111,f866(f866(f23(a1),x39471),f866(f866(f86(a1),x39472),f84(a1)))),f866(f40(a1),f313(a1,x39472,x39471)))
% 157.60/157.50 [3983]E(f866(f866(f161(a930,a930),a119),f146(a930,f866(f309(a930,x39831),x39832))),f146(a930,f866(f309(a930,f866(a119,x39831)),f866(a119,x39832))))
% 157.60/157.50 [3991]E(f866(f179(a1),f185(f866(f866(f86(a1),x39911),f84(a1)),f866(f866(f23(a1),x39912),f84(a1)))),f313(a1,x39911,x39912))
% 157.60/157.50 [4003]P107(f866(f866(f243(f937(x40031,a925)),f195(f937(x40031,a925))),x40032))
% 157.60/157.50 [4007]E(f91(x40071,f866(f866(f7(x40071,x40071,a925),a332),x40072)),x40072)
% 157.60/157.50 [4008]E(f96(x40081,f866(f866(f7(x40081,x40081,a925),a332),x40082)),x40082)
% 157.60/157.50 [4012]E(f866(f179(a930),f146(a930,f866(f309(a930,f866(a119,x40121)),f866(a119,x40122)))),f312(a930,x40121,x40122))
% 157.60/157.50 [4039]E(f866(f866(f262(x40391,x40392),f250(f937(x40391,a925))),f866(f16(f937(x40392,a925),x40391),f250(f937(x40392,a925)))),f250(f937(f936(x40391,x40392),a925)))
% 157.60/157.50 [4073]E(f866(f270(x40731),f866(f866(f8(a925,a925,x40731),a329),x40732)),f866(f85(f937(x40731,a925)),f866(f270(x40731),x40732)))
% 157.60/157.50 [4076]E(f866(f270(x40761),f866(f866(f7(x40761,x40761,a925),a332),x40762)),f866(f866(f316(x40761),x40762),f195(f937(x40761,a925))))
% 157.60/157.50 [4083]E(f866(f866(f86(a1),f866(f866(f23(a1),x40831),x40832)),f866(f866(f23(a1),x40831),x40832)),f866(f866(f23(a1),f866(f866(f86(a1),x40831),x40831)),f866(f866(f86(a1),x40832),x40832)))
% 157.60/157.50 [4084]E(f866(f866(f86(a1),f866(f866(f86(a1),x40841),x40841)),f866(f866(f86(a1),x40842),x40842)),f866(f866(f86(a1),f866(f866(f86(a1),x40841),x40842)),f866(f866(f86(a1),x40841),x40842)))
% 157.60/157.50 [4100]P107(f866(f866(f243(a930),f866(f40(x41001),f866(f179(x41001),x41002))),f866(f196(f931(x41001)),x41002)))
% 157.60/157.50 [4101]P107(f866(f866(f243(a930),f866(f196(f931(x41011)),f159(x41011,x41012))),f866(f196(f931(x41011)),x41012)))
% 157.60/157.50 [4112]E(f866(f270(x41121),f866(f866(f7(x41121,f937(x41121,a925),a925),f336(x41121)),x41122)),x41122)
% 157.60/157.50 [4126]E(f866(f866(f182(x41261),f866(f866(f23(a930),f866(f196(f931(x41261)),x41262)),f84(a930))),x41262),f121(x41261,x41262))
% 157.60/157.50 [4149]E(f192(a930,f2(a930),f866(f866(f8(a930,a930,a930),a119),f866(f241(a930),x41491)),x41492),f866(f866(f241(a930),f866(a119,x41491)),x41492))
% 157.60/157.50 [4154]E(f42(f937(x41541,a925),f866(f317(f937(f936(x41541,x41541),a925),f937(x41541,a925),f289(x41541)),x41542)),f866(f289(x41541),f42(f937(f936(x41541,x41541),a925),x41542)))
% 157.60/157.50 [4155]E(f192(a930,f866(a119,x41551),f866(f866(f8(a930,a930,a930),a119),f866(f242(a930),x41551)),x41552),f866(f866(f242(a930),f866(a119,x41551)),x41552))
% 157.60/157.50 [4157]E(f866(f866(f260(a1,a1),f866(f866(f41(a1),f866(f81(a1),x41571)),f866(f81(a1),x41572))),f50(a1,f866(f81(a1),x41571),f866(f81(a1),x41572))),f58(x41571,x41572))
% 157.60/157.50 [4180]P107(f866(f866(f243(f937(f937(x41801,a925),a925)),x41802),f866(f315(x41801),f42(f937(x41801,a925),x41802))))
% 157.60/157.50 [4212]E(f866(f866(f44(x42121,f937(x42121,a925)),x42122),f866(f866(f7(x42121,f937(x42121,a925),f937(x42121,a925)),f316(x42121)),f195(f937(x42121,a925)))),x42122)
% 157.60/157.50 [4213]E(f866(f866(f296(x42131,x42131,x42131),f866(f294(x42131,x42131),x42132)),f314(x42131,f866(f294(x42131,x42131),x42132))),f866(f294(x42131,x42131),f866(f866(f296(x42131,x42131,x42131),x42132),f314(x42131,x42132))))
% 157.60/157.50 [4277]E(f866(f179(x42771),f866(f149(f931(x42771),f931(x42771),f141(x42771),f120(x42771)),x42772)),f866(f866(f44(f931(x42771),f937(x42771,a925)),f866(f179(f931(x42771)),x42772)),f179(x42771)))
% 157.60/157.50 [4308]E(f866(f866(f117(f937(f936(x43081,x43081),a925)),f314(x43081,f195(f937(f936(x43081,x43081),a925)))),f866(f866(f296(x43081,x43081,x43081),f314(x43081,x43082)),x43082)),f314(x43081,x43082))
% 157.60/157.50 [4344]E(f866(f866(f188(x43441,x43441),x43442),x43442),f866(f866(f161(x43441,f936(x43441,x43441)),f866(f866(f18(x43441,x43441,f936(x43441,x43441)),f260(x43441,x43441)),f5(x43441))),x43442))
% 157.60/157.50 [4457]E(f866(f149(a930,f931(x44571),f866(f7(f931(x44571),a930,a930),f866(f866(f8(a930,f937(a930,a930),f931(x44571)),f242(a930)),f196(f931(x44571)))),f2(a930)),f866(f175(f931(x44571)),x44572)),f866(f196(f931(f931(x44571))),f186(x44571,x44572)))
% 157.60/157.50 [4529]E(f866(f866(f295(f936(a930,f931(x45291)),f931(x45291)),f326(a930,f931(x45291),a248,f152(x45291,x45292))),f866(f866(f18(f931(x45291),f931(x45291),f936(a930,f931(x45291))),f866(f866(f8(a930,f937(f931(x45291),f936(a930,f931(x45291))),f931(x45291)),f260(a930,f931(x45291))),f196(f931(x45291)))),f5(f931(x45291)))),f153(x45291,x45292))
% 157.60/157.50 [4656]E(f866(f270(x46561),f866(f866(f8(f937(f937(x46561,a925),a925),a925,x46561),f94(f937(x46561,a925))),f866(f866(f8(f937(f937(x46561,a925),a925),f937(f937(x46561,a925),a925),x46561),f866(f18(f937(x46561,a925),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x46561,a925)),a337),f866(f866(f7(f937(x46561,a925),f937(f937(x46561,a925),a925),a925),f336(f937(x46561,a925))),x46562)))),f336(x46561)))),f43(f937(x46561,a925),x46562))
% 157.60/157.50 [4657]E(f866(f270(x46571),f866(f866(f8(f937(f937(x46571,a925),a925),a925,x46571),f93(f937(x46571,a925))),f866(f866(f8(f937(f937(x46571,a925),a925),f937(f937(x46571,a925),a925),x46571),f866(f18(f937(x46571,a925),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x46571,a925)),a333),f866(f866(f7(f937(x46571,a925),f937(f937(x46571,a925),a925),a925),f336(f937(x46571,a925))),x46572)))),f336(x46571)))),f42(f937(x46571,a925),x46572))
% 157.60/157.50 [4799]~P107(f866(f866(f244(a1),f866(f107(a1),x47991)),f866(f85(a1),f866(f107(a1),x47992))))
% 157.60/157.50 [3743]E(f866(f866(f23(a930),f866(f866(f86(a930),x37431),x37432)),x37432),x37431)
% 157.60/157.50 [3744]E(f866(f866(f23(a930),f866(f866(f86(a930),x37441),x37442)),x37441),x37442)
% 157.60/157.50 [3813]E(f866(f866(f86(a930),f866(f866(f23(a930),x38131),x38132)),x38132),f866(f866(f242(a930),x38131),x38132))
% 157.60/157.50 [3924]E(f866(f866(f87(a930),f866(f866(f41(a930),x39241),x39242)),x39242),f866(f866(f23(a930),x39241),f50(a930,x39241,x39242)))
% 157.60/157.50 [3951]E(f866(f179(a930),f146(a930,f866(f309(a930,f866(a119,x39511)),x39512))),f313(a930,x39511,x39512))
% 157.60/157.50 [3959]E(f866(f107(a1),f225(f866(a111,f866(f81(a1),x39591)),f866(a111,f866(f81(a1),x39592)))),f866(f866(a226,x39591),x39592))
% 157.60/157.50 [3961]E(f866(f866(f117(f937(x39611,a925)),f866(f85(f937(x39611,a925)),x39612)),x39612),f250(f937(x39611,a925)))
% 157.60/157.50 [3962]E(f866(f866(f108(f937(x39621,a925)),f866(f85(f937(x39621,a925)),x39622)),x39622),f195(f937(x39621,a925)))
% 157.60/157.50 [3979]P107(f866(f866(f243(a930),f866(f866(f23(a930),x39791),x39792)),x39791))
% 157.60/157.50 [3980]P107(f866(f866(f243(a930),f866(f866(f41(a930),x39801),x39802)),x39801))
% 157.60/157.50 [4004]P107(f866(f866(f244(a930),x40041),f866(a119,f866(f866(f86(a930),x40042),x40041))))
% 157.60/157.50 [4005]P107(f866(f866(f244(a930),x40051),f866(a119,f866(f866(f86(a930),x40051),x40052))))
% 157.60/157.50 [4023]E(f866(f866(f87(a930),f866(a111,f866(f81(a1),x40231))),f866(a111,f866(f81(a1),x40232))),f866(a111,f866(f81(a1),f866(f866(f87(a1),x40231),x40232))))
% 157.60/157.50 [4035]P107(f866(f866(f243(a1),f2(a1)),f866(f866(f252(a1),f866(f81(a1),x40351)),x40352)))
% 157.60/157.50 [4105]E(f866(f293(f931(x41051),f931(x41051),f165(x41051,x41052)),f866(f866(f316(f931(x41051)),f120(x41051)),f195(f937(f931(x41051),a925)))),f866(f866(f316(f931(x41051)),f120(x41051)),f195(f937(f931(x41051),a925))))
% 157.60/157.50 [4124]E(f866(f866(f117(f937(f936(x41241,x41241),a925)),f314(x41241,x41242)),f314(x41241,f195(f937(f936(x41241,x41241),a925)))),f314(x41241,x41242))
% 157.60/157.50 [4137]E(f866(f866(f41(a1),f866(f110(a1),f866(f866(f86(a1),x41371),x41371))),f866(f110(a1),f866(f866(f86(a1),x41372),x41372))),f866(f866(f41(a1),f866(f110(a1),x41371)),f866(f110(a1),x41372)))
% 157.60/157.50 [4202]E(f866(f866(f252(a1),x42021),f866(f110(a930),f866(f866(f86(a1),x42022),x42022))),f866(f866(f92(a1,a1),f866(f866(f252(a1),x42021),f866(f110(a930),x42022))),f866(f866(f18(a1,a1,a1),f87(a1)),f5(a1))))
% 157.60/157.50 [4208]E(f866(f270(f937(x42081,a925)),f866(f866(f7(f937(x42081,a925),f937(x42081,a925),a925),f243(f937(x42081,a925))),x42082)),f866(f315(x42081),x42082))
% 157.60/157.50 [4224]E(f866(f866(f161(a1,a930),a111),f866(f866(f141(a1),f866(f866(f161(a930,a1),f107(a1)),x42241)),f866(f866(f161(a930,a1),f107(a1)),x42242))),f866(f866(f141(a930),x42241),x42242))
% 157.60/157.50 [4255]E(f866(f317(a1,a1,f866(f866(f7(a1,a1,a1),f86(a1)),x42551)),f866(f309(a1,f2(a1)),f866(f866(f23(a1),x42552),x42551))),f866(f309(a1,x42551),x42552))
% 157.60/157.50 [4257]P54(x42571,f866(f866(f23(f937(f936(x42571,x42571),a925)),x42572),f314(x42571,f195(f937(f936(x42571,x42571),a925)))))
% 157.60/157.50 [4275]E(f866(f196(f931(x42751)),f866(f149(f931(x42751),f931(x42751),f141(x42751),f120(x42751)),x42752)),f866(f172(a930),f866(f866(f161(f931(x42751),a930),f196(f931(x42751))),x42752)))
% 157.60/157.50 [4279]P53(x42791,f250(f937(x42791,a925)),f866(f866(f117(f937(f936(x42791,x42791),a925)),x42792),f314(x42791,f195(f937(f936(x42791,x42791),a925)))))
% 157.60/157.50 [4324]E(f192(a930,f2(a930),f866(f866(f8(a930,a930,a930),a119),f866(f866(f7(a930,a930,a930),f241(a930)),x43241)),x43242),f866(f866(f241(a930),x43242),f866(a119,x43241)))
% 157.60/157.50 [4327]E(f192(a930,f866(a119,x43271),f866(f866(f8(a930,a930,a930),a119),f866(f866(f7(a930,a930,a930),f242(a930)),x43271)),x43272),f866(f866(f242(a930),x43272),f866(a119,x43271)))
% 157.60/157.50 [4330]E(f866(f317(x43301,f931(x43301),f866(f866(f7(x43301,f931(x43301),f931(x43301)),f158(x43301)),f120(x43301))),x43302),f181(x43301,x43302,f866(f866(f316(f931(x43301)),f120(x43301)),f195(f937(f931(x43301),a925)))))
% 157.60/157.50 [4332]E(f866(f866(f117(f937(f936(x43321,x43321),a925)),f866(f866(f296(x43321,x43321,x43321),x43322),f314(x43321,x43322))),f314(x43321,f195(f937(f936(x43321,x43321),a925)))),f314(x43321,x43322))
% 157.60/157.50 [4339]P107(f866(f866(f243(f937(f936(x43391,x43391),a925)),f271(x43391,x43392)),f866(f866(f262(x43391,x43391),x43392),f866(f16(f937(x43391,a925),x43391),x43392))))
% 157.60/157.50 [4342]E(f866(f317(a1,a930,a111),f866(f866(f117(f937(a1,a925)),f866(f317(a930,a1,f107(a1)),x43421)),f866(f317(a930,a1,f107(a1)),x43422))),f866(f866(f117(f937(a930,a925)),x43421),x43422))
% 157.60/157.50 [4343]E(f866(f317(a1,a930,a111),f866(f866(f108(f937(a1,a925)),f866(f317(a930,a1,f107(a1)),x43431)),f866(f317(a930,a1,f107(a1)),x43432))),f866(f866(f108(f937(a930,a925)),x43431),x43432))
% 157.60/157.50 [4346]E(f866(f270(x43461),f866(f866(f8(a925,a925,x43461),a329),f866(f866(f7(x43461,f937(x43461,a925),a925),f336(x43461)),x43462))),f866(f85(f937(x43461,a925)),x43462))
% 157.60/157.50 [4373]E(f866(f149(f931(x43731),f931(x43731),f141(x43731),f120(x43731)),f866(f866(f161(f931(x43731),f931(x43731)),f175(x43731)),f866(f175(f931(x43731)),x43732))),f866(f175(x43731),f866(f149(f931(x43731),f931(x43731),f141(x43731),f120(x43731)),x43732)))
% 157.60/157.50 [4401]E(f866(f866(f44(a930,f937(f936(x44011,x44011),a925)),f250(f937(a930,a925))),f866(f866(f7(a930,f937(f936(x44011,x44011),a925),f937(f936(x44011,x44011),a925)),f190(f936(x44011,x44011),a925)),x44012)),f314(x44011,x44012))
% 157.60/157.50 [4419]E(f91(x44191,f866(f866(f8(f937(x44191,a925),a925,x44191),f866(a332,x44192)),f866(f866(f7(x44191,f937(x44191,a925),f937(x44191,a925)),f316(x44191)),f195(f937(x44191,a925))))),f319(x44191,x44192))
% 157.60/157.50 [4427]E(f866(f196(f931(x44271)),f159(x44271,f866(f149(f931(x44271),f931(x44271),f141(x44271),f120(x44271)),x44272))),f866(f40(x44271),f866(f866(f44(f931(x44271),f937(x44271,a925)),f866(f179(f931(x44271)),x44272)),f179(x44271))))
% 157.60/157.50 [4441]E(f866(f866(f117(f937(f936(x44411,x44411),a925)),x44412),f866(f866(f296(x44411,x44411,x44411),f866(f866(f296(x44411,x44411,x44411),x44412),f314(x44411,x44412))),x44412)),f866(f866(f296(x44411,x44411,x44411),x44412),f314(x44411,x44412)))
% 157.60/157.50 [4465]P107(f866(f866(f243(f937(f936(x44651,x44651),a925)),f866(f866(f296(x44651,x44651,x44651),x44652),f314(x44651,x44652))),f866(f866(f262(x44651,x44651),f866(f289(x44651),x44652)),f866(f16(f937(x44651,a925),x44651),f866(f289(x44651),x44652)))))
% 157.60/157.50 [4506]E(f866(f270(f931(x45061)),f866(f866(f7(f931(x45061),f937(x45061,a925),a925),f866(f866(f8(f937(x45061,a925),f937(f937(x45061,a925),a925),f931(x45061)),f243(f937(x45061,a925))),f179(x45061))),x45062)),f168(x45061,x45062))
% 157.60/157.50 [4517]E(f866(f163(f931(x45171),x45171,f120(x45171),f866(f866(f8(f931(x45171),f937(f931(x45171),f931(x45171)),x45171),f866(f7(f931(x45171),f931(x45171),f931(x45171)),f141(x45171))),f866(f866(f7(x45171,f931(x45171),f931(x45171)),f158(x45171)),f120(x45171)))),x45172),f866(f174(x45171),x45172))
% 157.60/157.50 [4557]P25(f937(x45571,x45572),f937(f936(x45571,x45572),a925),f866(f866(f8(f937(f936(x45571,x45572),a925),f937(f936(x45571,x45572),a925),f937(x45571,x45572)),f270(f936(x45571,x45572))),f866(f866(f8(f937(x45571,f937(x45572,a925)),f937(f936(x45571,x45572),a925),f937(x45571,x45572)),f265(x45571,x45572,a925)),f866(f8(x45572,f937(x45572,a925),x45571),f866(f7(x45572,x45572,a925),a332)))),f250(f937(f937(x45571,x45572),a925)))
% 157.60/157.50 [4562]E(f50(a1,f866(f110(a1),f866(f866(f86(a1),x45621),x45621)),f866(f110(a1),f866(f866(f86(a1),x45622),x45622))),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a1,f866(f110(a1),x45621),f866(f110(a1),x45622))))
% 157.60/157.50 [4606]E(f866(f866(f44(x46061,f937(f936(x46061,x46061),a925)),x46062),f866(f866(f7(x46061,f937(f936(x46061,x46061),a925),f937(f936(x46061,x46061),a925)),f866(f866(f8(f936(x46061,x46061),f937(f937(f936(x46061,x46061),a925),f937(f936(x46061,x46061),a925)),x46061),f316(f936(x46061,x46061))),f866(f866(f18(x46061,x46061,f936(x46061,x46061)),f260(x46061,x46061)),f5(x46061)))),f195(f937(f936(x46061,x46061),a925)))),f271(x46061,x46062))
% 157.60/157.50 [4614]E(f211(x46141,f866(f866(f260(a1,a1),f866(f85(a1),f866(f866(f78(f936(a1,a1),a1,x46141,f259(a1,a1)),f221(x46141)),x46142))),f866(f866(f78(f936(a1,a1),a1,x46141,f264(a1,a1)),f221(x46141)),x46142))),f236(x46141,x46142))
% 157.60/157.50 [4697]E(f866(f270(f937(x46971,a925)),f866(f866(f8(f937(f937(x46971,a925),a925),a925,f937(x46971,a925)),f93(f937(x46971,a925))),f866(f866(f7(f937(x46971,a925),f937(f937(x46971,a925),a925),f937(f937(x46971,a925),a925)),f866(f866(f8(f937(f937(x46971,a925),f937(a925,a925)),f937(f937(f937(x46971,a925),a925),f937(f937(x46971,a925),a925)),f937(x46971,a925)),f18(f937(x46971,a925),a925,a925)),f866(f866(f8(f937(f937(x46971,a925),a925),f937(f937(x46971,a925),f937(a925,a925)),f937(x46971,a925)),f866(f8(a925,f937(a925,a925),f937(x46971,a925)),a333)),f866(f866(f7(f937(x46971,a925),f937(f937(x46971,a925),f937(x46971,a925)),f937(f937(x46971,a925),a925)),f866(f866(f8(f937(f937(x46971,a925),a925),f937(f937(f937(x46971,a925),f937(x46971,a925)),f937(f937(x46971,a925),a925)),f937(x46971,a925)),f8(f937(x46971,a925),a925,f937(x46971,a925))),a332)),f85(f937(x46971,a925)))))),f866(f866(f8(f937(f937(x46971,a925),a925),a925,f937(x46971,a925)),f866(f336(f937(x46971,a925)),x46972)),f315(x46971))))),f866(f315(x46971),f866(f85(f937(x46971,a925)),x46972)))
% 157.60/157.50 [4797]~E(f866(f866(f86(a1),x47971),x47971),f866(f866(f23(a1),f866(f866(f86(a1),x47972),x47972)),a104))
% 157.60/157.50 [4801]~P107(f866(f866(f244(a930),f866(f866(f86(a930),x48011),x48012)),x48012))
% 157.60/157.50 [4802]~P107(f866(f866(f244(a930),f866(f866(f86(a930),x48021),x48022)),x48021))
% 157.60/157.50 [4040]E(f866(f866(f23(a930),x40401),f866(f866(f87(a930),f866(f866(f41(a930),x40401),x40402)),x40402)),f50(a930,x40401,x40402))
% 157.60/157.50 [4041]E(f866(f866(f23(a1),x40411),f866(f866(f87(a1),f866(f866(f41(a1),x40411),x40412)),x40412)),f50(a1,x40411,x40412))
% 157.60/157.50 [4074]E(f866(f866(f161(a930,x40741),f866(f171(x40741),x40742)),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(x40741)),x40742)))),x40742)
% 157.60/157.50 [4133]E(f866(f293(x41331,x41331,f314(x41331,f195(f937(f936(x41331,x41331),a925)))),x41332),x41332)
% 157.60/157.50 [4260]E(f314(x42601,f866(f866(f23(f937(f936(x42601,x42601),a925)),x42602),f314(x42601,f195(f937(f936(x42601,x42601),a925))))),f314(x42601,x42602))
% 157.60/157.50 [4261]E(f314(x42611,f866(f866(f117(f937(f936(x42611,x42611),a925)),x42612),f314(x42611,f195(f937(f936(x42611,x42611),a925))))),f314(x42611,x42612))
% 157.60/157.50 [4311]E(f866(f866(f23(a1),f866(f866(f23(a1),f866(f866(f86(a1),x43111),x43111)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x43112),x43112)),a104)),f866(f866(f86(a1),f866(f866(f23(a1),x43111),x43112)),f866(f866(f23(a1),x43111),x43112)))
% 157.60/157.50 [4351]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f86(a1),x43511),x43512)),f866(f866(f86(a1),x43511),x43512))),a104),f866(f866(f86(a1),f866(f866(f86(a1),x43511),x43511)),f866(f866(f23(a1),f866(f866(f86(a1),x43512),x43512)),a104)))
% 157.60/157.50 [4376]E(f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),x43761),x43761)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x43762),x43762)),a104)),f866(f866(f86(a1),f866(f866(f86(a1),x43761),f866(f866(f23(a1),x43762),a104))),f866(f866(f86(a1),x43761),f866(f866(f23(a1),x43762),a104))))
% 157.60/157.50 [4389]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),x43891),x43892)),f866(f866(f23(a1),x43891),x43892))),a104),f866(f866(f23(a1),f866(f866(f23(a1),f866(f866(f86(a1),x43891),x43891)),a104)),f866(f866(f86(a1),x43892),x43892)))
% 157.60/157.50 [4390]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f86(a1),x43901),x43902)),f866(f866(f86(a1),x43901),x43902))),a104),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),x43901),x43901)),a104)),f866(f866(f86(a1),x43902),x43902)))
% 157.60/157.50 [4438]E(f866(f107(a1),f866(f866(f41(a930),f866(f866(f87(a930),f866(a111,f866(f81(a1),x44381))),f866(a111,f866(f81(a1),x44382)))),f225(f866(a111,f866(f81(a1),x44381)),f866(a111,f866(f81(a1),x44382))))),f227(x44381,x44382))
% 157.60/157.50 [4483]E(f866(f866(f267(f936(a106,a106),a106,f936(a106,a106),f936(x44831,f936(a106,a106))),f275(f866(a3,f866(f196(f931(x44831)),x44832)))),f866(f866(f8(x44831,f937(f936(a106,a106),f936(x44831,f936(a106,a106))),a106),f260(x44831,f936(a106,a106))),f866(f866(f8(a930,x44831,a106),f866(f171(x44831),x44832)),a20))),f283(x44831,x44832))
% 157.60/157.50 [4563]E(f866(f149(a930,f931(x45631),f866(f7(f931(x45631),a930,a930),f866(f866(f8(a930,f937(a930,a930),f931(x45631)),f242(a930)),f196(f931(x45631)))),f2(a930)),f866(f175(f931(x45631)),f186(x45631,x45632))),f866(f196(f931(f931(x45631))),f866(f143(f931(x45631),f866(f866(f8(a925,a925,f931(x45631)),a329),f866(f866(f7(f931(x45631),f931(x45631),a925),a332),f120(x45631)))),x45632)))
% 157.60/157.50 [4569]E(f866(f866(f44(a930,f937(x45691,a925)),f250(f937(a930,a925))),f866(f866(f7(a930,f937(a930,f937(x45691,a925)),f937(x45691,a925)),f866(f866(f8(f937(a930,a925),f937(f937(a930,f937(x45691,a925)),f937(x45691,a925)),a930),f44(a930,f937(x45691,a925))),f309(a930,f2(a930)))),x45692)),f866(f866(f44(a930,f937(x45691,a925)),f250(f937(a930,a925))),x45692))
% 157.60/157.50 [4591]P107(f866(f66(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),x45911)),f866(f866(f7(a930,a930,a925),f244(a930)),x45912)))))
% 157.60/157.50 [4705]E(f866(f270(f936(f931(x47051),f931(x47051))),f866(f265(f931(x47051),f931(x47051),a925),f866(f866(f18(f931(x47051),f937(f931(x47051),a925),f937(f931(x47051),a925)),f866(f866(f8(f937(f931(x47051),f937(a925,a925)),f937(f937(f931(x47051),a925),f937(f931(x47051),a925)),f931(x47051)),f18(f931(x47051),a925,a925)),f866(f866(f8(f937(f931(x47051),a925),f937(f931(x47051),f937(a925,a925)),f931(x47051)),f866(f8(a925,f937(a925,a925),f931(x47051)),a334)),f866(f866(f7(f931(x47051),f937(f931(x47051),a930),f937(f931(x47051),a925)),f866(f866(f8(f937(a930,a925),f937(f937(f931(x47051),a930),f937(f931(x47051),a925)),f931(x47051)),f8(a930,a925,f931(x47051))),f866(f866(f8(a930,f937(a930,a925),f931(x47051)),f244(a930)),f196(f931(x47051))))),f196(f931(x47051)))))),f866(f866(f18(f931(x47051),f937(f931(x47051),a925),f937(f931(x47051),a925)),f866(f866(f8(f937(f931(x47051),f937(a925,a925)),f937(f937(f931(x47051),a925),f937(f931(x47051),a925)),f931(x47051)),f18(f931(x47051),a925,a925)),f866(f866(f8(f937(f931(x47051),a925),f937(f931(x47051),f937(a925,a925)),f931(x47051)),f866(f8(a925,f937(a925,a925),f931(x47051)),a333)),f866(f866(f7(f931(x47051),f937(f931(x47051),a930),f937(f931(x47051),a925)),f866(f866(f8(f937(a930,a925),f937(f937(f931(x47051),a930),f937(f931(x47051),a925)),f931(x47051)),f8(a930,a925,f931(x47051))),f866(f866(f8(a930,f937(a930,a925),f931(x47051)),a332),f196(f931(x47051))))),f196(f931(x47051)))))),f866(f866(f7(f931(x47051),f937(f936(f931(x47051),f931(x47051)),a925),f937(f931(x47051),a925)),f866(f866(f8(f937(f931(x47051),f937(f937(f936(f931(x47051),f931(x47051)),a925),a925)),f937(f937(f936(f931(x47051),f931(x47051)),a925),f937(f931(x47051),a925)),f931(x47051)),f7(f931(x47051),f937(f936(f931(x47051),f931(x47051)),a925),a925)),f866(f866(f8(f937(f931(x47051),f936(f931(x47051),f931(x47051))),f937(f931(x47051),f937(f937(f936(f931(x47051),f931(x47051)),a925),a925)),f931(x47051)),f866(f8(f936(f931(x47051),f931(x47051)),f937(f937(f936(f931(x47051),f931(x47051)),a925),a925),f931(x47051)),f336(f936(f931(x47051),f931(x47051))))),f260(f931(x47051),f931(x47051))))),f152(x47051,x47052)))))),f153(x47051,x47052))
% 157.60/157.50 [4379]E(f866(f866(f86(a1),f866(f866(f86(a1),f866(f866(f87(a1),x43791),x43792)),f866(f866(f87(a1),x43791),x43792))),x43792),f866(f866(f87(a1),f866(f866(f23(a1),f866(f866(f86(a1),x43791),x43791)),a104)),x43792))
% 157.60/157.50 [4482]E(f866(a111,f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x44821),x44822)),f195(f937(f936(a930,a930),a925)))))),f866(f866(f23(a930),x44821),x44822))
% 157.60/157.50 [4486]E(f866(f866(f296(x44861,x44861,x44861),f866(f866(f117(f937(f936(x44861,x44861),a925)),x44862),f314(x44861,f195(f937(f936(x44861,x44861),a925))))),f314(x44861,f866(f866(f117(f937(f936(x44861,x44861),a925)),x44862),f314(x44861,f195(f937(f936(x44861,x44861),a925)))))),f314(x44861,x44862))
% 157.60/157.50 [4523]E(f276(x45231,f866(f143(f936(a106,x45231),f866(f265(a106,x45231,a925),f866(f866(f8(a925,f937(x45231,a925),a106),f16(a925,x45231)),f866(f244(a106),f2(a106))))),x45232)),f276(x45231,x45232))
% 157.60/157.50 [4524]E(f274(x45241,f866(f143(f936(a106,x45241),f866(f265(a106,x45241,a925),f866(f866(f8(a925,f937(x45241,a925),a106),f16(a925,x45241)),f866(f244(a106),f2(a106))))),x45242)),f274(x45241,x45242))
% 157.60/157.50 [4526]E(f866(f85(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x45261),x45262)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x45262),x45261)),f195(f937(f936(a930,a930),a925))))))
% 157.60/157.50 [4582]E(f866(f866(f295(f931(a930),x45821),f152(a930,a248)),f866(f866(f7(x45821,f931(f937(x45821,a930)),f931(a930)),f866(f866(f8(f937(f937(x45821,a930),a930),f937(f931(f937(x45821,a930)),f931(a930)),x45821),f161(f937(x45821,a930),a930)),f866(f7(f937(x45821,a930),x45821,a930),f5(f937(x45821,a930))))),x45822)),f160(x45821,x45822))
% 157.60/157.50 [4603]E(f866(f866(f92(a1,a930),f866(f110(a1),f866(f866(f86(a1),x46031),a104))),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f2(a930))),f866(f866(f8(a930,a930,a1),a119),f866(f866(f8(a930,a930,a1),f866(f241(a930),x46032)),a111)))),f866(f866(f241(a930),f866(a119,x46032)),f866(f110(a930),x46031)))
% 157.60/157.50 [4604]E(f866(f866(f92(a1,a930),f866(f110(a1),f866(f866(f86(a1),x46041),a104))),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f866(a119,x46042))),f866(f866(f8(a930,a930,a1),a119),f866(f866(f8(a930,a930,a1),f866(f242(a930),x46042)),a111)))),f866(f866(f242(a930),f866(a119,x46042)),f866(f110(a930),x46041)))
% 157.60/157.50 [4624]E(f866(f149(f931(x46241),f931(x46241),f141(x46241),f120(x46241)),f866(f866(f161(f931(x46241),f931(x46241)),f163(f931(x46241),x46241,f120(x46241),f866(f866(f8(f931(x46241),f937(f931(x46241),f931(x46241)),x46241),f16(f931(x46241),f931(x46241))),f866(f866(f7(x46241,f931(x46241),f931(x46241)),f158(x46241)),f120(x46241))))),x46242)),f866(f866(f161(f931(x46241),x46241),f148(x46241)),f866(f143(f931(x46241),f866(f866(f8(a925,a925,f931(x46241)),a329),f866(f866(f7(f931(x46241),f931(x46241),a925),a332),f120(x46241)))),x46242)))
% 157.60/157.50 [4688]E(f866(f265(a1,a1,a925),f866(f866(f7(a1,f937(a1,a925),f937(a1,a925)),f866(f866(f8(f937(a1,f937(a925,a925)),f937(f937(a1,a925),f937(a1,a925)),a1),f18(a1,a925,a925)),f866(f866(f8(f937(a1,a925),f937(a1,f937(a925,a925)),a1),f866(f8(a925,f937(a925,a925),a1),a333)),f866(f866(f8(f937(a1,a1),f937(a1,a925),a1),f866(f8(a1,a925,a1),f866(a332,x46881))),f866(f866(f8(a1,f937(a1,a1),a1),f86(a1)),f866(f87(a1),x46882)))))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),f866(a337,f866(f866(f244(a1),f2(a1)),x46882))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),f866(f866(f7(a1,a1,a925),f244(a1)),x46882))))),f866(f866(f8(a925,a925,a1),f866(a337,f866(a329,f866(f866(f244(a1),f2(a1)),x46882)))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f244(a1),x46882))),f866(f866(f7(a1,a1,a925),f243(a1)),f2(a1))))))),f54(x46881,x46882))
% 157.60/157.50 [4691]E(f866(f270(x46911),f866(f866(f8(f937(a930,a925),a925,x46911),f93(a930)),f866(f866(f7(x46911,f937(a930,a925),f937(a930,a925)),f866(f866(f8(f937(a930,f937(a925,a925)),f937(f937(a930,a925),f937(a930,a925)),x46911),f18(a930,a925,a925)),f866(f866(f8(f937(a930,a925),f937(a930,f937(a925,a925)),x46911),f866(f8(a925,f937(a925,a925),a930),a333)),f866(f866(f7(x46911,f937(a930,x46911),f937(a930,a925)),f866(f866(f8(f937(x46911,a925),f937(f937(a930,x46911),f937(a930,a925)),x46911),f8(x46911,a925,a930)),a332)),f866(f171(x46911),x46912))))),f866(f866(f7(a930,a930,a925),f244(a930)),f866(f196(f931(x46911)),x46912))))),f866(f179(x46911),x46912))
% 157.60/157.50 [4496]E(f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),x44961),a104)),x44962)),f866(f866(f23(a1),f866(f866(f86(a1),x44961),a104)),x44962))),a104),f866(f866(f23(a1),f866(f866(f86(a1),x44961),x44961)),f866(f866(f23(a1),f866(f866(f86(a1),x44962),x44962)),a104)))
% 157.60/157.50 [4619]E(f866(f149(f931(f931(x46191)),f931(f931(x46191)),f141(f931(x46191)),f120(f931(x46191))),f866(f866(f161(f931(x46191),f931(f931(x46191))),f163(f931(f931(x46191)),x46191,f120(f931(x46191)),f866(f16(f937(f931(x46191),f931(f931(x46191))),x46191),f866(f866(f7(f931(x46191),f931(f931(x46191)),f931(f931(x46191))),f158(f931(x46191))),f120(f931(x46191)))))),x46192)),f866(f866(f161(f931(x46191),f931(x46191)),f178(x46191)),f866(f143(f931(x46191),f866(f866(f8(a925,a925,f931(x46191)),a329),f866(f866(f7(f931(x46191),f931(x46191),a925),a332),f120(x46191)))),x46192)))
% 157.60/157.50 [4629]E(f866(f866(f92(a1,a930),f866(f110(a1),f866(f866(f86(a1),x46291),a104))),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f2(a930))),f866(f866(f8(a930,a930,a1),a119),f866(f866(f7(a1,a930,a930),f866(f866(f8(a930,f937(a930,a930),a1),f241(a930)),a111)),x46292)))),f866(f866(f241(a930),f866(f110(a930),x46291)),f866(a119,x46292)))
% 157.60/157.50 [4630]E(f866(f866(f92(a1,a930),f866(f110(a1),f866(f866(f86(a1),x46301),a104))),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f866(a119,x46302))),f866(f866(f8(a930,a930,a1),a119),f866(f866(f7(a1,a930,a930),f866(f866(f8(a930,f937(a930,a930),a1),f242(a930)),a111)),x46302)))),f866(f866(f242(a930),f866(f110(a930),x46301)),f866(a119,x46302)))
% 157.60/157.50 [4618]E(f866(f265(x46181,x46181,a925),f866(f866(f18(x46181,a925,f937(x46181,a925)),f866(f866(f8(f937(x46181,f937(a925,a925)),f937(a925,f937(x46181,a925)),x46181),f7(x46181,a925,a925)),f866(f866(f8(f937(x46181,a925),f937(x46181,f937(a925,a925)),x46181),f866(f8(a925,f937(a925,a925),x46181),a333)),a332))),x46182)),f271(x46181,x46182))
% 157.60/157.50 [4663]E(f866(f866(f41(a930),x46631),f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46632)),f866(f866(f41(a930),x46631),f866(a119,f866(a119,f866(a119,x46632)))))
% 157.60/157.50 [4664]E(f50(a930,x46641,f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46642)),f50(a930,x46641,f866(a119,f866(a119,f866(a119,x46642)))))
% 157.60/157.50 [4665]E(f50(a930,f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46651),x46652),f50(a930,f866(a119,f866(a119,f866(a119,x46651))),x46652))
% 157.60/157.50 [4679]E(f130(f866(x46791,f866(f866(f87(a106),f866(f110(a106),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46792))),f866(f209(x46791),x46792))
% 157.60/157.50 [4680]E(f866(f866(f41(a930),f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),x46801)),x46802),f866(f866(f41(a930),f866(a119,f866(a119,f866(a119,x46801)))),x46802))
% 157.60/157.50 [4745]~E(f28(x47451,x47452,x47453),a25)
% 157.60/157.50 [4746]~E(f27(x47461,x47462,x47463),a25)
% 157.60/157.50 [4750]~E(f133(x47501,x47502,x47503),f126(x47501))
% 157.60/157.50 [3469]E(f866(f199(x34691,x34692),x34693),f128(x34691,x34692))
% 157.60/157.50 [3488]E(f866(f208(x34881,x34882),x34883),f866(f136(x34881),x34882))
% 157.60/157.50 [3564]E(f866(f866(f161(x35641,x35642),x35643),f120(x35641)),f120(x35642))
% 157.60/157.50 [3604]E(f866(f191(x36041,x36042,x36043),f2(a930)),x36042)
% 157.60/157.50 [3606]E(f866(f866(f188(x36061,x36062),x36063),f120(x36062)),f120(f936(x36061,x36062)))
% 157.60/157.50 [3621]E(f866(f196(f931(x36211)),f176(x36211,x36212,x36213)),x36212)
% 157.60/157.50 [3640]E(f91(x36401,f67(x36401,x36402,x36403)),f866(f68(x36401,x36402),x36403))
% 157.60/157.50 [3644]E(f251(x36441,x36442,f251(x36442,x36441,x36443)),x36443)
% 157.60/157.50 [3664]E(f866(f175(x36641),f176(x36641,x36642,x36643)),f176(x36641,x36642,x36643))
% 157.60/157.50 [3691]E(f147(x36911,x36912,f159(x36911,x36913)),f159(x36911,f147(x36911,x36912,x36913)))
% 157.60/157.50 [3709]E(f866(f259(f931(x37091),f931(x37091)),f173(x37091,x37092,x37093)),f866(f143(x37091,x37092),x37093))
% 157.60/157.50 [3752]E(f866(f866(f158(x37521),x37522),f176(x37521,x37523,x37522)),f176(x37521,f866(a119,x37523),x37522))
% 157.60/157.50 [3784]E(f192(x37841,x37842,x37843,f2(a930)),x37842)
% 157.60/157.50 [3785]E(f17(x37851,x37852,x37853,f2(a106)),x37852)
% 157.60/157.50 [3786]E(f19(x37861,x37862,x37863,f2(a106)),x37862)
% 157.60/157.50 [3793]E(f170(x37931,x37932,x37933,f120(x37931)),f120(x37932))
% 157.60/157.50 [3794]E(f137(x37941,x37942,x37943,f126(x37941)),f126(x37942))
% 157.60/157.50 [3800]E(f866(f866(f171(x38001),f866(f866(f158(x38001),x38002),x38003)),f2(a930)),x38002)
% 157.60/157.50 [3833]E(f64(x38331,x38332,f120(x38331),x38333),f120(f936(x38331,x38332)))
% 157.60/157.50 [3853]P25(x38531,x38532,x38533,f195(f937(x38531,a925)))
% 157.60/157.50 [3955]E(f273(x39551,x39552,x39553),f866(f260(f937(a106,f937(a925,f934(f932(x39551)))),f936(a106,a106)),f46(x39551)))
% 157.60/157.50 [4013]E(f866(f78(x40131,x40132,x40131,x40133),f32(x40131)),x40133)
% 157.60/157.50 [4194]P107(f866(f866(f336(f936(x41941,x41941)),f866(f866(f260(x41941,x41941),x41942),x41942)),f314(x41941,x41943)))
% 157.60/157.50 [4806]~P107(f866(f866(f336(f936(f931(x48061),f931(x48061))),f866(f866(f260(f931(x48061),f931(x48061)),x48062),f120(x48061))),f152(x48061,x48063)))
% 157.60/157.50 [4807]~P107(f866(f866(f336(f936(f931(x48071),f931(x48071))),f866(f866(f260(f931(x48071),f931(x48071)),x48072),f120(x48071))),f154(x48071,x48073)))
% 157.60/157.50 [4808]~P107(f866(f866(f336(f936(f931(x48081),f931(x48081))),f866(f866(f260(f931(x48081),f931(x48081)),x48082),f120(x48081))),f164(x48081,x48083)))
% 157.60/157.50 [4809]~P107(f866(f866(f336(f936(f931(x48091),f931(x48091))),f866(f866(f260(f931(x48091),f931(x48091)),f120(x48091)),x48092)),f152(x48091,x48093)))
% 157.60/157.50 [4810]~P107(f866(f866(f336(f936(f931(x48101),f931(x48101))),f866(f866(f260(f931(x48101),f931(x48101)),f120(x48101)),x48102)),f164(x48101,x48103)))
% 157.60/157.50 [3540]E(f866(f866(f210(x35401),x35402),x35403),f211(x35401,f224(x35402,x35403)))
% 157.60/157.50 [3593]E(f866(f294(x35931,x35932),f866(f294(x35932,x35931),x35933)),x35933)
% 157.60/157.50 [3616]E(f866(f866(f188(x36161,x36162),f120(x36161)),x36163),f120(f936(x36161,x36162)))
% 157.60/157.50 [3619]E(f183(x36191,x36192,f866(f290(a930),x36193)),f866(f866(f182(x36191),x36193),x36192))
% 157.60/157.50 [3637]E(f159(x36371,f866(f143(x36371,x36372),x36373)),f866(f143(x36371,x36372),f159(x36371,x36373)))
% 157.60/157.50 [3638]E(f866(f292(x36381,x36382),f866(f294(x36382,x36381),x36383)),f866(f272(x36382,x36381),x36383))
% 157.60/157.50 [3639]E(f866(f272(x36391,x36392),f866(f294(x36392,x36391),x36393)),f866(f292(x36392,x36391),x36393))
% 157.60/157.50 [3657]E(f866(f143(x36571,x36572),f866(f175(x36571),x36573)),f866(f175(x36571),f866(f143(x36571,x36572),x36573)))
% 157.60/157.50 [3670]E(f866(f866(f145(x36701),x36702),f866(f178(x36701),x36703)),f866(f866(f145(x36701),f866(a119,x36702)),x36703))
% 157.60/157.50 [3686]E(f29(f27(x36861,x36862,x36863)),f866(f866(f86(a930),f29(x36863)),f866(a119,f2(a930))))
% 157.60/157.50 [3687]E(f866(f317(x36871,x36872,x36873),f195(f937(x36871,a925))),f195(f937(x36872,a925)))
% 157.60/157.50 [3688]E(f866(f293(x36881,x36882,x36883),f195(f937(x36881,a925))),f195(f937(x36882,a925)))
% 157.60/157.50 [3689]E(f866(f318(x36891,x36892,x36893),f195(f937(x36892,a925))),f195(f937(x36891,a925)))
% 157.60/157.50 [3690]E(f866(f318(x36901,x36902,x36903),f250(f937(x36902,a925))),f250(f937(x36901,a925)))
% 157.60/157.50 [3715]E(f127(x37151,f133(f932(x37151),x37152,x37153)),f123(x37151,x37152,f127(x37151,x37153)))
% 157.60/157.50 [3717]E(f866(f866(f316(x37171),x37172),f866(f179(x37171),x37173)),f866(f179(x37171),f147(x37171,x37172,x37173)))
% 157.60/157.50 [3804]E(f866(f196(a927),f27(x38041,x38042,x38043)),f866(f866(f86(a930),f866(f196(a927),x38043)),f866(a119,f2(a930))))
% 157.60/157.50 [3805]E(f866(f317(f936(x38051,x38052),x38052,f264(x38051,x38052)),x38053),f866(f292(x38051,x38052),x38053))
% 157.60/157.50 [3806]E(f866(f317(f936(x38061,x38062),x38061,f259(x38061,x38062)),x38063),f866(f272(x38061,x38062),x38063))
% 157.60/157.50 [3825]E(f866(f179(x38251),f176(x38251,f866(a119,x38252),x38253)),f866(f866(f316(x38251),x38253),f195(f937(x38251,a925))))
% 157.60/157.50 [3882]E(f866(f866(f260(x38821,x38822),f866(f259(x38821,x38822),x38823)),f866(f264(x38821,x38822),x38823)),x38823)
% 157.60/157.50 [3889]E(f866(f196(f932(x38891)),f133(x38891,x38892,x38893)),f866(f866(f86(a930),f866(f196(f932(x38891)),x38893)),f866(a119,f2(a930))))
% 157.60/157.50 [3890]E(f866(f866(f265(x38901,x38902,x38901),f16(x38901,x38902)),x38903),f866(f259(x38901,x38902),x38903))
% 157.60/157.50 [3968]E(f29(f28(x39681,x39682,x39683)),f866(f866(f86(a930),f866(f866(f86(a930),f29(x39682)),f29(x39683))),f866(a119,f2(a930))))
% 157.60/157.50 [4018]E(f866(f78(x40181,x40181,x40182,f32(x40181)),x40183),x40183)
% 157.60/157.50 [4026]E(f866(f866(f141(x40261),f176(x40261,x40262,x40263)),f866(f866(f158(x40261),x40263),f120(x40261))),f866(f866(f158(x40261),x40263),f176(x40261,x40262,x40263)))
% 157.60/157.50 [4127]E(f866(f196(a927),f28(x41271,x41272,x41273)),f866(f866(f86(a930),f866(f866(f86(a930),f866(f196(a927),x41272)),f866(f196(a927),x41273))),f866(a119,f2(a930))))
% 157.60/157.50 [4203]P107(f866(f866(f243(f937(x42031,a925)),f866(f179(x42031),f866(f143(x42031,x42032),x42033))),f866(f179(x42031),x42033)))
% 157.60/157.50 [4246]P107(f866(f866(f243(f937(x42461,a925)),f866(f179(x42461),f866(f866(f182(x42461),x42462),x42463))),f866(f179(x42461),x42463)))
% 157.60/157.50 [4247]P107(f866(f866(f243(f937(x42471,a925)),f866(f179(x42471),f866(f866(f145(x42471),x42472),x42473))),f866(f179(x42471),x42473)))
% 157.60/157.50 [4251]P107(f866(f866(f243(f937(x42511,a925)),f866(f179(x42511),f183(x42511,x42512,x42513))),f866(f179(x42511),x42512)))
% 157.60/157.50 [4252]P107(f866(f866(f243(f937(x42521,a925)),f866(f179(x42521),f177(x42521,x42522,x42523))),f866(f179(x42521),x42523)))
% 157.60/157.50 [4273]P25(f936(x42731,x42732),f936(x42732,x42731),f866(f265(x42731,x42732,f936(x42732,x42731)),f866(f7(x42732,x42731,f936(x42732,x42731)),f260(x42732,x42731))),x42733)
% 157.60/157.50 [4284]E(f866(f866(f866(f190(f931(x42841),f931(x42841)),f50(a930,x42842,f866(f196(f931(x42841)),x42843))),f174(x42841)),x42843),f866(f866(f866(f190(f931(x42841),f931(x42841)),x42842),f174(x42841)),x42843))
% 157.60/157.50 [4328]P107(f866(f866(f336(f936(f931(x43281),f931(x43281))),f866(f866(f260(f931(x43281),f931(x43281)),x43282),x43282)),f165(x43281,f314(x43281,x43283))))
% 157.60/157.50 [4469]E(f91(f936(x44691,x44692),f866(f866(f18(f936(x44691,x44692),x44692,a925),f866(f866(f8(x44691,f937(x44692,a925),f936(x44691,x44692)),x44693),f259(x44691,x44692))),f264(x44691,x44692))),f91(f936(x44691,x44692),f866(f265(x44691,x44692,a925),x44693)))
% 157.60/157.50 [4470]E(f96(f936(x44701,x44702),f866(f866(f18(f936(x44701,x44702),x44702,a925),f866(f866(f8(x44701,f937(x44702,a925),f936(x44701,x44702)),x44703),f259(x44701,x44702))),f264(x44701,x44702))),f96(f936(x44701,x44702),f866(f265(x44701,x44702,a925),x44703)))
% 157.60/157.50 [4503]E(f866(f866(f295(f936(a930,x45031),x45031),f326(a930,x45031,a248,x45032)),f866(f866(f18(x45031,x45031,f936(a930,x45031)),f866(f866(f8(a930,f937(x45031,f936(a930,x45031)),x45031),f260(a930,x45031)),x45033)),f5(x45031))),f328(x45031,x45033,x45032))
% 157.60/157.50 [4565]E(f866(f266(x45651,x45651,x45652,x45652,f5(x45651),f5(x45652)),x45653),x45653)
% 157.60/157.50 [4638]E(f866(f149(f931(f931(x46381)),f931(f931(x46381)),f141(f931(x46381)),f120(f931(x46381))),f866(f866(f161(f931(x46381),f931(f931(x46381))),f866(f866(f7(f931(x46381),f931(x46381),f931(f931(x46381))),f866(f866(f8(f937(x46381,f931(x46381)),f937(f931(x46381),f931(f931(x46381))),f931(x46381)),f161(x46381,f931(x46381))),f866(f7(x46381,f931(x46381),f931(x46381)),f158(x46381)))),x46382)),f60(x46381,x46383,x46382))),f60(x46381,f866(a119,x46383),x46382))
% 157.60/157.50 [4696]E(f232(a930,f936(x46961,f932(x46961)),f2(a930),f866(f265(x46961,f932(x46961),a930),f866(f866(f7(x46961,a930,f937(f932(x46961),a930)),f866(f866(f8(f937(f932(x46961),f937(a930,a930)),f937(a930,f937(f932(x46961),a930)),x46961),f7(f932(x46961),a930,a930)),f866(f866(f8(f937(f932(x46961),a930),f937(f932(x46961),f937(a930,a930)),x46961),f866(f8(a930,f937(a930,a930),f932(x46961)),f86(a930))),f866(f866(f7(x46961,f937(f932(x46961),a930),f937(f932(x46961),a930)),f866(f866(f8(f937(a930,a930),f937(f937(f932(x46961),a930),f937(f932(x46961),a930)),x46961),f8(a930,a930,f932(x46961))),f866(f866(f8(a930,f937(a930,a930),x46961),f86(a930)),x46962))),f132(x46961,x46962))))),f84(a930))),f866(f142(x46961),x46963)),f866(f132(x46961,x46962),x46963))
% 157.60/157.50 [4704]E(f866(f866(f92(a1,x47041),f227(f866(f866(f78(f936(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47042),f866(f866(f78(f936(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47043))),f866(f866(f18(a1,a1,x47041),f866(f866(f8(a1,f937(a1,x47041),a1),f210(x47041)),f866(f866(f18(a1,a1,a1),f866(f866(f8(a1,f937(a1,a1),a1),f86(a1)),f866(f866(f8(a1,a1,a1),f866(f87(a1),f866(f866(f78(f936(a1,a1),a1,x47041,f259(a1,a1)),f221(x47041)),x47042))),f866(f866(f7(a1,a1,a1),f41(a1)),f866(f866(f78(f936(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47042))))),f866(f866(f8(a1,a1,a1),f866(f87(a1),f866(f866(f78(f936(a1,a1),a1,x47041,f259(a1,a1)),f221(x47041)),x47043))),f866(f866(f7(a1,a1,a1),f41(a1)),f866(f866(f78(f936(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47043)))))),f5(a1))),f239(x47041,x47042,x47043))
% 157.60/157.50 [4741]~E(f866(f866(f158(x47411),x47412),x47413),x47413)
% 157.60/157.50 [4748]~E(f866(f866(f158(x47481),x47482),x47483),f120(x47481))
% 157.60/157.50 [4766]~E(f866(f866(f316(x47661),x47662),x47663),f195(f937(x47661,a925)))
% 157.60/157.50 [4788]~E(f866(f317(x47881,f937(x47881,a925),x47882),x47883),f866(f315(x47881),x47883))
% 157.60/157.50 [3598]E(f866(f866(f166(x35981,f120(x35981)),x35982),x35983),f120(x35981))
% 157.60/157.50 [3599]E(f866(f148(x35991),f866(f866(f158(x35991),x35992),x35993)),x35992)
% 157.60/157.50 [3600]E(f866(f178(x36001),f866(f866(f158(x36001),x36002),x36003)),x36003)
% 157.60/157.50 [3643]E(f866(f866(f145(x36431),f84(a930)),f866(f866(f158(x36431),x36432),x36433)),x36433)
% 157.60/157.50 [3677]E(f121(x36771,f866(f866(f145(x36771),x36772),x36773)),f866(f866(f145(x36771),x36772),f121(x36771,x36773)))
% 157.60/157.50 [3679]E(f866(f866(f166(x36791,x36792),x36793),f866(f866(f171(x36791),x36792),x36793)),x36792)
% 157.60/157.50 [3700]E(f866(f866(f316(x37001),x37002),f866(f866(f316(x37001),x37002),x37003)),f866(f866(f316(x37001),x37002),x37003))
% 157.60/157.50 [3712]E(f866(f866(f316(x37121),x37122),f866(f179(x37121),x37123)),f866(f179(x37121),f866(f866(f158(x37121),x37122),x37123)))
% 157.60/157.50 [3714]E(f866(f866(f145(x37141),x37142),f866(f178(x37141),x37143)),f866(f178(x37141),f866(f866(f145(x37141),x37142),x37143)))
% 157.60/157.50 [3726]E(f866(f866(f182(x37261),f84(a930)),f866(f866(f158(x37261),x37262),x37263)),f866(f866(f158(x37261),x37262),f120(x37261)))
% 157.60/157.50 [3769]E(f866(f68(x37691,x37692),f866(f866(f316(x37691),x37693),f195(f937(x37691,a925)))),x37693)
% 157.60/157.50 [3815]E(f866(f866(f86(a930),x38151),f866(f866(f86(a930),x38152),x38153)),f866(f866(f86(a930),x38152),f866(f866(f86(a930),x38151),x38153)))
% 157.60/157.50 [3816]E(f866(f866(f86(a1),x38161),f866(f866(f86(a1),x38162),x38163)),f866(f866(f86(a1),x38162),f866(f866(f86(a1),x38161),x38163)))
% 157.60/157.50 [3821]E(f866(f866(f262(x38211,x38212),f195(f937(x38211,a925))),x38213),f195(f937(f936(x38211,x38212),a925)))
% 157.60/157.50 [3845]E(f866(f866(f117(f937(x38451,a925)),x38452),x38453),f866(f866(f117(f937(x38451,a925)),x38453),x38452))
% 157.60/157.50 [3846]E(f866(f866(f108(f937(x38461,a925)),x38462),x38463),f866(f866(f108(f937(x38461,a925)),x38463),x38462))
% 157.60/157.50 [3848]E(f866(f866(f141(x38481),x38482),f866(f866(f158(x38481),x38483),f120(x38481))),f866(f174(x38481),f866(f866(f158(x38481),x38483),x38482)))
% 157.60/157.50 [3849]E(f866(f866(f141(x38491),f866(f175(x38491),x38492)),f866(f175(x38491),x38493)),f866(f175(x38491),f866(f866(f141(x38491),x38493),x38492)))
% 157.60/157.50 [3859]E(f866(f178(x38591),f866(f866(f182(x38591),f866(a119,x38592)),x38593)),f866(f866(f182(x38591),x38592),f866(f178(x38591),x38593)))
% 157.60/157.50 [3867]P107(f866(f866(f336(x38671),x38672),f866(f866(f316(x38671),x38672),x38673)))
% 157.60/157.50 [3871]E(f866(f866(f45(x38711,f937(x38712,a925)),f195(f937(x38711,a925))),x38713),f250(f937(x38712,a925)))
% 157.60/157.50 [3874]E(f866(f293(x38741,x38741,f271(x38741,x38742)),x38743),f866(f866(f108(f937(x38741,a925)),x38742),x38743))
% 157.60/157.50 [3888]E(f866(f196(f931(x38881)),f866(f866(f158(x38881),x38882),x38883)),f866(f866(f86(a930),f866(f196(f931(x38881)),x38883)),f866(a119,f2(a930))))
% 157.60/157.50 [3892]E(f121(x38921,f866(f866(f141(x38921),x38922),f866(f866(f158(x38921),x38923),f120(x38921)))),x38922)
% 157.60/157.50 [3893]E(f151(x38931,f866(f866(f141(x38931),x38932),f866(f866(f158(x38931),x38933),f120(x38931)))),x38933)
% 157.60/157.50 [3902]E(f866(f866(f141(x39021),f866(f866(f182(x39021),x39022),x39023)),f866(f866(f145(x39021),x39022),x39023)),x39023)
% 157.60/157.50 [3911]E(f866(f866(f23(a930),f866(f866(f86(a930),x39111),x39112)),f866(f866(f86(a930),x39113),x39112)),f866(f866(f23(a930),x39111),x39113))
% 157.60/157.50 [3912]E(f866(f866(f23(a930),f866(f866(f86(a930),x39121),x39122)),f866(f866(f86(a930),x39121),x39123)),f866(f866(f23(a930),x39122),x39123))
% 157.60/157.50 [3918]E(f866(f866(f141(x39181),f866(f175(x39181),x39182)),f866(f866(f158(x39181),x39183),f120(x39181))),f866(f175(x39181),f866(f866(f158(x39181),x39183),x39182)))
% 157.60/157.50 [3920]E(f866(f866(f86(a930),f866(f196(f931(x39201)),x39202)),f866(f196(f931(x39201)),x39203)),f866(f196(f931(x39201)),f866(f866(f141(x39201),x39202),x39203)))
% 157.60/157.50 [3923]E(f866(f866(f86(a930),f866(f196(f931(x39231)),x39232)),f866(f196(f931(x39231)),x39233)),f866(f196(f931(x39231)),f180(x39231,x39232,x39233)))
% 157.60/157.50 [3930]E(f866(f866(f117(f937(x39301,a925)),f866(f179(x39301),x39302)),f866(f179(x39301),x39303)),f866(f179(x39301),f866(f866(f141(x39301),x39302),x39303)))
% 157.60/157.50 [3931]E(f50(a930,f866(f866(f87(a930),x39311),x39312),f866(f866(f87(a930),x39311),x39313)),f866(f866(f87(a930),x39311),f50(a930,x39312,x39313)))
% 157.60/157.50 [3943]E(f866(f866(f182(x39431),f866(f866(f23(a930),x39432),f84(a930))),f866(f178(x39431),x39433)),f866(f178(x39431),f866(f866(f182(x39431),x39432),x39433)))
% 157.60/157.50 [3948]E(f866(f866(f108(f937(x39481,a925)),x39482),f866(f85(f937(x39481,a925)),x39483)),f866(f866(f23(f937(x39481,a925)),x39482),x39483))
% 157.60/157.50 [3949]E(f866(f866(f23(f937(x39491,a925)),x39492),f866(f85(f937(x39491,a925)),x39493)),f866(f866(f108(f937(x39491,a925)),x39492),x39493))
% 157.60/157.50 [3972]E(f866(f866(f262(x39721,x39722),x39723),f866(f16(f937(x39722,a925),x39721),f195(f937(x39722,a925)))),f195(f937(f936(x39721,x39722),a925)))
% 157.60/157.50 [3974]E(f866(f866(f23(a930),f866(f866(f87(a930),x39741),x39742)),f866(f866(f87(a930),x39741),x39743)),f866(f866(f87(a930),x39741),f866(f866(f23(a930),x39742),x39743)))
% 157.60/157.50 [3975]E(f866(f866(f86(a930),f866(f866(f87(a930),x39751),x39752)),f866(f866(f87(a930),x39751),x39753)),f866(f866(f87(a930),x39751),f866(f866(f86(a930),x39752),x39753)))
% 157.60/157.50 [3976]E(f866(f866(f23(a1),f866(f866(f87(a1),x39761),x39762)),f866(f866(f87(a1),x39761),x39763)),f866(f866(f87(a1),x39761),f866(f866(f23(a1),x39762),x39763)))
% 157.60/157.50 [3977]E(f866(f866(f86(a1),f866(f866(f87(a1),x39771),x39772)),f866(f866(f87(a1),x39771),x39773)),f866(f866(f87(a1),x39771),f866(f866(f86(a1),x39772),x39773)))
% 157.60/157.50 [3978]E(f866(f866(f87(a1),f866(f866(f252(a1),x39781),x39782)),f866(f866(f252(a1),x39781),x39783)),f866(f866(f252(a1),x39781),f866(f866(f86(a930),x39782),x39783)))
% 157.60/157.50 [3992]E(f866(f866(f44(x39921,f937(x39922,a925)),x39923),f866(f16(f937(x39922,a925),x39921),f195(f937(x39922,a925)))),f195(f937(x39922,a925)))
% 157.60/157.50 [3994]E(f50(a930,f866(f866(f87(a930),x39941),x39942),f866(f866(f87(a930),x39943),x39942)),f866(f866(f87(a930),f50(a930,x39941,x39943)),x39942))
% 157.60/157.50 [3999]E(f50(a1,f866(f866(f23(a1),x39991),f50(a1,x39992,x39993)),x39993),f50(a1,f866(f866(f23(a1),x39991),x39992),x39993))
% 157.60/157.50 [4000]E(f50(a1,f866(f866(f87(a1),x40001),f50(a1,x40002,x40003)),x40003),f50(a1,f866(f866(f87(a1),x40001),x40002),x40003))
% 157.60/157.51 [4001]P107(f866(f866(f243(f937(x40011,a925)),x40012),f866(f866(f316(x40011),x40013),x40012)))
% 157.60/157.51 [4078]E(f866(f866(f45(f937(x40781,a925),f937(x40781,a925)),x40782),f866(f117(f937(x40781,a925)),x40783)),f866(f866(f117(f937(x40781,a925)),x40783),f43(f937(x40781,a925),x40782)))
% 157.60/157.51 [4079]E(f866(f866(f44(f937(x40791,a925),f937(x40791,a925)),x40792),f866(f108(f937(x40791,a925)),x40793)),f866(f866(f108(f937(x40791,a925)),x40793),f42(f937(x40791,a925),x40792)))
% 157.60/157.51 [4091]E(f866(f179(x40911),f866(f866(f866(f190(f931(x40911),f931(x40911)),x40912),f174(x40911)),x40913)),f866(f179(x40911),x40913))
% 157.60/157.51 [4095]E(f866(f866(f182(x40951),f866(f196(f931(x40951)),f184(x40951,x40952,x40953))),x40953),f184(x40951,x40952,x40953))
% 157.60/157.51 [4099]E(f866(f196(f931(x40991)),f866(f866(f866(f190(f931(x40991),f931(x40991)),x40992),f174(x40991)),x40993)),f866(f196(f931(x40991)),x40993))
% 157.60/157.51 [4102]E(f866(f866(f265(x41021,x41022,x41022),f866(f16(f937(x41022,x41022),x41021),f5(x41022))),x41023),f866(f264(x41021,x41022),x41023))
% 157.60/157.51 [4109]E(f50(a1,f866(f866(f23(a1),f50(a1,x41091,x41092)),x41093),x41092),f50(a1,f866(f866(f23(a1),x41091),x41093),x41092))
% 157.60/157.51 [4110]E(f50(a1,f866(f866(f252(a1),f50(a1,x41101,x41102)),x41103),x41102),f50(a1,f866(f866(f252(a1),x41101),x41103),x41102))
% 157.60/157.51 [4113]E(f866(f866(f44(f937(f936(x41131,x41132),a925),f937(x41132,a925)),x41133),f292(x41131,x41132)),f866(f292(x41131,x41132),f42(f937(f936(x41131,x41132),a925),x41133)))
% 157.60/157.51 [4114]E(f866(f866(f44(f937(f936(x41141,x41142),a925),f937(x41141,a925)),x41143),f272(x41141,x41142)),f866(f272(x41141,x41142),f42(f937(f936(x41141,x41142),a925),x41143)))
% 157.60/157.51 [4138]E(f866(f78(x41381,x41381,x41381,x41382),f866(f866(f190(x41381,x41381),x41383),x41382)),f866(f866(f190(x41381,x41381),f866(a119,x41383)),x41382))
% 157.60/157.51 [4158]E(f866(f866(f145(x41581),f866(f866(f23(a930),f866(f196(f931(x41581)),x41582)),x41583)),f866(f175(x41581),x41582)),f866(f175(x41581),f866(f866(f182(x41581),x41583),x41582)))
% 157.60/157.51 [4159]E(f866(f866(f182(x41591),f866(f866(f23(a930),f866(f196(f931(x41591)),x41592)),x41593)),f866(f175(x41591),x41592)),f866(f175(x41591),f866(f866(f145(x41591),x41593),x41592)))
% 157.60/157.51 [4161]E(f866(f866(f86(a930),f866(f172(a930),f866(f866(f161(x41611,a930),x41612),x41613))),f866(f196(f931(x41611)),x41613)),f162(x41611,x41612,x41613))
% 157.60/157.51 [4181]E(f866(f174(x41811),f866(f866(f866(f190(f931(x41811),f931(x41811)),x41812),f174(x41811)),x41813)),f866(f866(f866(f190(f931(x41811),f931(x41811)),f866(a119,x41812)),f174(x41811)),x41813))
% 157.60/157.51 [4195]P107(f866(f866(f243(a930),f866(f196(f931(x41951)),f866(f143(x41951,x41952),x41953))),f866(f196(f931(x41951)),x41953)))
% 157.60/157.51 [4211]E(f866(f866(f117(f937(f937(x42111,a925),a925)),f866(f315(x42111),x42112)),f866(f317(f937(x42111,a925),f937(x42111,a925),f866(f316(x42111),x42113)),f866(f315(x42111),x42112))),f866(f315(x42111),f866(f866(f316(x42111),x42113),x42112)))
% 157.60/157.51 [4243]P107(f866(f866(f243(a930),f866(f196(f931(x42431)),f184(x42431,x42432,x42433))),f866(f196(f931(x42431)),x42433)))
% 157.60/157.51 [4250]E(f866(f272(x42501,x42502),f866(f270(f936(x42501,x42502)),f866(f265(x42501,x42502,a925),x42503))),f866(f270(x42501),f866(f866(f8(f937(x42502,a925),a925,x42501),f93(x42502)),x42503)))
% 157.60/157.51 [4262]E(f866(f317(a930,a930,f866(f866(f7(a930,a930,a930),f86(a930)),x42621)),f310(a930,x42622,x42623)),f310(a930,f866(f866(f86(a930),x42622),x42621),f866(f866(f86(a930),x42623),x42621)))
% 157.60/157.51 [4276]E(f866(f317(a930,a930,f866(f866(f7(a930,a930,a930),f86(a930)),x42761)),f866(f309(a930,x42762),x42763)),f866(f309(a930,f866(f866(f86(a930),x42762),x42761)),f866(f866(f86(a930),x42763),x42761)))
% 157.60/157.51 [4294]E(f866(f866(f188(x42941,x42942),f866(f866(f161(f936(x42941,x42942),x42941),f259(x42941,x42942)),x42943)),f866(f866(f161(f936(x42941,x42942),x42942),f264(x42941,x42942)),x42943)),x42943)
% 157.60/157.51 [4299]E(f866(f866(f86(a930),f866(f866(f87(a930),x42991),f50(a930,f866(f866(f41(a930),x42992),x42991),x42993))),f50(a930,x42992,x42991)),f50(a930,x42992,f866(f866(f87(a930),x42991),x42993)))
% 157.60/157.51 [4312]E(f866(f866(f141(x43121),x43122),f866(f149(f931(x43121),f931(x43121),f141(x43121),f120(x43121)),x43123)),f866(f149(f931(x43121),f931(x43121),f141(x43121),x43122),x43123))
% 157.60/157.51 [4333]P107(f866(f866(f336(f936(x43331,x43331)),f866(f866(f260(x43331,x43331),x43332),x43332)),f866(f866(f190(f936(x43331,x43331),a925),f2(a930)),x43333)))
% 157.60/157.51 [4338]E(f866(f270(x43381),f866(f866(f8(f937(x43382,a925),a925,x43381),f93(x43382)),f866(f7(x43382,x43381,a925),x43383))),f866(f292(x43382,x43381),f866(f270(f936(x43382,x43381)),f866(f265(x43382,x43381,a925),x43383))))
% 157.60/157.51 [4355]E(f866(f866(f117(f937(x43551,a925)),f866(f866(f44(a930,f937(x43551,a925)),f310(a930,f84(a930),x43552)),x43553)),f866(x43553,f2(a930))),f866(f866(f44(a930,f937(x43551,a925)),f866(f308(a930),x43552)),x43553))
% 157.60/157.51 [4370]E(f866(f149(f931(x43701),f931(x43701),f141(x43701),f120(x43701)),f866(f866(f161(f931(x43701),f931(x43701)),f143(x43701,x43702)),x43703)),f866(f143(x43701,x43702),f866(f149(f931(x43701),f931(x43701),f141(x43701),f120(x43701)),x43703)))
% 157.60/157.51 [4374]E(f866(f264(f931(x43741),f931(x43741)),f173(x43741,x43742,x43743)),f866(f143(x43741,f866(f78(a925,a925,x43741,a329),x43742)),x43743))
% 157.60/157.51 [4384]P24(x43841,x43842,f866(f866(f316(f929(x43841)),f98(x43841,x43843,a25,x43843)),f195(f937(f929(x43841),a925))))
% 157.60/157.51 [4421]E(f866(f866(f86(a1),f866(f866(f86(a1),f866(f866(f87(a1),x44211),f866(f866(f41(a1),x44212),x44211))),f50(a1,x44212,x44211))),x44213),f866(f866(f86(a1),x44212),x44213))
% 157.60/157.51 [4458]E(f866(f866(f86(a1),f866(f866(f86(a1),f866(f866(f87(a1),f866(f866(f41(a1),x44581),x44582)),x44582)),f50(a1,x44581,x44582))),x44583),f866(f866(f86(a1),x44581),x44583))
% 157.60/157.51 [4484]E(f91(f936(x44841,x44842),f866(f265(x44841,x44842,a925),f866(f866(f8(f937(x44842,f936(x44841,x44842)),f937(x44842,a925),x44841),f866(f8(f936(x44841,x44842),a925,x44842),x44843)),f260(x44841,x44842)))),f91(f936(x44841,x44842),x44843))
% 157.60/157.51 [4485]E(f96(f936(x44851,x44852),f866(f265(x44851,x44852,a925),f866(f866(f8(f937(x44852,f936(x44851,x44852)),f937(x44852,a925),x44851),f866(f8(f936(x44851,x44852),a925,x44852),x44853)),f260(x44851,x44852)))),f96(f936(x44851,x44852),x44853))
% 157.60/157.51 [4512]P107(f866(f866(f243(f937(x45121,a925)),f42(f937(x45121,a925),f866(f866(f108(f937(f937(x45121,a925),a925)),x45122),x45123))),f866(f866(f108(f937(x45121,a925)),f42(f937(x45121,a925),x45122)),f42(f937(x45121,a925),x45123))))
% 157.60/157.51 [4513]E(f866(f175(x45131),f866(f866(f866(f190(f931(x45131),f931(x45131)),f866(f866(f23(a930),f866(f196(f931(x45131)),x45132)),f50(a930,x45133,f866(f196(f931(x45131)),x45132)))),f174(x45131)),x45132)),f866(f866(f866(f190(f931(x45131),f931(x45131)),x45133),f174(x45131)),f866(f175(x45131),x45132)))
% 157.60/157.51 [4550]P107(f866(f866(f243(a930),f866(f196(f931(x45501)),f866(f866(f145(x45501),f866(f196(f931(x45501)),f184(x45501,x45502,x45503))),x45503))),f866(f196(f931(x45501)),x45503)))
% 157.60/157.51 [4800]~P107(f866(f67(x48001,x48002,f195(f937(x48001,a925))),x48003))
% 157.60/157.51 [4805]~P107(f866(f866(f336(f936(x48051,x48051)),f866(f866(f260(x48051,x48051),x48052),x48053)),f160(x48051,f120(f937(x48051,a930)))))
% 157.60/157.51 [3860]E(f866(f196(f931(x38601)),f866(f866(f182(x38601),x38602),x38603)),f866(f866(f241(a930),f866(f196(f931(x38601)),x38603)),x38602))
% 157.60/157.51 [3861]E(f866(f196(f931(x38611)),f866(f866(f145(x38611),x38612),x38613)),f866(f866(f23(a930),f866(f196(f931(x38611)),x38613)),x38612))
% 157.60/157.51 [3887]E(f866(f196(f931(f931(x38871))),f60(x38871,x38872,x38873)),f866(f866(f252(a930),f866(f196(f931(x38871)),x38873)),x38872))
% 157.60/157.51 [3904]E(f866(f866(f41(a930),f866(f866(f41(a930),x39041),x39042)),x39043),f866(f866(f41(a930),x39041),f866(f866(f87(a930),x39042),x39043)))
% 157.60/157.51 [3905]E(f866(f866(f23(a930),f866(f866(f23(a930),x39051),x39052)),x39053),f866(f866(f23(a930),x39051),f866(f866(f86(a930),x39052),x39053)))
% 157.60/157.51 [3906]E(f866(f866(f87(a930),f866(f866(f87(a930),x39061),x39062)),x39063),f866(f866(f87(a930),x39061),f866(f866(f87(a930),x39062),x39063)))
% 157.60/157.51 [3907]E(f866(f866(f87(a1),f866(f866(f87(a1),x39071),x39072)),x39073),f866(f866(f87(a1),x39071),f866(f866(f87(a1),x39072),x39073)))
% 157.60/157.51 [3908]E(f866(f866(f86(a930),f866(f866(f86(a930),x39081),x39082)),x39083),f866(f866(f86(a930),x39081),f866(f866(f86(a930),x39082),x39083)))
% 157.60/157.51 [3909]E(f866(f866(f86(a1),f866(f866(f86(a1),x39091),x39092)),x39093),f866(f866(f86(a1),x39091),f866(f866(f86(a1),x39092),x39093)))
% 157.60/157.51 [3910]E(f866(f866(f252(a1),f866(f866(f252(a1),x39101),x39102)),x39103),f866(f866(f252(a1),x39101),f866(f866(f87(a930),x39102),x39103)))
% 157.60/157.51 [3929]E(f169(x39291,f866(f866(f158(f937(x39291,a925)),x39292),x39293)),f181(x39291,x39292,f169(x39291,x39293)))
% 157.60/157.51 [3973]E(f866(f866(f23(a930),f866(f866(f23(a930),x39731),x39732)),x39733),f866(f866(f23(a930),f866(f866(f23(a930),x39731),x39733)),x39732))
% 157.60/157.51 [3981]E(f866(f866(f108(f937(x39811,a925)),x39812),f866(f866(f23(f937(x39811,a925)),x39813),x39812)),f195(f937(x39811,a925)))
% 157.60/157.51 [3985]E(f866(f866(f161(a930,x39851),f866(f16(x39851,a930),x39852)),f146(a930,f866(f309(a930,f2(a930)),x39853))),f176(x39851,x39853,x39852))
% 157.60/157.51 [4024]E(f43(f937(x40241,a925),f866(f866(f316(f937(x40241,a925)),x40242),x40243)),f866(f866(f108(f937(x40241,a925)),x40242),f43(f937(x40241,a925),x40243)))
% 157.60/157.51 [4025]E(f42(f937(x40251,a925),f866(f866(f316(f937(x40251,a925)),x40252),x40253)),f866(f866(f117(f937(x40251,a925)),x40252),f42(f937(x40251,a925),x40253)))
% 157.60/157.51 [4027]E(f176(x40271,f866(f196(f931(x40271)),f866(f143(x40271,f866(a332,x40272)),x40273)),x40272),f866(f143(x40271,f866(a332,x40272)),x40273))
% 157.60/157.51 [4029]E(f866(f866(f23(a930),f866(f866(f87(a930),x40291),x40292)),f866(f866(f87(a930),x40293),x40292)),f866(f866(f87(a930),f866(f866(f23(a930),x40291),x40293)),x40292))
% 157.60/157.51 [4030]E(f866(f866(f86(a930),f866(f866(f87(a930),x40301),x40302)),f866(f866(f87(a930),x40303),x40302)),f866(f866(f87(a930),f866(f866(f86(a930),x40301),x40303)),x40302))
% 157.60/157.51 [4031]E(f866(f866(f23(a1),f866(f866(f87(a1),x40311),x40312)),f866(f866(f87(a1),x40313),x40312)),f866(f866(f87(a1),f866(f866(f23(a1),x40311),x40313)),x40312))
% 157.60/157.51 [4032]E(f866(f866(f86(a1),f866(f866(f87(a1),x40321),x40322)),f866(f866(f87(a1),x40323),x40322)),f866(f866(f87(a1),f866(f866(f86(a1),x40321),x40323)),x40322))
% 157.60/157.51 [4034]E(f866(f866(f241(a930),f866(f866(f23(a930),x40341),x40342)),f866(f866(f23(a930),x40343),x40342)),f866(f866(f23(a930),f866(f866(f241(a930),x40341),x40343)),x40342))
% 157.60/157.51 [4055]E(f866(f866(f108(f937(f931(x40551),a925)),f167(x40551,x40552)),f167(x40551,x40553)),f167(x40551,f866(f866(f108(f937(x40551,a925)),x40552),x40553)))
% 157.60/157.51 [4058]E(f866(f866(f117(f937(x40581,a925)),x40582),f866(f866(f23(f937(x40581,a925)),x40583),x40582)),f866(f866(f117(f937(x40581,a925)),x40582),x40583))
% 157.60/157.51 [4059]E(f866(f866(f117(f937(x40591,a925)),x40592),f866(f866(f117(f937(x40591,a925)),x40592),x40593)),f866(f866(f117(f937(x40591,a925)),x40592),x40593))
% 157.60/157.51 [4060]E(f866(f866(f108(f937(x40601,a925)),x40602),f866(f866(f108(f937(x40601,a925)),x40602),x40603)),f866(f866(f108(f937(x40601,a925)),x40602),x40603))
% 157.60/157.51 [4072]E(f866(f866(f296(x40721,x40722,x40722),x40723),f314(x40722,f195(f937(f936(x40722,x40722),a925)))),x40723)
% 157.60/157.51 [4075]E(f866(f866(f117(f937(x40751,a925)),f866(f866(f316(x40751),x40752),f195(f937(x40751,a925)))),x40753),f866(f866(f316(x40751),x40752),x40753))
% 157.60/157.51 [4094]E(f866(f866(f23(a930),f866(f866(f23(a930),f866(a119,x40941)),x40942)),f866(a119,x40943)),f866(f866(f23(a930),f866(f866(f23(a930),x40941),x40942)),x40943))
% 157.60/157.51 [4122]E(f866(f866(f108(f937(f937(x41221,a925),a925)),f866(f315(x41221),x41222)),f866(f315(x41221),x41223)),f866(f315(x41221),f866(f866(f108(f937(x41221,a925)),x41222),x41223)))
% 157.60/157.51 [4125]E(f866(f866(f117(f937(x41251,a925)),f866(f85(f937(x41251,a925)),x41252)),x41253),f866(f85(f937(x41251,a925)),f866(f866(f23(f937(x41251,a925)),x41252),x41253)))
% 157.60/157.51 [4135]E(f866(f866(f316(x41351),x41352),f866(f866(f23(f937(x41351,a925)),x41353),f866(f866(f316(x41351),x41352),f195(f937(x41351,a925))))),f866(f866(f316(x41351),x41352),x41353))
% 157.60/157.51 [4147]P107(f866(f866(f243(f937(x41471,a925)),x41472),f866(f866(f117(f937(x41471,a925)),x41473),x41472)))
% 157.60/157.51 [4148]P107(f866(f866(f243(f937(x41481,a925)),x41482),f866(f866(f117(f937(x41481,a925)),x41482),x41483)))
% 157.60/157.51 [4152]E(f866(f866(f108(f937(x41521,a925)),f866(f85(f937(x41521,a925)),x41522)),f866(f85(f937(x41521,a925)),x41523)),f866(f85(f937(x41521,a925)),f866(f866(f117(f937(x41521,a925)),x41522),x41523)))
% 157.60/157.51 [4153]E(f866(f866(f117(f937(x41531,a925)),f866(f85(f937(x41531,a925)),x41532)),f866(f85(f937(x41531,a925)),x41533)),f866(f85(f937(x41531,a925)),f866(f866(f108(f937(x41531,a925)),x41532),x41533)))
% 157.60/157.51 [4167]P107(f866(f866(f243(f937(x41671,a925)),f866(f179(x41671),x41672)),f866(f179(x41671),f866(f866(f158(x41671),x41673),x41672))))
% 157.60/157.51 [4179]E(f866(f866(f117(f937(x41791,a925)),f866(f866(f23(f937(x41791,a925)),x41792),x41793)),f866(f866(f108(f937(x41791,a925)),x41792),x41793)),x41792)
% 157.60/157.51 [4230]E(f866(f866(f9(x42301,a1),f866(f866(f8(a930,a1,x42301),f107(a1)),x42302)),x42303),f866(f107(a1),f866(f866(f9(x42301,a930),x42302),x42303)))
% 157.60/157.51 [4231]E(f866(f866(f6(x42311,a1),f866(f866(f8(a930,a1,x42311),f107(a1)),x42312)),x42313),f866(f107(a1),f866(f866(f6(x42311,a930),x42312),x42313)))
% 157.60/157.51 [4278]E(f866(f866(f141(x42781),f184(x42781,x42782,x42783)),f866(f866(f145(x42781),f866(f196(f931(x42781)),f184(x42781,x42782,x42783))),x42783)),x42783)
% 157.60/157.51 [4282]E(f866(f85(f937(f936(x42821,x42822),a925)),f866(f866(f262(x42821,x42822),x42823),f866(f16(f937(x42822,a925),x42821),f250(f937(x42822,a925))))),f866(f866(f262(x42821,x42822),f866(f85(f937(x42821,a925)),x42823)),f866(f16(f937(x42822,a925),x42821),f250(f937(x42822,a925)))))
% 157.60/157.51 [4283]E(f866(f85(f937(f936(x42831,x42832),a925)),f866(f866(f262(x42831,x42832),f250(f937(x42831,a925))),f866(f16(f937(x42832,a925),x42831),x42833))),f866(f866(f262(x42831,x42832),f250(f937(x42831,a925))),f866(f16(f937(x42832,a925),x42831),f866(f85(f937(x42832,a925)),x42833))))
% 157.60/157.51 [4334]E(f866(f866(f44(f937(x43341,a925),f937(x43341,a925)),x43342),f866(f866(f7(f937(x43341,a925),f937(x43341,a925),f937(x43341,a925)),f108(f937(x43341,a925))),x43343)),f866(f866(f108(f937(x43341,a925)),f42(f937(x43341,a925),x43342)),x43343))
% 157.60/157.51 [4340]E(f866(f149(f931(x43401),f931(x43401),f141(x43401),f120(x43401)),f866(f866(f158(f931(x43401)),x43402),x43403)),f866(f866(f141(x43401),x43402),f866(f149(f931(x43401),f931(x43401),f141(x43401),f120(x43401)),x43403)))
% 157.60/157.51 [4361]E(f866(f866(f316(f937(x43611,a925)),f866(f293(x43611,x43611,x43612),f866(f866(f316(x43611),x43613),f195(f937(x43611,a925))))),f195(f937(f937(x43611,a925),a925))),f866(f866(f65(x43611),f866(f866(f316(x43611),x43613),f195(f937(x43611,a925)))),x43612))
% 157.60/157.51 [4371]E(f866(f866(f86(a930),f866(f866(f87(a930),x43711),f866(f866(f41(a930),x43712),x43713))),f866(f866(f41(a930),f866(f866(f87(a930),x43711),f50(a930,x43712,x43713))),x43713)),f866(f866(f41(a930),f866(f866(f87(a930),x43711),x43712)),x43713))
% 157.60/157.51 [4372]E(f866(f866(f86(a1),f866(f866(f87(a1),x43721),f866(f866(f41(a1),x43722),x43723))),f866(f866(f41(a1),f866(f866(f87(a1),x43721),f50(a1,x43722,x43723))),x43723)),f866(f866(f41(a1),f866(f866(f87(a1),x43721),x43722)),x43723))
% 157.60/157.51 [4406]E(f866(f866(f23(f937(x44061,a925)),f866(f179(x44061),x44062)),f866(f866(f316(x44061),x44063),f195(f937(x44061,a925)))),f866(f179(x44061),f866(f143(x44061,f866(f866(f8(a925,a925,x44061),a329),f866(a332,x44063))),x44062)))
% 157.60/157.51 [4456]E(f866(f866(f141(x44561),f866(f149(f931(x44561),f931(x44561),f141(x44561),f120(x44561)),x44562)),f866(f149(f931(x44561),f931(x44561),f141(x44561),f120(x44561)),x44563)),f866(f149(f931(x44561),f931(x44561),f141(x44561),f120(x44561)),f866(f866(f141(f931(x44561)),x44562),x44563)))
% 157.60/157.51 [4459]E(f866(f866(f260(f931(x44591),f931(x44591)),f866(f143(x44591,x44592),x44593)),f866(f143(x44591,f866(f78(a925,a925,x44591,a329),x44592)),x44593)),f173(x44591,x44592,x44593))
% 157.60/157.51 [4462]E(f866(f866(f86(a930),f866(f866(f86(a930),f866(f866(f41(a930),x44621),x44622)),f866(f866(f41(a930),x44623),x44622))),f866(f866(f41(a930),f866(f866(f86(a930),f50(a930,x44621,x44622)),f50(a930,x44623,x44622))),x44622)),f866(f866(f41(a930),f866(f866(f86(a930),x44621),x44623)),x44622))
% 157.60/157.51 [4463]E(f866(f866(f86(a1),f866(f866(f86(a1),f866(f866(f41(a1),x44631),x44632)),f866(f866(f41(a1),x44633),x44632))),f866(f866(f41(a1),f866(f866(f86(a1),f50(a1,x44631,x44632)),f50(a1,x44633,x44632))),x44632)),f866(f866(f41(a1),f866(f866(f86(a1),x44631),x44633)),x44632))
% 157.60/157.51 [4516]E(f866(f866(f108(f937(f931(x45161),a925)),f866(f866(f7(f931(x45161),f937(f931(x45161),a925),a925),f336(f931(x45161))),f168(x45161,x45162))),f866(f866(f7(f931(x45161),f937(f931(x45161),a925),a925),f336(f931(x45161))),f168(x45161,x45163))),f167(x45161,f866(f866(f108(f937(x45161,a925)),f866(f866(f7(x45161,f937(x45161,a925),a925),f336(x45161)),x45162)),f866(f866(f7(x45161,f937(x45161,a925),a925),f336(x45161)),x45163))))
% 157.60/157.51 [4528]E(f866(f270(x45281),f866(f866(f18(x45281,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45281),a334),f866(f866(f7(x45281,x45281,a925),a332),x45282))),f866(f866(f7(x45281,f937(x45281,a925),a925),f336(x45281)),x45283))),f866(f866(f316(x45281),x45282),x45283))
% 157.60/157.51 [4548]E(f866(f866(f92(f931(f931(x45481)),f931(f931(x45481))),f59(x45481,x45482)),f866(f866(f18(f931(f931(x45481)),f931(f931(x45481)),f931(f931(x45481))),f866(f866(f8(f931(f931(x45481)),f937(f931(f931(x45481)),f931(f931(x45481))),f931(f931(x45481))),f141(f931(x45481))),f866(f161(f931(x45481),f931(x45481)),f866(f158(x45481),x45483)))),f5(f931(f931(x45481))))),f59(x45481,f866(f866(f158(x45481),x45483),x45482)))
% 157.60/157.51 [4551]E(f866(f270(x45511),f866(f866(f18(x45511,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45511),a334),f866(f866(f7(x45511,f937(x45511,a925),a925),f336(x45511)),x45512))),f866(f866(f7(x45511,f937(x45511,a925),a925),f336(x45511)),x45513))),f866(f866(f117(f937(x45511,a925)),x45512),x45513))
% 157.60/157.51 [4552]E(f866(f270(x45521),f866(f866(f18(x45521,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45521),a333),f866(f866(f7(x45521,f937(x45521,a925),a925),f336(x45521)),x45522))),f866(f866(f7(x45521,f937(x45521,a925),a925),f336(x45521)),x45523))),f866(f866(f108(f937(x45521,a925)),x45522),x45523))
% 157.60/157.51 [4641]E(f866(f866(f44(x46411,f937(f937(x46411,a925),a925)),x46412),f866(f866(f7(x46411,f937(f937(x46411,a925),a925),f937(f937(x46411,a925),a925)),f866(f866(f8(f937(x46411,a925),f937(f937(f937(x46411,a925),a925),f937(f937(x46411,a925),a925)),x46411),f316(f937(x46411,a925))),f866(f866(f8(f937(x46411,a925),f937(x46411,a925),x46411),f293(x46411,x46411,x46413)),f866(f866(f7(x46411,f937(x46411,a925),f937(x46411,a925)),f316(x46411)),f195(f937(x46411,a925)))))),f195(f937(f937(x46411,a925),a925)))),f866(f866(f65(x46411),x46412),x46413))
% 157.60/157.51 [4643]E(f866(f866(f210(x46431),f866(f866(f87(a1),f866(f866(f78(f936(a1,a1),a1,x46431,f259(a1,a1)),f221(x46431)),x46432)),f866(f866(f78(f936(a1,a1),a1,x46431,f259(a1,a1)),f221(x46431)),x46433))),f866(f866(f87(a1),f866(f866(f78(f936(a1,a1),a1,x46431,f264(a1,a1)),f221(x46431)),x46432)),f866(f866(f78(f936(a1,a1),a1,x46431,f264(a1,a1)),f221(x46431)),x46433))),f237(x46431,x46432,x46433))
% 157.60/157.51 [4646]E(f866(f270(f931(x46461)),f866(f866(f18(f931(x46461),a925,a925),f866(f866(f8(a925,f937(a925,a925),f931(x46461)),a333),f866(f866(f7(f931(x46461),a930,a925),f866(f866(f8(a930,f937(a930,a925),f931(x46461)),a332),f196(f931(x46461)))),x46462))),f866(f866(f7(f931(x46461),f937(x46461,a925),a925),f866(f866(f8(f937(x46461,a925),f937(f937(x46461,a925),a925),f931(x46461)),f243(f937(x46461,a925))),f179(x46461))),f866(f179(x46461),x46463)))),f866(f179(f931(x46461)),f60(x46461,x46462,x46463)))
% 157.60/157.51 [4048]E(f50(a930,f866(f866(f86(a930),f866(f866(f87(a930),x40481),x40482)),x40483),x40482),f50(a930,x40483,x40482))
% 157.60/157.51 [4093]E(f146(a930,f866(f309(a930,f866(f866(f86(a930),x40931),x40932)),x40933)),f866(f866(f145(a930),x40932),f146(a930,f866(f309(a930,x40931),x40933))))
% 157.60/157.51 [4134]E(f866(f866(f86(a1),f866(f107(a1),x41341)),f866(f866(f86(a1),f866(f107(a1),x41342)),x41343)),f866(f866(f86(a1),f866(f107(a1),f866(f866(f86(a930),x41341),x41342))),x41343))
% 157.60/157.51 [4143]E(f866(f866(f23(f937(x41431,a925)),f866(f866(f23(f937(x41431,a925)),x41432),x41433)),x41433),f866(f866(f23(f937(x41431,a925)),x41432),x41433))
% 157.60/157.51 [4144]E(f866(f866(f117(f937(x41441,a925)),f866(f866(f23(f937(x41441,a925)),x41442),x41443)),x41443),f866(f866(f117(f937(x41441,a925)),x41442),x41443))
% 157.60/157.51 [4168]E(f866(f866(f296(x41681,x41681,x41682),f314(x41681,f195(f937(f936(x41681,x41681),a925)))),x41683),x41683)
% 157.60/157.51 [4176]E(f866(f866(f117(f937(x41761,a925)),f866(f289(x41761),x41762)),f866(f289(x41761),x41763)),f866(f289(x41761),f866(f866(f117(f937(f936(x41761,x41761),a925)),x41762),x41763)))
% 157.60/157.51 [4186]E(f274(x41861,f866(f866(f158(f936(a106,x41861)),f866(f866(f260(a106,x41861),f2(a106)),x41862)),x41863)),f274(x41861,x41863))
% 157.60/157.51 [4188]E(f866(f866(f108(f937(x41881,a925)),f43(f937(x41881,a925),x41882)),f43(f937(x41881,a925),x41883)),f43(f937(x41881,a925),f866(f866(f117(f937(f937(x41881,a925),a925)),x41882),x41883)))
% 157.60/157.51 [4189]E(f866(f866(f117(f937(x41891,a925)),f42(f937(x41891,a925),x41892)),f42(f937(x41891,a925),x41893)),f42(f937(x41891,a925),f866(f866(f117(f937(f937(x41891,a925),a925)),x41892),x41893)))
% 157.60/157.51 [4226]E(f866(f866(f296(x42261,x42261,x42261),f866(f866(f190(f936(x42261,x42261),a925),x42262),x42263)),x42263),f866(f866(f190(f936(x42261,x42261),a925),f866(a119,x42262)),x42263))
% 157.60/157.51 [4270]P107(f866(f866(f243(f937(x42701,a925)),f866(f866(f23(f937(x42701,a925)),x42702),x42703)),x42702))
% 157.60/157.51 [4271]P107(f866(f866(f243(f937(x42711,a925)),f866(f866(f108(f937(x42711,a925)),x42712),x42713)),x42713))
% 157.60/157.51 [4272]P107(f866(f866(f243(f937(x42721,a925)),f866(f866(f108(f937(x42721,a925)),x42722),x42723)),x42722))
% 157.60/157.51 [4296]E(f314(x42961,f866(f866(f117(f937(f936(x42961,x42961),a925)),f314(x42961,x42962)),f314(x42961,x42963))),f314(x42961,f866(f866(f117(f937(f936(x42961,x42961),a925)),x42962),x42963)))
% 157.60/157.51 [4300]E(f42(f937(x43001,a925),f866(f866(f316(f937(x43001,a925)),x43002),f866(f866(f316(f937(x43001,a925)),x43003),f195(f937(f937(x43001,a925),a925))))),f866(f866(f117(f937(x43001,a925)),x43002),x43003))
% 157.60/157.51 [4301]E(f43(f937(x43011,a925),f866(f866(f316(f937(x43011,a925)),x43012),f866(f866(f316(f937(x43011,a925)),x43013),f195(f937(f937(x43011,a925),a925))))),f866(f866(f108(f937(x43011,a925)),x43012),x43013))
% 157.60/157.51 [4306]E(f866(f866(f296(x43061,x43061,x43061),f866(f866(f190(f936(x43061,x43061),a925),x43062),x43063)),x43063),f866(f866(f296(x43061,x43061,x43061),x43063),f866(f866(f190(f936(x43061,x43061),a925),x43062),x43063)))
% 157.60/157.51 [4375]E(f866(f866(f117(f937(x43751,a925)),f866(f270(x43751),f866(f866(f7(x43751,x43751,a925),a332),x43752))),x43753),f866(f866(f316(x43751),x43752),x43753))
% 157.60/157.51 [4377]E(f866(a111,f866(f866(f9(x43771,a1),f866(f866(f8(a930,a1,x43771),f107(a1)),x43772)),x43773)),f866(f866(f9(x43771,a930),x43772),x43773))
% 157.60/157.51 [4378]E(f866(a111,f866(f866(f6(x43781,a1),f866(f866(f8(a930,a1,x43781),f107(a1)),x43782)),x43783)),f866(f866(f6(x43781,a930),x43782),x43783))
% 157.60/157.51 [4453]E(f866(f163(f931(x44531),x44531,f866(f178(x44531),x44532),f866(f16(f937(f931(x44531),f931(x44531)),x44531),f866(f866(f7(f931(x44531),f931(x44531),f931(x44531)),f141(x44531)),x44532))),x44533),f866(f178(x44531),f866(f866(f141(x44531),x44533),x44532)))
% 157.60/157.51 [4481]P107(f866(f866(f243(f937(f937(x44811,a925),a925)),f866(f866(f117(f937(f937(x44811,a925),a925)),f866(f315(x44811),x44812)),f866(f315(x44811),x44813))),f866(f315(x44811),f866(f866(f117(f937(x44811,a925)),x44812),x44813))))
% 157.60/157.51 [4570]E(f866(f270(x45701),f866(f866(f18(x45701,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45701),a333),f866(f866(f7(x45701,f937(x45701,a925),a925),f336(x45701)),x45702))),f866(f866(f8(a925,a925,x45701),a329),f866(f866(f7(x45701,f937(x45701,a925),a925),f336(x45701)),x45703)))),f866(f866(f23(f937(x45701,a925)),x45702),x45703))
% 157.60/157.51 [4594]E(f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,a930,a925),f244(a930)),f866(f196(f931(x45941)),x45942)))),f866(f866(f8(x45941,a925,a930),x45943),f866(f171(x45941),x45942))))),f866(f196(f931(x45941)),f866(f143(x45941,x45943),x45942)))
% 157.60/157.51 [4596]E(f866(f196(f931(x45961)),f183(x45961,x45962,x45963)),f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,a930,a925),f244(a930)),f866(f196(f931(x45961)),x45962)))),f866(f866(f7(a930,f937(a930,a925),a925),f336(a930)),x45963)))))
% 157.60/157.51 [4694]E(f866(f866(f108(f937(f936(f931(x46941),f931(x46941)),a925)),f866(f317(f936(f936(x46941,f931(x46941)),f936(x46941,f931(x46941))),f936(f931(x46941),f931(x46941)),f266(f936(x46941,f931(x46941)),f931(x46941),f936(x46941,f931(x46941)),f931(x46941),f866(f265(x46941,f931(x46941),f931(x46941)),f158(x46941)),f866(f265(x46941,f931(x46941),f931(x46941)),f158(x46941)))),f326(x46941,f931(x46941),x46942,f866(f150(x46941,x46942),x46943)))),f866(f270(f936(f931(x46941),f931(x46941))),f866(f265(f931(x46941),f931(x46941),a925),f866(f866(f7(f931(x46941),f937(f931(x46941),a925),f937(f931(x46941),a925)),f866(f866(f8(f937(a925,a925),f937(f937(f931(x46941),a925),f937(f931(x46941),a925)),f931(x46941)),f8(a925,a925,f931(x46941))),f866(f866(f8(a925,f937(a925,a925),f931(x46941)),a333),f866(f866(f7(f931(x46941),a930,a925),f866(f866(f8(a930,f937(a930,a925),f931(x46941)),a332),f196(f931(x46941)))),f866(a119,x46943))))),f866(f866(f7(f931(x46941),a930,a925),f866(f866(f8(a930,f937(a930,a925),f931(x46941)),a332),f196(f931(x46941)))),f866(a119,x46943)))))),f866(f150(x46941,x46942),f866(a119,x46943)))
% 157.60/157.51 [4190]E(f50(a930,f866(a119,f866(f866(f86(a930),f866(f866(f87(a930),x41901),x41902)),x41903)),x41902),f50(a930,f866(a119,x41903),x41902))
% 157.60/157.51 [4439]E(f866(f270(x44391),f866(f866(f18(x44391,a925,a925),f866(f866(f8(a925,f937(a925,a925),x44391),a333),x44392)),x44393)),f866(f866(f108(f937(x44391,a925)),f866(f270(x44391),x44392)),f866(f270(x44391),x44393)))
% 157.60/157.51 [4440]E(f866(f270(x44401),f866(f866(f18(x44401,a925,a925),f866(f866(f8(a925,f937(a925,a925),x44401),a334),x44402)),x44403)),f866(f866(f117(f937(x44401,a925)),f866(f270(x44401),x44402)),f866(f270(x44401),x44403)))
% 157.60/157.51 [4442]E(f866(f866(f141(x44421),f866(f866(f145(x44421),f50(a930,x44422,f866(f196(f931(x44421)),x44423))),x44423)),f866(f866(f182(x44421),f50(a930,x44422,f866(f196(f931(x44421)),x44423))),x44423)),f866(f866(f866(f190(f931(x44421),f931(x44421)),x44422),f174(x44421)),x44423))
% 157.60/157.51 [4448]E(f866(f270(x44481),f866(f866(f18(x44481,a925,a925),f866(f866(f8(a925,f937(a925,a925),x44481),a337),x44482)),x44483)),f866(f866(f117(f937(x44481,a925)),f866(f85(f937(x44481,a925)),f866(f270(x44481),x44482))),f866(f270(x44481),x44483)))
% 157.60/157.51 [4464]E(f866(f866(f86(a930),f866(f196(f931(x44641)),f866(f143(x44641,x44642),x44643))),f866(f196(f931(x44641)),f866(f143(x44641,f866(f866(f8(a925,a925,x44641),a329),x44642)),x44643))),f866(f196(f931(x44641)),x44643))
% 157.60/157.51 [4487]P107(f866(f866(f243(f937(x44871,a925)),f866(f866(f117(f937(x44871,a925)),f43(f937(x44871,a925),x44872)),f43(f937(x44871,a925),x44873))),f43(f937(x44871,a925),f866(f866(f108(f937(f937(x44871,a925),a925)),x44872),x44873))))
% 157.60/157.51 [4501]E(f866(f179(x45011),f866(f143(x45011,f866(f866(f8(a925,a925,x45011),a329),f866(f866(f7(x45011,x45011,a925),a332),x45012))),x45013)),f866(f866(f23(f937(x45011,a925)),f866(f179(x45011),x45013)),f866(f866(f316(x45011),x45012),f195(f937(x45011,a925)))))
% 157.60/157.51 [4510]P107(f866(f866(f243(f937(f936(x45101,x45101),a925)),f866(f866(f117(f937(f936(x45101,x45101),a925)),f314(x45101,x45102)),f314(x45101,x45103))),f314(x45101,f866(f866(f117(f937(f936(x45101,x45101),a925)),x45102),x45103))))
% 157.60/157.51 [4533]E(f866(f866(f87(a930),f866(a119,f866(a119,f2(a930)))),f866(f866(f6(a930,a930),f866(f866(f8(a930,a930,a930),f866(f86(a930),x45331)),f866(f866(f7(a930,a930,a930),f87(a930)),x45332))),f866(f290(a930),x45333))),f866(f866(f87(a930),x45333),f866(f866(f86(a930),x45331),f866(f866(f86(a930),x45331),f866(f866(f87(a930),f866(f866(f23(a930),x45333),f84(a930))),x45332)))))
% 157.60/157.51 [4543]E(f866(f270(x45431),f866(f866(f18(x45431,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45431),a333),f866(f866(f7(x45431,f937(x45431,a925),a925),f336(x45431)),f866(f179(x45431),x45432)))),x45433)),f866(f179(x45431),f866(f143(x45431,x45433),x45432)))
% 157.60/157.51 [4693]E(f866(f270(x46931),f866(f866(f8(f937(a930,a925),a925,x46931),f93(a930)),f866(f866(f7(x46931,f937(a930,a925),f937(a930,a925)),f866(f866(f8(f937(a930,f937(a925,a925)),f937(f937(a930,a925),f937(a930,a925)),x46931),f18(a930,a925,a925)),f866(f866(f8(f937(a930,a925),f937(a930,f937(a925,a925)),x46931),f866(f8(a925,f937(a925,a925),a930),a333)),f866(f866(f7(x46931,f937(a930,x46931),f937(a930,a925)),f866(f866(f8(f937(x46931,a925),f937(f937(a930,x46931),f937(a930,a925)),x46931),f8(x46931,a925,a930)),a332)),f866(f171(x46931),x46932))))),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,a930,a925),f244(a930)),f866(f196(f931(x46931)),x46932)))),f866(f866(f7(a930,f937(a930,a925),a925),f336(a930)),x46933))))),f866(f179(x46931),f183(x46931,x46932,x46933)))
% 157.60/157.51 [4583]E(f866(f270(x45831),f866(f866(f18(x45831,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45831),a337),f866(f866(f8(a925,a925,x45831),a329),f866(f866(f7(x45831,x45831,a925),a332),x45832)))),x45833)),f866(f866(f316(x45831),x45832),f866(f270(x45831),x45833)))
% 157.60/157.51 [4615]E(f866(f866(f161(f936(x46151,a930),x46151),f259(x46151,a930)),f866(f143(f936(x46151,a930),f866(f866(f7(f936(x46151,a930),f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),f936(x46151,a930)),f336(a930)),f264(x46151,a930))),x46152)),f866(f866(f188(x46151,a930),x46153),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(x46151)),x46153)))))),f183(x46151,x46153,x46152))
% 157.60/157.51 [4642]E(f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f6(a930,a1),f866(f866(f8(a1,a1,a930),f866(f86(a1),x46421)),f866(f866(f7(a930,a1,a1),f866(f866(f8(a1,f937(a1,a1),a930),f87(a1)),f107(a1))),x46422))),f866(f290(a930),x46423))),f866(f866(f87(a1),f866(f107(a1),x46423)),f866(f866(f86(a1),x46421),f866(f866(f86(a1),x46421),f866(f866(f87(a1),f866(f107(a1),f866(f866(f23(a930),x46423),f84(a930)))),x46422)))))
% 157.60/157.51 [4686]E(f866(f270(f936(x46861,x46862)),f866(f265(x46861,x46862,a925),f866(f866(f7(x46861,f937(f936(x46862,x46861),a925),f937(x46862,a925)),f866(f866(f8(f937(x46862,f937(f937(f936(x46862,x46861),a925),a925)),f937(f937(f936(x46862,x46861),a925),f937(x46862,a925)),x46861),f7(x46862,f937(f936(x46862,x46861),a925),a925)),f866(f866(f8(f937(x46862,f936(x46862,x46861)),f937(x46862,f937(f937(f936(x46862,x46861),a925),a925)),x46861),f866(f8(f936(x46862,x46861),f937(f937(f936(x46862,x46861),a925),a925),x46862),f336(f936(x46862,x46861)))),f866(f7(x46862,x46861,f936(x46862,x46861)),f260(x46862,x46861))))),x46863))),f866(f294(x46862,x46861),x46863))
% 157.60/157.51 [4706]E(f866(f270(f931(x47061)),f866(f866(f8(f937(x47061,a925),a925,f931(x47061)),f93(x47061)),f866(f866(f8(f937(x47061,f937(f931(x47061),a925)),f937(x47061,a925),f931(x47061)),f866(f8(f937(f931(x47061),a925),a925,x47061),f93(f931(x47061)))),f866(f866(f7(f931(x47061),f937(x47061,f937(f931(x47061),a925)),f937(x47061,f937(f931(x47061),a925))),f866(f866(f8(f937(x47061,f937(f937(f931(x47061),a925),f937(f931(x47061),a925))),f937(f937(x47061,f937(f931(x47061),a925)),f937(x47061,f937(f931(x47061),a925))),f931(x47061)),f18(x47061,f937(f931(x47061),a925),f937(f931(x47061),a925))),f866(f866(f8(f937(x47061,f937(f931(x47061),f937(a925,a925))),f937(x47061,f937(f937(f931(x47061),a925),f937(f931(x47061),a925))),f931(x47061)),f866(f8(f937(f931(x47061),f937(a925,a925)),f937(f937(f931(x47061),a925),f937(f931(x47061),a925)),x47061),f18(f931(x47061),a925,a925))),f866(f866(f8(f937(x47061,f937(f931(x47061),a925)),f937(x47061,f937(f931(x47061),f937(a925,a925))),f931(x47061)),f866(f8(f937(f931(x47061),a925),f937(f931(x47061),f937(a925,a925)),x47061),f866(f8(a925,f937(a925,a925),f931(x47061)),a333))),f866(f866(f7(f931(x47061),f937(x47061,f937(f931(x47061),f931(x47061))),f937(x47061,f937(f931(x47061),a925))),f866(f866(f8(f937(f937(f931(x47061),f931(x47061)),f937(f931(x47061),a925)),f937(f937(x47061,f937(f931(x47061),f931(x47061))),f937(x47061,f937(f931(x47061),a925))),f931(x47061)),f8(f937(f931(x47061),f931(x47061)),f937(f931(x47061),a925),x47061)),f866(f866(f8(f937(f931(x47061),a925),f937(f937(f931(x47061),f931(x47061)),f937(f931(x47061),a925)),f931(x47061)),f8(f931(x47061),a925,f931(x47061))),a332))),f158(x47061)))))),f866(f866(f7(x47061,f937(f931(x47061),a925),f937(f931(x47061),a925)),f866(f866(f8(f937(a925,a925),f937(f937(f931(x47061),a925),f937(f931(x47061),a925)),x47061),f8(a925,a925,f931(x47061))),f866(f866(f8(a925,f937(a925,a925),x47061),a333),f866(f866(f7(x47061,f937(x47061,a925),a925),f336(x47061)),x47062)))),f866(f866(f7(f931(x47061),f937(f931(x47061),a925),a925),f336(f931(x47061))),x47063)))))),f181(x47061,x47062,x47063))
% 157.60/157.51 [4703]E(f866(f866(f92(a1,f936(a1,a1)),f866(f866(f23(a1),x47031),x47032)),f866(f866(f7(a1,f936(a1,a1),f936(a1,a1)),f866(f866(f18(a1,f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),f866(f866(f8(a925,f937(f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),a1),f103(f936(a1,a1))),f866(f243(a1),f2(a1)))),f866(f260(a1,a1),f866(f866(f86(a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x47033)),f84(a1))))),f866(f866(f260(a1,a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x47033)),x47031))),f866(f48(x47032),f866(f866(f260(a1,a1),x47033),x47031)))
% 157.60/157.51 [4730]~E(f26(x47301,x47302),f31(x47303,x47304))
% 157.60/157.51 [4733]~E(f30(x47331,x47332),f31(x47333,x47334))
% 157.60/157.51 [4734]~E(f30(x47341,x47342),f26(x47343,x47344))
% 157.60/157.51 [3742]E(f123(x37421,f866(x37422,x37423),f866(x37424,x37423)),f866(f212(x37421,x37422,x37424),x37423))
% 157.60/157.51 [3795]E(f866(f866(f253(x37951,x37952,x37953),x37954),f2(a930)),x37952)
% 157.60/157.51 [3808]E(f36(x38081,x38082,x38083,f33(x38084)),f866(x38083,x38084))
% 157.60/157.51 [3809]E(f36(x38091,x38092,x38093,f34(x38094)),f866(x38092,x38094))
% 157.60/157.51 [3810]E(f37(x38101,x38102,x38103,f33(x38104)),f866(x38103,x38104))
% 157.60/157.51 [3811]E(f37(x38111,x38112,x38113,f34(x38114)),f866(x38112,x38114))
% 157.60/157.51 [3838]E(f192(x38381,x38382,x38383,f866(a119,x38384)),f866(x38383,x38384))
% 157.60/157.51 [3879]E(f177(x38791,x38792,f177(x38791,x38793,x38794)),f177(x38791,x38793,f177(x38791,x38792,x38794)))
% 157.60/157.51 [3880]E(f133(x38801,x38802,f123(x38801,x38803,x38804)),f123(x38801,f133(x38801,x38802,x38803),x38804))
% 157.60/157.51 [4014]E(f866(f163(x40141,x40142,x40143,x40144),f120(x40142)),x40143)
% 157.60/157.51 [4015]E(f866(f149(x40151,x40152,x40153,x40154),f120(x40152)),x40154)
% 157.60/157.51 [4022]E(f866(f196(f929(x40221)),f98(x40221,x40222,x40223,x40224)),f2(a930))
% 157.60/157.51 [4054]E(f866(f196(f935(x40541,x40542)),f229(x40541,x40542,x40543,x40544)),f2(a930))
% 157.60/157.51 [4077]E(f866(f265(x40771,x40772,x40773),f263(x40771,x40772,x40773,x40774)),x40774)
% 157.60/157.51 [4121]E(f866(f866(f141(x41211),f176(x41211,x41212,x41213)),f176(x41211,x41214,x41213)),f866(f866(f141(x41211),f176(x41211,x41214,x41213)),f176(x41211,x41212,x41213)))
% 157.60/157.51 [4209]E(f866(f866(f267(x42091,x42092,x42093,f936(x42092,x42093)),x42094),f260(x42092,x42093)),x42094)
% 157.60/157.51 [4219]E(f134(x42191,x42192,x42193,x42194,f126(x42192)),x42193)
% 157.60/157.51 [4225]E(f80(x42251,x42252,x42253,x42254,f866(x42253,x42254)),x42253)
% 157.60/157.51 [4494]P42(x44941,x44942,x44943,x44944,f195(f937(x44941,a925)),x44944)
% 157.60/157.51 [3546]E(f866(f866(f16(x35461,x35462),x35463),x35464),x35463)
% 157.60/157.51 [3828]E(f177(x38281,x38282,f866(f143(x38281,x38283),x38284)),f866(f143(x38281,x38283),f177(x38281,x38282,x38284)))
% 157.60/157.51 [3862]E(f866(f866(f69(x38621,x38622,x38623),x38624),f195(f937(x38621,a925))),x38624)
% 157.60/157.51 [3886]E(f866(f866(f171(x38861),f866(f866(f158(x38861),x38862),x38863)),f866(a119,x38864)),f866(f866(f171(x38861),x38863),x38864))
% 157.60/157.51 [3953]E(f866(f866(x39531,x39532),f866(f191(x39533,x39534,x39531),x39532)),f866(f191(x39533,x39534,x39531),f866(a119,x39532)))
% 157.60/157.51 [3995]E(f263(x39951,x39952,x39953,f866(f265(x39951,x39952,x39953),x39954)),x39954)
% 157.60/157.51 [4052]E(f866(f866(f166(x40521,f866(f866(f158(x40521),x40522),x40523)),f2(a930)),x40524),f866(f866(f158(x40521),x40524),x40523))
% 157.60/157.51 [4062]E(f866(f866(f44(f937(x40621,a925),f937(x40622,a925)),x40623),f317(x40621,x40622,x40624)),f866(f317(x40621,x40622,x40624),f42(f937(x40621,a925),x40623)))
% 157.60/157.51 [4063]E(f866(f866(f44(f937(x40631,a925),f937(x40632,a925)),x40633),f318(x40632,x40631,x40634)),f866(f318(x40632,x40631,x40634),f42(f937(x40631,a925),x40633)))
% 157.60/157.51 [4088]E(f127(x40881,f137(x40882,f932(x40881),x40883,x40884)),f866(f125(x40882,x40881,x40884),x40883))
% 157.60/157.51 [4164]E(f866(f132(x41641,x41642),f133(x41641,x41643,x41644)),f866(f866(f86(a930),f866(f866(f86(a930),f866(x41642,x41643)),f866(f132(x41641,x41642),x41644))),f866(a119,f2(a930))))
% 157.60/157.51 [4185]E(f866(f149(x41851,x41852,f866(f7(x41852,x41851,x41851),x41853),x41854),f866(f175(x41852),f120(x41852))),x41854)
% 157.60/157.51 [4229]E(f82(x42291,x42292,x42293,x42294,f195(f937(x42291,a925))),x42293)
% 157.60/157.51 [4290]E(f232(x42901,f936(x42902,f932(x42902)),x42903,f866(f265(x42902,f932(x42902),x42901),x42904),f866(f142(x42902),f126(x42902))),x42903)
% 157.60/157.51 [4424]E(f866(f265(x44241,x44242,x44243),f866(f866(f8(f937(x44242,f936(x44241,x44242)),f937(x44242,x44243),x44241),f866(f8(f936(x44241,x44242),x44243,x44242),x44244)),f260(x44241,x44242))),x44244)
% 157.60/157.51 [3733]E(f866(f264(x37331,x37332),f866(f866(f260(x37331,x37332),x37333),x37334)),x37334)
% 157.60/157.51 [3734]E(f866(f259(x37341,x37342),f866(f866(f260(x37341,x37342),x37343),x37344)),x37343)
% 157.60/157.51 [3767]E(f866(f196(f931(x37671)),f866(f866(f166(x37671,x37672),x37673),x37674)),f866(f196(f931(x37671)),x37672))
% 157.60/157.51 [3768]E(f866(f196(f931(x37681)),f866(f866(f161(x37682,x37681),x37683),x37684)),f866(f196(f931(x37682)),x37684))
% 157.60/157.51 [3789]E(f866(f866(f145(x37891),f866(a119,x37892)),f866(f866(f158(x37891),x37893),x37894)),f866(f866(f145(x37891),x37892),x37894))
% 157.60/157.51 [3857]E(f866(f866(f182(x38571),x38572),f176(x38571,x38573,x38574)),f176(x38571,f866(f866(f241(a930),x38572),x38573),x38574))
% 157.60/157.51 [3858]E(f866(f866(f145(x38581),x38582),f176(x38581,x38583,x38584)),f176(x38581,f866(f866(f23(a930),x38583),x38582),x38584))
% 157.60/157.51 [3864]E(f866(f866(f316(x38641),x38642),f866(f866(f316(x38641),x38643),x38644)),f866(f866(f316(x38641),x38643),f866(f866(f316(x38641),x38642),x38644)))
% 157.60/157.51 [3868]E(f866(f866(f161(x38681,x38682),x38683),f121(x38681,x38684)),f121(x38682,f866(f866(f161(x38681,x38682),x38683),x38684)))
% 157.60/157.51 [3884]E(f866(f175(x38841),f866(f866(f161(x38842,x38841),x38843),x38844)),f866(f866(f161(x38842,x38841),x38843),f866(f175(x38842),x38844)))
% 157.60/157.51 [3885]E(f866(f866(f161(x38851,x38852),x38853),f866(f178(x38851),x38854)),f866(f178(x38852),f866(f866(f161(x38851,x38852),x38853),x38854)))
% 157.60/157.51 [3899]E(f866(f866(f182(x38991),f866(a119,x38992)),f866(f866(f158(x38991),x38993),x38994)),f866(f866(f158(x38991),x38993),f866(f866(f182(x38991),x38992),x38994)))
% 157.60/157.51 [3903]E(f866(f179(x39031),f866(f866(f161(x39032,x39031),x39033),x39034)),f866(f317(x39032,x39031,x39033),f866(f179(x39032),x39034)))
% 157.60/157.51 [3916]E(f866(f866(f161(x39161,x39162),f866(f16(x39162,x39161),x39163)),x39164),f176(x39162,f866(f196(f931(x39161)),x39164),x39163))
% 157.60/157.51 [3952]E(f17(x39521,x39522,x39523,f866(a3,f866(a119,f866(a20,x39524)))),f866(x39523,x39524))
% 157.60/157.51 [3956]E(f866(f866(f141(x39561),f866(f143(x39561,x39562),x39563)),f866(f143(x39561,x39562),x39564)),f866(f143(x39561,x39562),f866(f866(f141(x39561),x39563),x39564)))
% 157.60/157.51 [3969]E(f159(x39691,f866(f866(f161(x39692,x39691),x39693),f159(x39692,x39694))),f159(x39691,f866(f866(f161(x39692,x39691),x39693),x39694)))
% 157.60/157.51 [3984]E(f866(f294(x39841,x39841),f866(f866(f295(x39842,x39841),x39843),x39844)),f866(f866(f295(x39842,x39841),f866(f294(x39842,x39842),x39843)),x39844))
% 157.60/157.51 [3996]E(f866(f866(f296(x39961,x39962,x39963),x39964),f195(f937(f936(x39962,x39963),a925))),f195(f937(f936(x39961,x39963),a925)))
% 157.60/157.51 [3997]E(f866(f866(f182(x39971),f866(f866(f23(a930),x39972),x39973)),f866(f866(f145(x39971),x39973),x39974)),f866(f866(f145(x39971),x39973),f866(f866(f182(x39971),x39972),x39974)))
% 157.60/157.51 [4016]E(f866(f866(f141(x40161),f176(x40161,x40162,x40163)),f176(x40161,x40164,x40163)),f176(x40161,f866(f866(f86(a930),x40162),x40164),x40163))
% 157.60/157.51 [4017]E(f866(f866(f866(f286(x40171),x40172),x40173),x40174),f866(f260(f937(a106,f937(a925,f934(f932(x40171)))),f936(a106,a106)),f866(f47(x40171),x40172)))
% 157.60/157.51 [4045]E(f43(f937(x40451,a925),f866(f317(x40452,f937(x40451,a925),x40453),x40454)),f866(f866(f45(x40452,f937(x40451,a925)),x40454),x40453))
% 157.60/157.51 [4046]E(f42(f937(x40461,a925),f866(f317(x40462,f937(x40461,a925),x40463),x40464)),f866(f866(f44(x40462,f937(x40461,a925)),x40464),x40463))
% 157.60/157.51 [4047]E(f866(f196(f931(f936(x40471,x40472))),f866(f866(f188(x40471,x40472),x40473),x40474)),f866(f866(f241(a930),f866(f196(f931(x40471)),x40473)),f866(f196(f931(x40472)),x40474)))
% 157.60/157.51 [4049]E(f866(f318(x40491,x40492,x40493),f866(f85(f937(x40492,a925)),x40494)),f866(f85(f937(x40491,a925)),f866(f318(x40491,x40492,x40493),x40494)))
% 157.60/157.51 [4098]E(f866(f318(x40981,x40982,x40983),f866(f270(x40982),x40984)),f866(f270(x40981),f866(f866(f8(x40982,a925,x40981),x40984),x40983)))
% 157.60/157.51 [4116]E(f866(f866(f171(x41161),f866(f866(f141(x41161),x41162),f866(f866(f158(x41161),x41163),x41164))),f866(f196(f931(x41161)),x41162)),x41163)
% 157.60/157.51 [4141]E(f866(f317(x41411,x41412,x41413),f866(f318(x41411,x41412,x41413),x41414)),f866(f866(f108(f937(x41412,a925)),x41414),f866(f317(x41411,x41412,x41413),f250(f937(x41411,a925)))))
% 157.60/157.51 [4160]P107(f866(f866(f336(x41601),f866(x41602,x41603)),f866(f317(x41604,x41601,x41602),f250(f937(x41604,a925)))))
% 157.60/157.51 [4169]E(f19(x41691,x41692,x41693,f866(a3,f866(a119,f866(a20,x41694)))),f866(f866(x41693,x41694),f19(x41691,x41692,x41693,x41694)))
% 157.60/157.51 [4173]E(f866(f866(f141(x41731),f176(x41731,x41732,x41733)),f866(f866(f158(x41731),x41733),x41734)),f866(f866(f158(x41731),x41733),f866(f866(f141(x41731),f176(x41731,x41732,x41733)),x41734)))
% 157.60/157.51 [4175]E(f866(f866(f262(x41751,x41752),f866(f179(x41751),x41753)),f866(f16(f937(x41752,a925),x41751),f866(f179(x41752),x41754))),f866(f179(f936(x41751,x41752)),f64(x41751,x41752,x41753,x41754)))
% 157.60/157.51 [4187]E(f162(x41871,x41872,f866(f866(f158(x41871),x41873),x41874)),f866(f866(f86(a930),f866(f866(f86(a930),f866(x41872,x41873)),f162(x41871,x41872,x41874))),f866(a119,f2(a930))))
% 157.60/157.51 [4200]E(f192(f931(x42001),f866(f866(f158(x42001),x42002),x42003),f866(f866(f7(a930,f931(x42001),f931(x42001)),f145(x42001)),x42003),x42004),f866(f866(f145(x42001),x42004),f866(f866(f158(x42001),x42002),x42003)))
% 157.60/157.51 [4201]P25(x42011,f936(x42012,x42011),f338(x42013,x42014,x42012,x42011),f866(f866(f44(x42012,f937(x42011,a925)),x42014),x42013))
% 157.60/157.51 [4210]E(f866(f866(f23(f937(x42101,a925)),f866(f866(f23(f937(x42101,a925)),x42102),x42103)),f866(f866(f316(x42101),x42104),f195(f937(x42101,a925)))),f866(f866(f23(f937(x42101,a925)),x42102),f866(f866(f316(x42101),x42104),x42103)))
% 157.60/157.51 [4223]E(f866(f866(f190(f937(x42231,x42232),f937(x42231,x42232)),x42233),f78(x42232,x42232,x42231,x42234)),f78(x42232,x42232,x42231,f866(f866(f190(x42232,x42232),x42233),x42234)))
% 157.60/157.51 [4295]E(f866(f866(f866(f190(f931(x42951),f931(x42951)),x42952),f174(x42951)),f866(f866(f866(f190(f931(x42951),f931(x42951)),x42953),f174(x42951)),x42954)),f866(f866(f866(f190(f931(x42951),f931(x42951)),f866(f866(f86(a930),x42952),x42953)),f174(x42951)),x42954))
% 157.60/157.51 [4380]P107(f866(f866(f243(f937(x43801,a925)),f866(f179(x43801),f866(f866(f166(x43801,x43802),x43803),x43804))),f866(f866(f316(x43801),x43804),f866(f179(x43801),x43802))))
% 157.60/157.51 [4414]E(f866(f866(f44(f937(x44141,a925),f937(f936(x44141,x44142),a925)),x44143),f866(f866(f7(f937(x44141,a925),f937(x44141,f937(x44142,a925)),f937(f936(x44141,x44142),a925)),f262(x44141,x44142)),x44144)),f866(f866(f262(x44141,x44142),f42(f937(x44141,a925),x44143)),x44144))
% 157.60/157.51 [4452]E(f218(x44521,x44522,x44523,f866(f78(x44522,f937(a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(x44522))))),x44521,f213(x44522)),x44524)),f219(x44521,x44522,x44524,x44523))
% 157.60/157.51 [4467]E(f215(x44671,x44672,x44673,f866(f78(x44672,f937(a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(f934(x44672)))))),x44671,f214(x44672)),x44674)),f216(x44671,x44672,x44674,x44673))
% 157.60/157.51 [4472]P107(f866(f71(x44721,x44722,x44723,x44724,f195(f937(x44721,a925))),x44724))
% 157.60/157.51 [4511]E(f866(f866(f44(x45111,f937(x45112,a925)),x45113),f866(f866(f7(x45111,f937(x45112,a925),f937(x45112,a925)),f866(f866(f8(x45112,f937(f937(x45112,a925),f937(x45112,a925)),x45111),f316(x45112)),x45114)),f195(f937(x45112,a925)))),f866(f317(x45111,x45112,x45114),x45113))
% 157.60/157.51 [4518]P107(f866(f866(f243(f937(x45181,a925)),f866(f292(x45182,x45181),f866(f866(f108(f937(f936(x45182,x45181),a925)),x45183),x45184))),f866(f866(f108(f937(x45181,a925)),f866(f292(x45182,x45181),x45183)),f866(f292(x45182,x45181),x45184))))
% 157.60/157.51 [4519]P107(f866(f866(f243(f937(x45191,a925)),f866(f272(x45191,x45192),f866(f866(f108(f937(f936(x45191,x45192),a925)),x45193),x45194))),f866(f866(f108(f937(x45191,a925)),f866(f272(x45191,x45192),x45193)),f866(f272(x45191,x45192),x45194))))
% 157.60/157.51 [4579]P107(f866(f866(f243(f937(f936(x45791,x45792),a925)),f866(f317(x45792,f936(x45791,x45792),f338(x45793,x45794,x45791,x45792)),f866(f866(f44(x45791,f937(x45792,a925)),x45794),x45793))),f866(f866(f262(x45791,x45792),x45794),x45793)))
% 157.60/157.51 [4580]E(f866(f125(x45801,f936(x45801,x45802),x45803),f866(f866(f8(f937(x45802,f932(f936(x45801,x45802))),f932(f936(x45801,x45802)),x45801),f125(x45802,f936(x45801,x45802),x45804)),f866(f866(f8(f937(x45802,f936(x45801,x45802)),f937(x45802,f932(f936(x45801,x45802))),x45801),f866(f8(f936(x45801,x45802),f932(f936(x45801,x45802)),x45802),f136(f936(x45801,x45802)))),f260(x45801,x45802)))),f138(x45801,x45802,x45803,x45804))
% 157.60/157.51 [4581]E(f284(x45811,x45812,x45813,f866(f78(x45812,f937(a106,f937(a106,f937(f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x45812)))),f936(a106,a106))))),x45811,f286(x45812)),x45814)),f287(x45811,x45812,x45814,x45813))
% 157.60/157.51 [4621]E(f91(f936(x46211,x46212),f866(f265(x46211,x46212,a925),f866(f866(f7(x46211,f937(x46212,a925),f937(x46212,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x46212,a925),f937(x46212,a925)),x46211),f8(a925,a925,x46212)),f866(f866(f8(a925,f937(a925,a925),x46211),a333),f866(a332,x46213)))),f866(a332,x46214)))),f866(f866(f260(x46211,x46212),x46213),x46214))
% 157.60/157.51 [4622]E(f96(f936(x46221,x46222),f866(f265(x46221,x46222,a925),f866(f866(f7(x46221,f937(x46222,a925),f937(x46222,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x46222,a925),f937(x46222,a925)),x46221),f8(a925,a925,x46222)),f866(f866(f8(a925,f937(a925,a925),x46221),a333),f866(a332,x46223)))),f866(a332,x46224)))),f866(f866(f260(x46221,x46222),x46223),x46224))
% 157.60/157.51 [4695]E(f866(f866(f265(f931(x46951),f931(x46951),f936(f931(x46951),f931(x46951))),f866(f866(f18(f931(x46951),f937(f931(x46951),f936(f931(x46951),f931(x46951))),f937(f931(x46951),f936(f931(x46951),f931(x46951)))),f866(f866(f8(f937(f931(x46951),f937(f936(f931(x46951),f931(x46951)),f936(f931(x46951),f931(x46951)))),f937(f937(f931(x46951),f936(f931(x46951),f931(x46951))),f937(f931(x46951),f936(f931(x46951),f931(x46951)))),f931(x46951)),f18(f931(x46951),f936(f931(x46951),f931(x46951)),f936(f931(x46951),f931(x46951)))),f866(f866(f8(f937(f931(x46951),f936(f931(x46951),f931(x46951))),f937(f931(x46951),f937(f936(f931(x46951),f931(x46951)),f936(f931(x46951),f931(x46951)))),f931(x46951)),f866(f8(f936(f931(x46951),f931(x46951)),f937(f936(f931(x46951),f931(x46951)),f936(f931(x46951),f931(x46951))),f931(x46951)),f866(f103(f936(f931(x46951),f931(x46951))),f866(x46952,x46953)))),f866(f866(f8(f931(x46951),f937(f931(x46951),f936(f931(x46951),f931(x46951))),f931(x46951)),f260(f931(x46951),f931(x46951))),f866(f158(x46951),x46953))))),f866(f866(f7(f931(x46951),f937(f931(x46951),f931(x46951)),f937(f931(x46951),f936(f931(x46951),f931(x46951)))),f866(f866(f8(f937(f931(x46951),f936(f931(x46951),f931(x46951))),f937(f937(f931(x46951),f931(x46951)),f937(f931(x46951),f936(f931(x46951),f931(x46951)))),f931(x46951)),f8(f931(x46951),f936(f931(x46951),f931(x46951)),f931(x46951))),f260(f931(x46951),f931(x46951)))),f866(f158(x46951),x46953)))),f173(x46951,x46952,x46954)),f173(x46951,x46952,f866(f866(f158(x46951),x46953),x46954)))
% 157.60/157.51 [3932]E(f866(f866(f182(x39321),x39322),f866(f866(f182(x39321),x39323),x39324)),f866(f866(f182(x39321),f866(f866(f241(a930),x39322),x39323)),x39324))
% 157.60/157.51 [3933]E(f866(f866(f145(x39331),x39332),f866(f866(f145(x39331),x39333),x39334)),f866(f866(f145(x39331),f866(f866(f86(a930),x39332),x39333)),x39334))
% 157.60/157.51 [3944]E(f866(f866(f141(x39441),f866(f866(f158(x39441),x39442),x39443)),x39444),f866(f866(f158(x39441),x39442),f866(f866(f141(x39441),x39443),x39444)))
% 157.60/157.51 [3945]E(f866(f866(f141(x39451),f866(f866(f141(x39451),x39452),x39453)),x39454),f866(f866(f141(x39451),x39452),f866(f866(f141(x39451),x39453),x39454)))
% 157.60/157.51 [4028]E(f866(f866(f171(x40281),f866(f866(f158(x40281),x40282),x40283)),x40284),f192(x40281,x40282,f866(f171(x40281),x40283),x40284))
% 157.60/157.51 [4037]E(f866(f866(f190(x40371,x40371),x40372),f866(f866(f190(x40371,x40371),x40373),x40374)),f866(f866(f190(x40371,x40371),f866(f866(f87(a930),x40373),x40372)),x40374))
% 157.60/157.51 [4065]E(f866(f866(f117(f937(x40651,a925)),x40652),f866(f866(f316(x40651),x40653),x40654)),f866(f866(f316(x40651),x40653),f866(f866(f117(f937(x40651,a925)),x40652),x40654)))
% 157.60/157.51 [4080]E(f866(f866(f866(f190(x40801,x40801),x40802),x40803),f866(x40803,x40804)),f866(x40803,f866(f866(f866(f190(x40801,x40801),x40802),x40803),x40804)))
% 157.60/157.51 [4089]E(f866(f866(f296(x40891,x40892,x40893),f195(f937(f936(x40891,x40892),a925))),x40894),f195(f937(f936(x40891,x40893),a925)))
% 157.60/157.51 [4104]E(f866(f866(f117(f937(x41041,a925)),f866(f866(f316(x41041),x41042),x41043)),x41044),f866(f866(f316(x41041),x41042),f866(f866(f117(f937(x41041,a925)),x41043),x41044)))
% 157.60/157.51 [4123]E(f866(f40(f936(x41231,x41232)),f866(f866(f262(x41231,x41232),x41233),f866(f16(f937(x41232,a925),x41231),x41234))),f866(f866(f87(a930),f866(f40(x41231),x41233)),f866(f40(x41232),x41234)))
% 157.60/157.51 [4130]E(f866(f866(f108(f937(x41301,a925)),f866(f866(f316(x41301),x41302),x41303)),f866(f866(f316(x41301),x41302),x41304)),f866(f866(f316(x41301),x41302),f866(f866(f108(f937(x41301,a925)),x41303),x41304)))
% 157.60/157.51 [4145]E(f866(f866(f117(f937(x41451,a925)),x41452),f866(f866(f117(f937(x41451,a925)),x41453),x41454)),f866(f866(f117(f937(x41451,a925)),x41453),f866(f866(f117(f937(x41451,a925)),x41452),x41454)))
% 157.60/157.51 [4146]E(f866(f866(f108(f937(x41461,a925)),x41462),f866(f866(f108(f937(x41461,a925)),x41463),x41464)),f866(f866(f108(f937(x41461,a925)),x41463),f866(f866(f108(f937(x41461,a925)),x41462),x41464)))
% 157.60/157.51 [4156]E(f69(x41561,x41562,f866(f866(f8(x41562,f937(x41562,x41562),x41561),x41563),x41564)),f866(f70(x41562,x41561,x41563),x41564))
% 157.60/157.51 [4165]E(f186(x41651,f866(f866(f161(f931(x41652),f931(x41651)),f866(f161(x41652,x41651),x41653)),x41654)),f866(f866(f161(f931(x41652),f931(x41651)),f866(f161(x41652,x41651),x41653)),f186(x41652,x41654)))
% 157.60/157.51 [4184]E(f866(f149(f931(x41841),f931(x41841),f141(x41841),f120(x41841)),f866(f866(f161(x41842,f931(x41841)),x41843),x41844)),f170(x41842,x41841,x41843,x41844))
% 157.60/157.51 [4242]E(f866(f78(x42421,x42421,x42421,f866(f866(f190(x42421,x42421),x42422),x42423)),f866(f866(f190(x42421,x42421),x42424),x42423)),f866(f866(f190(x42421,x42421),f866(f866(f86(a930),x42422),x42424)),x42423))
% 157.60/157.51 [4265]E(f866(f866(f108(f937(x42651,a925)),f866(f866(f23(f937(x42651,a925)),x42652),x42653)),f866(f866(f23(f937(x42651,a925)),x42652),x42654)),f866(f866(f23(f937(x42651,a925)),x42652),f866(f866(f117(f937(x42651,a925)),x42653),x42654)))
% 157.60/157.51 [4266]E(f866(f866(f117(f937(x42661,a925)),f866(f866(f23(f937(x42661,a925)),x42662),x42663)),f866(f866(f23(f937(x42661,a925)),x42662),x42664)),f866(f866(f23(f937(x42661,a925)),x42662),f866(f866(f108(f937(x42661,a925)),x42663),x42664)))
% 157.60/157.51 [4267]E(f866(f866(f108(f937(x42671,a925)),f866(f866(f117(f937(x42671,a925)),x42672),x42673)),f866(f866(f117(f937(x42671,a925)),x42672),x42674)),f866(f866(f117(f937(x42671,a925)),x42672),f866(f866(f108(f937(x42671,a925)),x42673),x42674)))
% 157.60/157.51 [4268]E(f866(f866(f23(f937(x42681,a925)),f866(f866(f108(f937(x42681,a925)),x42682),x42683)),f866(f866(f108(f937(x42681,a925)),x42682),x42684)),f866(f866(f108(f937(x42681,a925)),x42682),f866(f866(f23(f937(x42681,a925)),x42683),x42684)))
% 157.60/157.51 [4269]E(f866(f866(f117(f937(x42691,a925)),f866(f866(f108(f937(x42691,a925)),x42692),x42693)),f866(f866(f108(f937(x42691,a925)),x42692),x42694)),f866(f866(f108(f937(x42691,a925)),x42692),f866(f866(f117(f937(x42691,a925)),x42693),x42694)))
% 157.60/157.51 [4274]E(f866(f40(f936(x42741,x42742)),f866(f866(f262(x42741,x42742),f866(f866(f316(x42741),x42743),f195(f937(x42741,a925)))),f866(f16(f937(x42742,a925),x42741),x42744))),f866(f40(x42742),x42744))
% 157.60/157.51 [4309]E(f866(f866(f45(x43091,f937(x43092,a925)),x43093),f866(f866(f8(f937(x43092,a925),f937(x43092,a925),x43091),f85(f937(x43092,a925))),x43094)),f866(f85(f937(x43092,a925)),f866(f866(f44(x43091,f937(x43092,a925)),x43093),x43094)))
% 157.60/157.51 [4310]E(f866(f866(f44(x43101,f937(x43102,a925)),x43103),f866(f866(f8(f937(x43102,a925),f937(x43102,a925),x43101),f85(f937(x43102,a925))),x43104)),f866(f85(f937(x43102,a925)),f866(f866(f45(x43101,f937(x43102,a925)),x43103),x43104)))
% 157.60/157.51 [4326]E(f866(f866(f296(x43261,x43261,x43261),f866(f866(f190(f936(x43261,x43261),a925),x43262),x43263)),f866(f866(f190(f936(x43261,x43261),a925),x43264),x43263)),f866(f866(f190(f936(x43261,x43261),a925),f866(f866(f86(a930),x43262),x43264)),x43263))
% 157.60/157.51 [4356]E(f866(f866(f45(x43561,f937(f937(x43562,a925),a925)),x43563),f866(f866(f8(f937(x43562,a925),f937(f937(x43562,a925),a925),x43561),f315(x43562)),x43564)),f866(f315(x43562),f866(f866(f45(x43561,f937(x43562,a925)),x43563),x43564)))
% 157.60/157.51 [4387]E(f866(f866(f44(f937(x43871,a925),f937(x43872,a925)),x43873),f866(f866(f7(f937(x43871,a925),f937(x43871,f937(x43872,a925)),f937(x43872,a925)),f44(x43871,f937(x43872,a925))),x43874)),f866(f866(f44(x43871,f937(x43872,a925)),f42(f937(x43871,a925),x43873)),x43874))
% 157.60/157.51 [4388]E(f866(f866(f45(f937(x43881,a925),f937(x43882,a925)),x43883),f866(f866(f7(f937(x43881,a925),f937(x43881,f937(x43882,a925)),f937(x43882,a925)),f45(x43881,f937(x43882,a925))),x43884)),f866(f866(f45(x43881,f937(x43882,a925)),f42(f937(x43881,a925),x43883)),x43884))
% 157.60/157.51 [4393]E(f866(f866(f161(x43931,x43932),x43933),f866(f149(f931(x43931),f931(x43931),f141(x43931),f120(x43931)),x43934)),f866(f149(f931(x43932),f931(x43932),f141(x43932),f120(x43932)),f866(f866(f161(f931(x43931),f931(x43932)),f866(f161(x43931,x43932),x43933)),x43934)))
% 157.60/157.51 [4395]E(f192(f931(x43951),f120(x43951),f866(f866(f8(f931(x43951),f931(x43951),a930),f866(f158(x43951),x43952)),f866(f866(f7(a930,f931(x43951),f931(x43951)),f182(x43951)),x43953)),x43954),f866(f866(f182(x43951),x43954),f866(f866(f158(x43951),x43952),x43953)))
% 157.60/157.51 [4433]P107(f866(f866(f243(f937(x44331,a925)),f866(f317(x44332,x44331,x44333),f866(f318(x44332,x44331,x44333),x44334))),x44334))
% 157.60/157.51 [4435]E(f866(f317(f936(x44351,x44352),f936(x44352,x44351),f866(f265(x44351,x44352,f936(x44352,x44351)),f866(f7(x44352,x44351,f936(x44352,x44351)),f260(x44352,x44351)))),f866(f866(f262(x44351,x44352),x44353),f866(f16(f937(x44352,a925),x44351),x44354))),f866(f866(f262(x44352,x44351),x44354),f866(f16(f937(x44351,a925),x44352),x44353)))
% 157.60/157.51 [4444]E(f866(f866(f44(x44441,f937(x44442,a925)),x44443),f866(f866(f8(f937(x44441,a925),f937(x44442,a925),x44441),f293(x44441,x44442,x44444)),f866(f866(f7(x44441,f937(x44441,a925),f937(x44441,a925)),f316(x44441)),f195(f937(x44441,a925))))),f866(f293(x44441,x44442,x44444),x44443))
% 157.60/157.51 [4445]E(f866(f866(f44(x44451,f937(x44452,a925)),x44453),f866(f866(f8(f937(x44451,a925),f937(x44452,a925),x44451),f318(x44452,x44451,x44454)),f866(f866(f7(x44451,f937(x44451,a925),f937(x44451,a925)),f316(x44451)),f195(f937(x44451,a925))))),f866(f318(x44452,x44451,x44454),x44453))
% 157.60/157.51 [4532]E(f866(f866(f117(f937(x45321,a925)),f866(f866(f117(f937(x45321,a925)),f866(f866(f108(f937(x45321,a925)),x45322),x45323)),f866(f866(f108(f937(x45321,a925)),x45323),x45324))),f866(f866(f108(f937(x45321,a925)),x45324),x45322)),f866(f866(f108(f937(x45321,a925)),f866(f866(f108(f937(x45321,a925)),f866(f866(f117(f937(x45321,a925)),x45322),x45323)),f866(f866(f117(f937(x45321,a925)),x45323),x45324))),f866(f866(f117(f937(x45321,a925)),x45324),x45322)))
% 157.60/157.51 [4595]E(f866(f149(f931(x45951),f931(x45951),f141(x45951),f120(x45951)),f866(f866(f161(x45952,f931(x45951)),f866(f866(f7(x45952,f931(x45951),f931(x45951)),f866(f866(f8(x45951,f937(f931(x45951),f931(x45951)),x45952),f158(x45951)),x45953)),f120(x45951))),x45954)),f866(f866(f161(x45952,x45951),x45953),x45954))
% 157.60/157.51 [4605]E(f866(f866(f92(a1,x46051),f866(f110(a1),f866(f866(f86(a1),x46052),a104))),f866(f866(f18(a1,x46051,x46051),f866(f866(f7(a1,x46051,f937(x46051,x46051)),f866(f866(f8(a925,f937(x46051,f937(x46051,x46051)),a1),f103(x46051)),a200)),x46053)),f866(f866(f8(a930,x46051,a1),x46054),a111))),f192(x46051,x46053,x46054,f866(f110(a930),x46052)))
% 157.60/157.51 [4636]E(f866(f270(x46361),f866(f866(f8(f937(x46362,a925),a925,x46361),f93(x46362)),f866(f866(f8(f937(x46362,a925),f937(x46362,a925),x46361),f866(f18(x46362,a925,a925),f866(f866(f8(a925,f937(a925,a925),x46362),a333),f866(f866(f7(x46362,f937(x46362,a925),a925),f336(x46362)),x46363)))),f866(f7(x46362,x46361,a925),x46364)))),f866(f293(x46362,x46361,f866(f270(f936(x46362,x46361)),f866(f265(x46362,x46361,a925),x46364))),x46363))
% 157.60/157.51 [4804]~P107(f866(f866(f195(f937(x48041,f937(x48042,a925))),x48043),x48044))
% 157.60/157.51 [4092]E(f866(f866(f171(x40921),f866(f866(f141(x40921),x40922),x40923)),f866(f866(f86(a930),f866(f196(f931(x40921)),x40922)),x40924)),f866(f866(f171(x40921),x40923),x40924))
% 157.60/157.51 [4097]E(f866(f866(f145(x40971),x40972),f866(f866(f182(x40971),f866(f866(f86(a930),x40973),x40972)),x40974)),f866(f866(f182(x40971),x40973),f866(f866(f145(x40971),x40972),x40974)))
% 157.60/157.51 [4198]E(f866(f866(f117(f937(x41981,a925)),f866(f292(x41982,x41981),x41983)),f866(f292(x41982,x41981),x41984)),f866(f292(x41982,x41981),f866(f866(f117(f937(f936(x41982,x41981),a925)),x41983),x41984)))
% 157.60/157.51 [4199]E(f866(f866(f117(f937(x41991,a925)),f866(f272(x41991,x41992),x41993)),f866(f272(x41991,x41992),x41994)),f866(f272(x41991,x41992),f866(f866(f117(f937(f936(x41991,x41992),a925)),x41993),x41994)))
% 157.60/157.51 [4204]E(f866(f866(f23(f937(x42041,a925)),f866(f866(f108(f937(x42041,a925)),x42042),x42043)),x42044),f866(f866(f108(f937(x42041,a925)),x42042),f866(f866(f23(f937(x42041,a925)),x42043),x42044)))
% 157.60/157.51 [4205]E(f866(f866(f117(f937(x42051,a925)),f866(f866(f117(f937(x42051,a925)),x42052),x42053)),x42054),f866(f866(f117(f937(x42051,a925)),x42052),f866(f866(f117(f937(x42051,a925)),x42053),x42054)))
% 157.60/157.51 [4206]E(f866(f866(f108(f937(x42061,a925)),f866(f866(f108(f937(x42061,a925)),x42062),x42063)),x42064),f866(f866(f108(f937(x42061,a925)),x42062),f866(f866(f108(f937(x42061,a925)),x42063),x42064)))
% 157.60/157.51 [4244]E(f866(f866(f117(f937(f936(x42441,x42442),a925)),f866(f294(x42442,x42441),x42443)),f866(f294(x42442,x42441),x42444)),f866(f294(x42442,x42441),f866(f866(f117(f937(f936(x42442,x42441),a925)),x42443),x42444)))
% 157.60/157.51 [4245]E(f866(f866(f108(f937(f936(x42451,x42452),a925)),f866(f294(x42452,x42451),x42453)),f866(f294(x42452,x42451),x42454)),f866(f294(x42452,x42451),f866(f866(f108(f937(f936(x42452,x42451),a925)),x42453),x42454)))
% 157.60/157.51 [4258]E(f866(f866(f117(f937(x42581,f937(x42582,a925))),f251(x42582,x42581,x42583)),f251(x42582,x42581,x42584)),f251(x42582,x42581,f866(f866(f117(f937(x42582,f937(x42581,a925))),x42583),x42584)))
% 157.60/157.51 [4259]E(f866(f866(f108(f937(x42591,f937(x42592,a925))),f251(x42592,x42591,x42593)),f251(x42592,x42591,x42594)),f251(x42592,x42591,f866(f866(f108(f937(x42592,f937(x42591,a925))),x42593),x42594)))
% 157.60/157.51 [4313]E(f866(f866(f117(f937(x43131,a925)),f866(f866(f23(f937(x43131,a925)),x43132),x43133)),f866(f866(f23(f937(x43131,a925)),x43134),x43133)),f866(f866(f23(f937(x43131,a925)),f866(f866(f117(f937(x43131,a925)),x43132),x43134)),x43133))
% 157.60/157.51 [4314]E(f866(f866(f108(f937(x43141,a925)),f866(f866(f117(f937(x43141,a925)),x43142),x43143)),f866(f866(f117(f937(x43141,a925)),x43144),x43143)),f866(f866(f117(f937(x43141,a925)),f866(f866(f108(f937(x43141,a925)),x43142),x43144)),x43143))
% 157.60/157.51 [4315]E(f866(f866(f23(f937(x43151,a925)),f866(f866(f108(f937(x43151,a925)),x43152),x43153)),f866(f866(f108(f937(x43151,a925)),x43154),x43153)),f866(f866(f108(f937(x43151,a925)),f866(f866(f23(f937(x43151,a925)),x43152),x43154)),x43153))
% 157.60/157.51 [4316]E(f866(f866(f117(f937(x43161,a925)),f866(f866(f108(f937(x43161,a925)),x43162),x43163)),f866(f866(f108(f937(x43161,a925)),x43164),x43163)),f866(f866(f108(f937(x43161,a925)),f866(f866(f117(f937(x43161,a925)),x43162),x43164)),x43163))
% 157.60/157.51 [4317]E(f866(f866(f23(f937(x43171,a925)),f866(f866(f108(f937(x43171,a925)),x43172),x43173)),f866(f866(f108(f937(x43171,a925)),x43174),x43173)),f866(f866(f23(f937(x43171,a925)),f866(f866(f108(f937(x43171,a925)),x43172),x43173)),x43174))
% 157.60/157.51 [4329]E(f866(f866(f23(f937(x43291,a925)),f866(f866(f23(f937(x43291,a925)),x43292),f866(f866(f316(x43291),x43293),f195(f937(x43291,a925))))),x43294),f866(f866(f23(f937(x43291,a925)),x43292),f866(f866(f316(x43291),x43293),x43294)))
% 157.60/157.51 [4382]E(f866(f866(f117(f937(x43821,a925)),f866(f866(f316(x43821),x43822),f866(f866(f316(x43821),x43823),f195(f937(x43821,a925))))),f866(f289(x43821),x43824)),f866(f289(x43821),f866(f866(f316(f936(x43821,x43821)),f866(f866(f260(x43821,x43821),x43822),x43823)),x43824)))
% 157.60/157.51 [4409]E(f866(f866(f44(a930,f937(x44091,a925)),f866(f308(a930),x44092)),f866(f866(f8(a930,f937(x44091,a925),a930),x44093),f866(f866(f7(a930,a930,a930),f86(a930)),x44094))),f866(f866(f44(a930,f937(x44091,a925)),f310(a930,x44094,f866(f866(f86(a930),x44092),x44094))),x44093))
% 157.60/157.51 [4410]E(f181(x44101,f866(f293(x44101,x44101,x44102),f866(f866(f316(x44101),x44103),f195(f937(x44101,a925)))),f866(f293(f931(x44101),f931(x44101),f165(x44101,x44102)),f866(f866(f316(f931(x44101)),x44104),f195(f937(f931(x44101),a925))))),f866(f293(f931(x44101),f931(x44101),f165(x44101,x44102)),f866(f866(f316(f931(x44101)),f866(f866(f158(x44101),x44103),x44104)),f195(f937(f931(x44101),a925)))))
% 157.60/157.51 [4474]E(f866(f270(x44741),f866(f866(f7(x44741,f937(x44742,a925),a925),f866(f866(f8(x44742,f937(f937(x44742,a925),a925),x44741),f336(x44742)),x44743)),x44744)),f866(f318(x44741,x44742,x44743),x44744))
% 157.60/157.51 [4564]E(f866(f270(x45641),f866(f866(f7(x45641,f937(f936(x45642,x45641),a925),a925),f866(f866(f8(f936(x45642,x45641),f937(f937(f936(x45642,x45641),a925),a925),x45641),f336(f936(x45642,x45641))),f866(f260(x45642,x45641),x45643))),x45644)),f866(f293(x45642,x45641,x45644),f866(f866(f316(x45642),x45643),f195(f937(x45642,a925)))))
% 157.60/157.51 [4578]E(f866(f866(f161(f936(x45781,a930),x45781),f259(x45781,a930)),f866(f143(f936(x45781,a930),f866(f866(f8(a930,a925,f936(x45781,a930)),x45782),f866(f866(f8(a930,a930,f936(x45781,a930)),a119),f264(x45781,a930)))),f866(f866(f188(x45781,a930),x45783),x45784))),f866(f866(f161(f936(x45781,a930),x45781),f259(x45781,a930)),f866(f143(f936(x45781,a930),f866(f866(f8(a930,a925,f936(x45781,a930)),x45782),f264(x45781,a930))),f866(f866(f188(x45781,a930),x45783),f866(f866(f161(a930,a930),a119),x45784)))))
% 157.60/157.51 [4587]P107(f866(f866(f243(f937(f937(x45871,a925),a925)),f866(f866(f44(x45872,f937(f937(x45871,a925),a925)),x45873),f866(f866(f8(f937(x45871,a925),f937(f937(x45871,a925),a925),x45872),f315(x45871)),x45874))),f866(f315(x45871),f866(f866(f44(x45872,f937(x45871,a925)),x45873),x45874))))
% 157.60/157.51 [4628]E(f866(f866(f92(a1,x46281),f866(f110(a1),f866(f866(f86(a1),x46282),a104))),f866(f866(f18(a1,x46281,x46281),f866(f866(f7(a1,x46281,f937(x46281,x46281)),f866(f866(f8(a925,f937(x46281,f937(x46281,x46281)),a1),f103(x46281)),a200)),x46283)),f866(f866(f18(a1,x46281,x46281),f866(f866(f8(a930,f937(x46281,x46281),a1),x46284),a111)),f866(f866(f8(a930,x46281,a1),f191(x46281,x46283,x46284)),a111)))),f866(f191(x46281,x46283,x46284),f866(f110(a930),x46282)))
% 157.60/157.51 [4652]E(f866(f270(f936(x46521,x46522)),f866(f265(x46521,x46522,a925),f866(f866(f7(x46521,f937(x46522,a925),f937(x46522,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x46522,a925),f937(x46522,a925)),x46521),f8(a925,a925,x46522)),f866(f866(f8(a925,f937(a925,a925),x46521),a333),f866(f866(f7(x46521,f937(x46521,a925),a925),f336(x46521)),x46523)))),f866(f866(f7(x46522,f937(x46522,a925),a925),f336(x46522)),x46524)))),f238(x46521,x46522,x46523,x46524))
% 157.60/157.51 [4690]E(f866(f866(f44(x46901,f937(f936(x46901,x46902),a925)),x46903),f866(f866(f18(x46901,f937(x46902,f937(f936(x46901,x46902),a925)),f937(f936(x46901,x46902),a925)),f866(f866(f8(f937(x46902,a925),f937(f937(x46902,f937(f936(x46901,x46902),a925)),f937(f936(x46901,x46902),a925)),x46901),f44(x46902,f937(f936(x46901,x46902),a925))),x46904)),f866(f866(f7(x46901,f937(f936(x46901,x46902),a925),f937(x46902,f937(f936(x46901,x46902),a925))),f866(f866(f8(f937(x46902,f937(f937(f936(x46901,x46902),a925),f937(f936(x46901,x46902),a925))),f937(f937(f936(x46901,x46902),a925),f937(x46902,f937(f936(x46901,x46902),a925))),x46901),f7(x46902,f937(f936(x46901,x46902),a925),f937(f936(x46901,x46902),a925))),f866(f866(f8(f937(x46902,f936(x46901,x46902)),f937(x46902,f937(f937(f936(x46901,x46902),a925),f937(f936(x46901,x46902),a925))),x46901),f866(f8(f936(x46901,x46902),f937(f937(f936(x46901,x46902),a925),f937(f936(x46901,x46902),a925)),x46902),f316(f936(x46901,x46902)))),f260(x46901,x46902)))),f195(f937(f936(x46901,x46902),a925))))),f866(f866(f262(x46901,x46902),x46903),x46904))
% 157.60/157.51 [4253]E(f866(f866(f141(x42531),f866(f866(f182(x42531),x42532),x42533)),f866(f866(f182(x42531),f866(f866(f23(a930),x42532),f866(f196(f931(x42531)),x42533))),x42534)),f866(f866(f182(x42531),x42532),f866(f866(f141(x42531),x42533),x42534)))
% 157.60/157.51 [4254]E(f866(f866(f141(x42541),f866(f866(f145(x42541),x42542),x42543)),f866(f866(f145(x42541),f866(f866(f23(a930),x42542),f866(f196(f931(x42541)),x42543))),x42544)),f866(f866(f145(x42541),x42542),f866(f866(f141(x42541),x42543),x42544)))
% 157.60/157.51 [4303]E(f866(f866(f86(a930),f866(f866(f87(a930),x43031),x43032)),f866(f866(f86(a930),f866(f866(f87(a930),x43033),x43032)),x43034)),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f86(a930),x43031),x43033)),x43032)),x43034))
% 157.60/157.51 [4450]E(f96(x44501,f866(f866(f7(x44501,x44502,a925),f866(f866(f8(x44502,f937(x44502,a925),x44501),a332),x44503)),x44504)),f866(f97(x44501,x44502,f250(f937(x44501,a925)),x44503),x44504))
% 157.60/157.51 [4498]P107(f866(f866(f243(f937(x44981,a925)),f866(f866(f23(f937(x44981,a925)),f866(f292(x44982,x44981),x44983)),f866(f292(x44982,x44981),x44984))),f866(f292(x44982,x44981),f866(f866(f23(f937(f936(x44982,x44981),a925)),x44983),x44984))))
% 157.60/157.51 [4499]P107(f866(f866(f243(f937(x44991,a925)),f866(f866(f23(f937(x44991,a925)),f866(f272(x44991,x44992),x44993)),f866(f272(x44991,x44992),x44994))),f866(f272(x44991,x44992),f866(f866(f23(f937(f936(x44991,x44992),a925)),x44993),x44994))))
% 157.60/157.51 [4607]E(f866(f866(f86(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x46071),x46072)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x46073),x46074)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),f866(f866(f86(a930),x46071),x46073)),f866(f866(f86(a930),x46072),x46074))),f195(f937(f936(a930,a930),a925))))))
% 157.60/157.51 [4647]E(f866(f866(f87(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x46471),x46472)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x46473),x46474)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),f866(f866(f86(a930),f866(f866(f87(a930),x46471),x46473)),f866(f866(f87(a930),x46472),x46474))),f866(f866(f86(a930),f866(f866(f87(a930),x46471),x46474)),f866(f866(f87(a930),x46472),x46473)))),f195(f937(f936(a930,a930),a925))))))
% 157.60/157.51 [4668]E(f866(f270(x46681),f866(f866(f8(f937(x46682,a925),a925,x46681),f94(x46682)),f866(f866(f8(f937(x46682,a925),f937(x46682,a925),x46681),f866(f18(x46682,a925,a925),f866(f866(f8(a925,f937(a925,a925),x46682),a337),f866(f866(f7(x46682,f937(x46682,a925),a925),f336(x46682)),x46683)))),f866(f866(f7(x46681,f937(x46682,f937(x46681,a925)),f937(x46682,a925)),f866(f866(f8(f937(f937(x46681,a925),a925),f937(f937(x46682,f937(x46681,a925)),f937(x46682,a925)),x46681),f8(f937(x46681,a925),a925,x46682)),f336(x46681))),x46684)))),f866(f866(f45(x46682,f937(x46681,a925)),x46683),x46684))
% 157.60/157.51 [4702]E(f866(f866(f296(x47021,x47021,x47021),f866(f866(f316(f936(x47021,x47021)),f866(f866(f260(x47021,x47021),x47022),x47023)),x47024)),f314(x47021,f866(f866(f316(f936(x47021,x47021)),f866(f866(f260(x47021,x47021),x47022),x47023)),x47024))),f866(f866(f117(f937(f936(x47021,x47021),a925)),f866(f866(f296(x47021,x47021,x47021),x47024),f314(x47021,x47024))),f866(f270(f936(x47021,x47021)),f866(f265(x47021,x47021,a925),f866(f866(f7(x47021,f937(x47021,a925),f937(x47021,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x47021,a925),f937(x47021,a925)),x47021),f8(a925,a925,x47021)),f866(f866(f8(a925,f937(a925,a925),x47021),a333),f866(f866(f7(x47021,f937(f936(x47021,x47021),a925),a925),f866(f866(f8(f936(x47021,x47021),f937(f937(f936(x47021,x47021),a925),a925),x47021),f336(f936(x47021,x47021))),f866(f866(f7(x47021,x47021,f936(x47021,x47021)),f260(x47021,x47021)),x47022))),f314(x47021,x47024))))),f866(f866(f7(x47021,f937(f936(x47021,x47021),a925),a925),f866(f866(f8(f936(x47021,x47021),f937(f937(f936(x47021,x47021),a925),a925),x47021),f336(f936(x47021,x47021))),f866(f260(x47021,x47021),x47023))),f314(x47021,x47024)))))))
% 157.60/157.51 [4500]E(f866(f143(x45001,f866(f866(f18(x45001,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45001),a333),x45002)),x45003)),x45004),f866(f143(x45001,x45003),f866(f143(x45001,x45002),x45004)))
% 157.60/157.51 [4601]E(f866(f866(f141(x46011),f866(f866(f866(f103(f931(x46011)),f866(f866(f336(a930),f2(a930)),x46012)),f866(f866(f158(x46011),x46013),f120(x46011))),f120(x46011))),f183(x46011,x46014,f866(f270(a930),f866(f866(f7(a930,f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),a930),f336(a930)),a119)),x46012)))),f183(x46011,f866(f866(f158(x46011),x46013),x46014),x46012))
% 157.60/157.51 [4698]E(f866(f270(f936(x46981,x46982)),f866(f866(f8(f937(a930,a925),a925,f936(x46981,x46982)),f93(a930)),f866(f866(f7(f936(x46981,x46982),f937(a930,a925),f937(a930,a925)),f866(f866(f8(f937(a930,f937(a925,a925)),f937(f937(a930,a925),f937(a930,a925)),f936(x46981,x46982)),f18(a930,a925,a925)),f866(f866(f8(f937(a930,a925),f937(a930,f937(a925,a925)),f936(x46981,x46982)),f866(f8(a925,f937(a925,a925),a930),a333)),f866(f866(f7(f936(x46981,x46982),f937(a930,f936(x46981,x46982)),f937(a930,a925)),f866(f866(f8(f937(f936(x46981,x46982),a925),f937(f937(a930,f936(x46981,x46982)),f937(a930,a925)),f936(x46981,x46982)),f8(f936(x46981,x46982),a925,a930)),a332)),f866(f866(f18(a930,x46982,f936(x46981,x46982)),f866(f866(f8(x46981,f937(x46982,f936(x46981,x46982)),a930),f260(x46981,x46982)),f866(f171(x46981),x46983))),f866(f171(x46982),x46984)))))),f866(f866(f7(a930,a930,a925),f244(a930)),f866(f866(f241(a930),f866(f196(f931(x46981)),x46983)),f866(f196(f931(x46982)),x46984)))))),f866(f179(f936(x46981,x46982)),f866(f866(f188(x46981,x46982),x46983),x46984)))
% 157.60/157.51 [4620]E(f866(f270(f936(x46201,x46202)),f866(f265(x46201,x46202,a925),f866(f866(f7(x46201,f937(x46202,a925),f937(x46202,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x46202,a925),f937(x46202,a925)),x46201),f8(a925,a925,x46202)),f866(f866(f8(a925,f937(a925,a925),x46201),a333),x46203))),x46204))),f866(f866(f262(x46201,x46202),f866(f270(x46201),x46203)),f866(f16(f937(x46202,a925),x46201),f866(f270(x46202),x46204))))
% 157.60/157.51 [4623]E(f866(f270(f936(x46231,x46232)),f866(f265(x46231,x46232,a925),f866(f866(f18(x46231,f937(x46232,a925),f937(x46232,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x46232,a925),f937(x46232,a925)),x46231),f8(a925,a925,x46232)),f866(f866(f8(a925,f937(a925,a925),x46231),a333),x46233))),x46234))),f866(f866(f262(x46231,x46232),f866(f270(x46231),x46233)),f866(f866(f8(f937(x46232,a925),f937(x46232,a925),x46231),f270(x46232)),x46234)))
% 157.60/157.51 [4635]E(f866(f270(x46351),f866(f866(f8(f937(x46352,a925),a925,x46351),f94(x46352)),f866(f866(f8(f937(x46352,a925),f937(x46352,a925),x46351),f866(f18(x46352,a925,a925),f866(f866(f8(a925,f937(a925,a925),x46352),a337),f866(f866(f7(x46352,f937(x46352,a925),a925),f336(x46352)),x46353)))),x46354))),f866(f866(f45(x46352,f937(x46351,a925)),x46353),f866(f866(f8(f937(x46351,a925),f937(x46351,a925),x46352),f270(x46351)),f866(f7(x46351,x46352,a925),x46354))))
% 157.60/157.51 [4682]E(f866(f866(f161(f936(x46821,a930),x46821),f259(x46821,a930)),f866(f143(f936(x46821,a930),f866(f866(f7(f936(x46821,a930),f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),f936(x46821,a930)),f336(a930)),f264(x46821,a930))),x46822)),f866(f866(f188(x46821,a930),x46823),f146(a930,f866(f309(a930,x46824),f866(f866(f86(a930),x46824),f866(f196(f931(x46821)),x46823))))))),f866(f866(f161(f936(x46821,a930),x46821),f259(x46821,a930)),f866(f143(f936(x46821,a930),f866(f866(f7(f936(x46821,a930),f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),f936(x46821,a930)),f336(a930)),f866(f866(f7(f936(x46821,a930),a930,a930),f866(f866(f8(a930,f937(a930,a930),f936(x46821,a930)),f86(a930)),f264(x46821,a930))),x46824))),x46822)),f866(f866(f188(x46821,a930),x46823),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(x46821)),x46823)))))))
% 157.60/157.51 [4683]E(f866(a119,f866(f866(f242(a930),f866(f196(f931(x46831)),x46832)),f866(f149(a930,f931(x46833),f866(f7(f931(x46833),a930,a930),f866(f866(f8(a930,f937(a930,a930),f931(x46833)),f242(a930)),f866(f866(f7(f931(x46833),a930,a930),f866(f866(f8(a930,f937(a930,a930),f931(x46833)),f23(a930)),f196(f931(x46833)))),f866(a119,f2(a930))))),f2(a930)),f866(f175(f931(x46833)),f866(f143(f931(x46833),f866(f866(f8(a925,a925,f931(x46833)),a329),f866(f866(f7(f931(x46833),f931(x46833),a925),a332),f120(x46833)))),x46834))))),f866(f866(f242(a930),f866(a119,f866(f196(f931(x46831)),x46832))),f866(f149(a930,f931(x46833),f866(f7(f931(x46833),a930,a930),f866(f866(f8(a930,f937(a930,a930),f931(x46833)),f242(a930)),f196(f931(x46833)))),f2(a930)),f866(f175(f931(x46833)),x46834))))
% 157.60/157.51 [4634]E(f866(f866(f141(x46341),f183(x46341,x46342,x46343)),f183(x46341,x46344,f866(f270(a930),f866(f866(f7(a930,f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),a930),f336(a930)),f866(f866(f7(a930,a930,a930),f86(a930)),f866(f196(f931(x46341)),x46342)))),x46343)))),f183(x46341,f866(f866(f141(x46341),x46342),x46344),x46343))
% 157.60/157.51 [4684]E(f42(f937(x46841,a925),f866(f270(f937(x46841,a925)),f866(f866(f8(f937(x46842,a925),a925,f937(x46841,a925)),f93(x46842)),f866(f866(f8(f937(x46842,a925),f937(x46842,a925),f937(x46841,a925)),f866(f18(x46842,a925,a925),f866(f866(f8(a925,f937(a925,a925),x46842),a333),f866(f866(f7(x46842,f937(x46842,a925),a925),f336(x46842)),x46843)))),f866(f866(f7(f937(x46841,a925),f937(x46842,f937(x46841,a925)),f937(x46842,a925)),f866(f866(f8(f937(f937(x46841,a925),a925),f937(f937(x46842,f937(x46841,a925)),f937(x46842,a925)),f937(x46841,a925)),f8(f937(x46841,a925),a925,x46842)),a332)),x46844))))),f866(f866(f44(x46842,f937(x46841,a925)),x46843),x46844))
% 157.60/157.51 [4685]E(f43(f937(x46851,a925),f866(f270(f937(x46851,a925)),f866(f866(f8(f937(x46852,a925),a925,f937(x46851,a925)),f93(x46852)),f866(f866(f8(f937(x46852,a925),f937(x46852,a925),f937(x46851,a925)),f866(f18(x46852,a925,a925),f866(f866(f8(a925,f937(a925,a925),x46852),a333),f866(f866(f7(x46852,f937(x46852,a925),a925),f336(x46852)),x46853)))),f866(f866(f7(f937(x46851,a925),f937(x46852,f937(x46851,a925)),f937(x46852,a925)),f866(f866(f8(f937(f937(x46851,a925),a925),f937(f937(x46852,f937(x46851,a925)),f937(x46852,a925)),f937(x46851,a925)),f8(f937(x46851,a925),a925,x46852)),a332)),x46854))))),f866(f866(f45(x46852,f937(x46851,a925)),x46853),x46854))
% 157.60/157.51 [4692]E(f866(f866(f158(f931(x46921)),f866(f866(f158(x46921),x46922),f866(f149(f931(x46921),f931(x46921),f141(x46921),f120(x46921)),f866(f866(f161(f931(x46921),f931(x46921)),f163(f931(x46921),x46921,f120(x46921),f866(f866(f8(f931(x46921),f937(f931(x46921),f931(x46921)),x46921),f16(f931(x46921),f931(x46921))),f866(f866(f7(x46921,f931(x46921),f931(x46921)),f158(x46921)),f120(x46921))))),x46923)))),f186(x46921,f866(f866(f158(f931(x46921)),x46924),f866(f149(f931(f931(x46921)),f931(f931(x46921)),f141(f931(x46921)),f120(f931(x46921))),f866(f866(f161(f931(x46921),f931(f931(x46921))),f163(f931(f931(x46921)),x46921,f120(f931(x46921)),f866(f16(f937(f931(x46921),f931(f931(x46921))),x46921),f866(f866(f7(f931(x46921),f931(f931(x46921)),f931(f931(x46921))),f158(f931(x46921))),f120(f931(x46921)))))),x46923))))),f186(x46921,f866(f866(f158(f931(x46921)),f866(f866(f158(x46921),x46922),x46924)),x46923)))
% 157.60/157.51 [4699]E(f866(f270(f936(x46991,x46991)),f866(f265(x46991,x46991,a925),f866(f866(f7(x46991,f937(f936(x46992,x46992),a925),f937(x46991,a925)),f866(f866(f8(f937(x46991,f937(f937(f936(x46992,x46992),a925),a925)),f937(f937(f936(x46992,x46992),a925),f937(x46991,a925)),x46991),f7(x46991,f937(f936(x46992,x46992),a925),a925)),f866(f866(f8(f937(x46991,f936(x46992,x46992)),f937(x46991,f937(f937(f936(x46992,x46992),a925),a925)),x46991),f866(f8(f936(x46992,x46992),f937(f937(f936(x46992,x46992),a925),a925),x46991),f336(f936(x46992,x46992)))),f866(f866(f7(x46991,f937(x46991,x46992),f937(x46991,f936(x46992,x46992))),f866(f866(f8(f937(x46992,f936(x46992,x46992)),f937(f937(x46991,x46992),f937(x46991,f936(x46992,x46992))),x46991),f8(x46992,f936(x46992,x46992),x46991)),f866(f866(f8(x46992,f937(x46992,f936(x46992,x46992)),x46991),f260(x46992,x46992)),x46993))),x46993)))),x46994))),f866(f866(f295(x46992,x46991),x46994),x46993))
% 157.60/157.51 [4753]~E(f31(x47531,x47532),f28(x47533,x47534,x47535))
% 157.60/157.51 [4754]~E(f31(x47541,x47542),f27(x47543,x47544,x47545))
% 157.60/157.51 [4755]~E(f26(x47551,x47552),f28(x47553,x47554,x47555))
% 157.60/157.51 [4756]~E(f26(x47561,x47562),f27(x47563,x47564,x47565))
% 157.60/157.51 [4757]~E(f30(x47571,x47572),f28(x47573,x47574,x47575))
% 157.60/157.51 [4758]~E(f30(x47581,x47582),f27(x47583,x47584,x47585))
% 157.60/157.51 [4759]~E(f28(x47591,x47592,x47593),f31(x47594,x47595))
% 157.60/157.51 [4760]~E(f28(x47601,x47602,x47603),f26(x47604,x47605))
% 157.60/157.51 [4761]~E(f28(x47611,x47612,x47613),f30(x47614,x47615))
% 157.60/157.51 [4762]~E(f27(x47621,x47622,x47623),f31(x47624,x47625))
% 157.60/157.51 [4763]~E(f27(x47631,x47632,x47633),f26(x47634,x47635))
% 157.60/157.51 [4764]~E(f27(x47641,x47642,x47643),f30(x47644,x47645))
% 157.60/157.51 [3829]E(f866(f866(f161(x38291,x38292),x38293),f176(x38291,x38294,x38295)),f176(x38292,x38294,f866(x38293,x38295)))
% 157.60/157.51 [4042]E(f100(x40421,x40422,f98(x40421,x40423,x40424,x40425)),f2(a930))
% 157.60/157.51 [4166]E(f137(x41661,x41662,x41663,f133(x41661,x41664,x41665)),f133(x41662,f866(x41663,x41664),f137(x41661,x41662,x41663,x41665)))
% 157.60/157.51 [4399]E(f866(f80(x43991,x43992,x43993,x43994,x43995),x43994),x43995)
% 157.60/157.51 [4451]E(f261(x44511,x44512,x44513,f251(x44512,x44511,x44514),f251(x44513,x44512,x44515)),f251(x44513,x44511,f261(x44513,x44512,x44511,x44515,x44514)))
% 157.60/157.51 [4021]E(f866(f866(f265(x40211,x40212,x40213),x40214),x40215),f866(f866(x40214,f866(f259(x40211,x40212),x40215)),f866(f264(x40211,x40212),x40215)))
% 157.60/157.51 [4057]E(f866(f866(f866(f70(x40571,x40572,x40573),x40574),x40575),f195(f937(x40572,a925))),x40575)
% 157.60/157.51 [4337]E(f866(f78(f931(x43371),f931(x43372),f931(x43373),f866(f161(x43371,x43372),x43374)),f866(f161(x43373,x43371),x43375)),f866(f161(x43373,x43372),f866(f78(x43371,x43372,x43373,x43374),x43375)))
% 157.60/157.51 [4413]E(f91(x44131,f71(x44132,x44131,x44133,x44134,x44135)),f866(f866(f69(x44132,x44131,x44133),x44134),x44135))
% 157.60/157.51 [4447]E(f866(f866(f86(a930),f866(f866(f86(a930),f866(x44471,f866(f259(x44472,x44473),x44474))),f866(x44475,f866(f264(x44472,x44473),x44474)))),f866(a119,f2(a930))),f269(x44472,x44473,x44471,x44475,x44474))
% 157.60/157.51 [3957]E(f866(f866(f182(x39571),x39572),f866(f866(f161(x39573,x39571),x39574),x39575)),f866(f866(f161(x39573,x39571),x39574),f866(f866(f182(x39573),x39572),x39575)))
% 157.60/157.51 [3958]E(f866(f866(f145(x39581),x39582),f866(f866(f161(x39583,x39581),x39584),x39585)),f866(f866(f161(x39583,x39581),x39584),f866(f866(f145(x39583),x39582),x39585)))
% 157.60/157.51 [3990]E(f866(f866(f161(x39901,x39902),x39903),f866(f866(f158(x39901),x39904),x39905)),f866(f866(f158(x39902),f866(x39903,x39904)),f866(f866(f161(x39901,x39902),x39903),x39905)))
% 157.60/157.51 [4053]E(f866(f317(x40531,x40532,x40533),f866(f866(f316(x40531),x40534),x40535)),f866(f866(f316(x40532),f866(x40533,x40534)),f866(f317(x40531,x40532,x40533),x40535)))
% 157.60/157.51 [4081]E(f180(x40811,f866(f866(f158(x40811),x40812),x40813),f866(f866(f158(x40811),x40814),x40815)),f866(f866(f158(x40811),x40812),f866(f866(f158(x40811),x40814),f180(x40811,x40813,x40815))))
% 157.60/157.51 [4118]E(f866(f866(f188(x41181,x41182),f866(f866(f182(x41181),x41183),x41184)),f866(f866(f182(x41182),x41183),x41185)),f866(f866(f182(f936(x41181,x41182)),x41183),f866(f866(f188(x41181,x41182),x41184),x41185)))
% 157.60/157.51 [4119]E(f866(f866(f188(x41191,x41192),f866(f866(f145(x41191),x41193),x41194)),f866(f866(f145(x41192),x41193),x41195)),f866(f866(f145(f936(x41191,x41192)),x41193),f866(f866(f188(x41191,x41192),x41194),x41195)))
% 157.60/157.51 [4129]E(f866(f866(f166(x41291,f866(f866(f158(x41291),x41292),x41293)),f866(a119,x41294)),x41295),f866(f866(f158(x41291),x41292),f866(f866(f166(x41291,x41293),x41294),x41295)))
% 157.60/157.51 [4132]E(f866(f866(f141(x41321),f866(f866(f161(x41322,x41321),x41323),x41324)),f866(f866(f161(x41322,x41321),x41323),x41325)),f866(f866(f161(x41322,x41321),x41323),f866(f866(f141(x41322),x41324),x41325)))
% 157.60/157.51 [4136]E(f866(f866(x41361,x41362),f866(f866(f253(x41363,x41364,x41361),x41362),x41365)),f866(f866(f253(x41363,x41364,x41361),x41362),f866(a119,x41365)))
% 157.60/157.51 [4170]E(f170(x41701,x41702,x41703,f866(f866(f158(x41701),x41704),x41705)),f866(f866(f141(x41702),f866(x41703,x41704)),f170(x41701,x41702,x41703,x41705)))
% 157.60/157.51 [4182]E(f866(f866(f296(x41821,x41822,x41823),f866(f294(x41822,x41821),x41824)),f866(f294(x41823,x41822),x41825)),f866(f294(x41823,x41821),f866(f866(f296(x41823,x41822,x41821),x41825),x41824)))
% 157.60/157.51 [4214]E(f866(f866(f866(f190(f931(x42141),f931(x42141)),x42142),f174(x42141)),f866(f866(f161(x42143,x42141),x42144),x42145)),f866(f866(f161(x42143,x42141),x42144),f866(f866(f866(f190(f931(x42143),f931(x42143)),x42142),f174(x42143)),x42145)))
% 157.60/157.51 [4215]E(f866(f866(f267(x42151,x42152,x42151,x42153),f866(f260(x42152,x42151),x42154)),x42155),f866(x42155,x42154))
% 157.60/157.51 [4239]E(f162(x42391,x42392,f866(f866(f161(x42393,x42391),x42394),x42395)),f162(x42393,f866(f78(x42391,a930,x42393,x42392),x42394),x42395))
% 157.60/157.51 [4302]E(f184(f936(x43021,x43022),f866(f78(x43022,a925,f936(x43021,x43022),x43023),f264(x43021,x43022)),f866(f866(f188(x43021,x43022),x43024),x43025)),f866(f866(f188(x43021,x43022),x43024),f184(x43022,x43023,x43025)))
% 157.60/157.51 [4307]E(f866(f317(x43071,x43072,f866(f866(f8(x43073,x43072,x43071),x43074),x43075)),f250(f937(x43071,a925))),f866(f317(x43073,x43072,x43074),f866(f317(x43071,x43073,x43075),f250(f937(x43071,a925)))))
% 157.60/157.51 [4320]E(f184(f936(x43201,x43202),f866(f78(x43201,a925,f936(x43201,x43202),x43203),f259(x43201,x43202)),f866(f866(f188(x43201,x43202),x43204),x43205)),f866(f866(f188(x43201,x43202),f184(x43201,x43203,x43204)),x43205))
% 157.60/157.51 [4341]E(f866(f866(f117(f937(x43411,a925)),f866(f318(x43411,x43412,x43413),f866(f866(f316(x43412),x43414),f195(f937(x43412,a925))))),f866(f318(x43411,x43412,x43413),x43415)),f866(f318(x43411,x43412,x43413),f866(f866(f316(x43412),x43414),x43415)))
% 157.60/157.51 [4398]E(f866(f866(f141(f936(x43981,x43982)),f866(f866(f161(x43982,f936(x43981,x43982)),f866(f260(x43981,x43982),x43983)),x43984)),f64(x43981,x43982,x43985,x43984)),f64(x43981,x43982,f866(f866(f158(x43981),x43983),x43985),x43984))
% 157.60/157.51 [4400]E(f866(f866(f161(x44001,x44002),x44003),f184(x44001,f866(f78(x44002,a925,x44001,x44004),x44003),x44005)),f184(x44002,x44004,f866(f866(f161(x44001,x44002),x44003),x44005)))
% 157.60/157.51 [4405]E(f866(f149(x44051,x44052,f866(f7(x44052,x44051,x44051),f866(f7(x44051,x44052,x44051),x44053)),x44054),f866(f175(x44052),f866(f175(x44052),x44055))),f866(f149(x44051,x44052,x44053,x44054),x44055))
% 157.60/157.51 [4508]P107(f866(f866(f243(f937(x45081,a925)),f866(f317(x45082,x45081,x45083),f866(f866(f108(f937(x45082,a925)),x45084),x45085))),f866(f866(f108(f937(x45081,a925)),f866(f317(x45082,x45081,x45083),x45084)),f866(f317(x45082,x45081,x45083),x45085))))
% 157.60/157.51 [4509]P107(f866(f866(f243(f937(x45091,a925)),f866(f293(x45092,x45091,x45093),f866(f866(f108(f937(x45092,a925)),x45094),x45095))),f866(f866(f108(f937(x45091,a925)),f866(f293(x45092,x45091,x45093),x45094)),f866(f293(x45092,x45091,x45093),x45095))))
% 157.60/157.51 [4608]E(f866(f264(x46081,x46082),f866(f266(x46083,x46081,x46082,x46082,x46084,f32(x46082)),x46085)),f866(f264(x46083,x46082),x46085))
% 157.60/157.51 [4609]E(f866(f259(x46091,x46092),f866(f266(x46091,x46091,x46093,x46092,f32(x46091),x46094),x46095)),f866(f259(x46091,x46093),x46095))
% 157.60/157.51 [4674]P24(x46741,x46742,f866(f866(f316(f929(x46741)),f98(x46741,f866(f866(f7(x46741,f937(a926,a926),f937(a926,a925)),f866(f866(f8(f937(a926,a925),f937(f937(a926,a926),f937(a926,a925)),x46741),f8(a926,a925,a926)),x46743)),f866(f866(f18(a926,a930,a926),f866(f866(f7(a926,a928,f937(a930,a926)),a203),x46744)),x46745)),f26(x46744,x46745),x46743)),f195(f937(f929(x46741),a925))))
% 157.60/157.51 [3796]E(f866(f866(f866(f866(f213(x37961),x37962),x37963),x37964),x37965),f208(x37961,x37962))
% 157.60/157.51 [3797]E(f866(f866(f866(f866(f214(x37971),x37972),x37973),x37974),x37975),f199(x37971,x37972))
% 157.60/157.51 [4171]E(f866(f866(f44(x41711,f937(x41712,a925)),f866(f866(f316(x41711),x41713),x41714)),x41715),f866(f866(f117(f937(x41712,a925)),f866(x41715,x41713)),f866(f866(f44(x41711,f937(x41712,a925)),x41714),x41715)))
% 157.60/157.51 [4172]E(f866(f866(f45(x41721,f937(x41722,a925)),f866(f866(f316(x41721),x41723),x41724)),x41725),f866(f866(f108(f937(x41722,a925)),f866(x41725,x41723)),f866(f866(f45(x41721,f937(x41722,a925)),x41724),x41725)))
% 157.60/157.51 [4222]E(f866(f125(x42221,x42222,f866(x42223,x42224)),f866(f866(f7(x42221,a106,f932(x42222)),x42225),x42224)),f866(f206(x42221,x42222,x42223,x42225),x42224))
% 157.60/157.51 [4233]E(f866(f866(f117(f937(x42331,a925)),f866(f317(x42332,x42331,x42333),x42334)),f866(f317(x42332,x42331,x42333),x42335)),f866(f317(x42332,x42331,x42333),f866(f866(f117(f937(x42332,a925)),x42334),x42335)))
% 157.60/157.51 [4234]E(f866(f866(f117(f937(x42341,a925)),f866(f293(x42342,x42341,x42343),x42344)),f866(f293(x42342,x42341,x42343),x42345)),f866(f293(x42342,x42341,x42343),f866(f866(f117(f937(x42342,a925)),x42344),x42345)))
% 157.60/157.51 [4235]E(f866(f866(f23(f937(x42351,a925)),f866(f318(x42351,x42352,x42353),x42354)),f866(f318(x42351,x42352,x42353),x42355)),f866(f318(x42351,x42352,x42353),f866(f866(f23(f937(x42352,a925)),x42354),x42355)))
% 157.60/157.51 [4236]E(f866(f866(f117(f937(x42361,a925)),f866(f318(x42361,x42362,x42363),x42364)),f866(f318(x42361,x42362,x42363),x42365)),f866(f318(x42361,x42362,x42363),f866(f866(f117(f937(x42362,a925)),x42364),x42365)))
% 157.60/157.51 [4237]E(f866(f866(f108(f937(x42371,a925)),f866(f318(x42371,x42372,x42373),x42374)),f866(f318(x42371,x42372,x42373),x42375)),f866(f318(x42371,x42372,x42373),f866(f866(f108(f937(x42372,a925)),x42374),x42375)))
% 157.60/157.51 [4298]E(f866(f866(f166(x42981,f866(f866(f141(x42981),x42982),f866(f866(f158(x42981),x42983),x42984))),f866(f196(f931(x42981)),x42982)),x42985),f866(f866(f141(x42981),x42982),f866(f866(f158(x42981),x42985),x42984)))
% 157.60/157.51 [4305]E(f866(f866(f45(x43051,f937(x43052,a925)),x43053),f866(f866(f8(f937(x43052,a925),f937(x43052,a925),x43051),f866(f316(x43052),x43054)),x43055)),f866(f866(f316(x43052),x43054),f866(f866(f45(x43051,f937(x43052,a925)),x43053),x43055)))
% 157.60/157.51 [4460]E(f866(f866(f161(x44601,x44602),x44603),f866(f143(x44601,f866(f78(x44602,a925,x44601,x44604),x44603)),x44605)),f866(f143(x44602,x44604),f866(f866(f161(x44601,x44602),x44603),x44605)))
% 157.60/157.51 [4466]E(f866(f196(f931(x44661)),f866(f143(x44661,x44662),f866(f866(f161(x44663,x44661),x44664),x44665))),f866(f196(f931(x44663)),f866(f143(x44663,f866(f78(x44661,a925,x44663,x44662),x44664)),x44665)))
% 157.60/157.51 [4675]E(f866(f163(f931(f936(x46751,x46752)),x46752,f120(f936(x46751,x46752)),f866(f866(f7(x46752,f937(f931(x46752),f931(f936(x46751,x46752))),f937(f931(x46752),f931(f936(x46751,x46752)))),f866(f866(f8(f937(f931(f936(x46751,x46752)),f931(f936(x46751,x46752))),f937(f937(f931(x46752),f931(f936(x46751,x46752))),f937(f931(x46752),f931(f936(x46751,x46752)))),x46752),f8(f931(f936(x46751,x46752)),f931(f936(x46751,x46752)),f931(x46752))),f866(f866(f8(f936(x46751,x46752),f937(f931(f936(x46751,x46752)),f931(f936(x46751,x46752))),x46752),f158(f936(x46751,x46752))),f866(f260(x46751,x46752),x46753)))),f866(f188(x46751,x46752),x46754))),x46755),f866(f866(f188(x46751,x46752),f866(f866(f158(x46751),x46753),x46754)),x46755))
% 157.60/157.51 [4163]E(f866(f866(f166(x41631,f866(f866(f166(x41631,x41632),x41633),x41634)),x41633),x41635),f866(f866(f166(x41631,x41632),x41633),x41635))
% 157.60/157.51 [4216]E(f866(f292(x42161,x42162),f866(f866(f316(f936(x42161,x42162)),f866(f866(f260(x42161,x42162),x42163),x42164)),x42165)),f866(f866(f316(x42162),x42164),f866(f292(x42161,x42162),x42165)))
% 157.60/157.51 [4217]E(f866(f272(x42171,x42172),f866(f866(f316(f936(x42171,x42172)),f866(f866(f260(x42171,x42172),x42173),x42174)),x42175)),f866(f866(f316(x42171),x42173),f866(f272(x42171,x42172),x42175)))
% 157.60/157.51 [4263]E(f129(x42631,x42632,f866(x42633,x42634),f866(f866(f7(x42631,a106,f932(f934(x42632))),x42635),x42634)),f866(f202(x42631,x42632,x42633,x42635),x42634))
% 157.60/157.51 [4291]E(f866(f866(f23(f937(f936(x42911,x42912),a925)),f866(f866(f262(x42911,x42912),x42913),x42914)),f866(f866(f262(x42911,x42912),x42915),x42914)),f866(f866(f262(x42911,x42912),f866(f866(f23(f937(x42911,a925)),x42913),x42915)),x42914))
% 157.60/157.51 [4292]E(f866(f866(f117(f937(f936(x42921,x42922),a925)),f866(f866(f262(x42921,x42922),x42923),x42924)),f866(f866(f262(x42921,x42922),x42925),x42924)),f866(f866(f262(x42921,x42922),f866(f866(f117(f937(x42921,a925)),x42923),x42925)),x42924))
% 157.60/157.51 [4293]E(f866(f866(f108(f937(f936(x42931,x42932),a925)),f866(f866(f262(x42931,x42932),x42933),x42934)),f866(f866(f262(x42931,x42932),x42935),x42934)),f866(f866(f262(x42931,x42932),f866(f866(f108(f937(x42931,a925)),x42933),x42935)),x42934))
% 157.60/157.51 [4352]E(f866(f866(f117(f937(x43521,a925)),f866(f866(f44(x43522,f937(x43521,a925)),x43523),x43524)),f866(f866(f44(x43522,f937(x43521,a925)),x43525),x43524)),f866(f866(f44(x43522,f937(x43521,a925)),f866(f866(f117(f937(x43522,a925)),x43523),x43525)),x43524))
% 157.60/157.51 [4353]E(f866(f866(f108(f937(x43531,a925)),f866(f866(f45(x43532,f937(x43531,a925)),x43533),x43534)),f866(f866(f45(x43532,f937(x43531,a925)),x43535),x43534)),f866(f866(f45(x43532,f937(x43531,a925)),f866(f866(f117(f937(x43532,a925)),x43533),x43535)),x43534))
% 157.60/157.51 [4367]E(f866(f866(f44(x43671,f937(x43672,a925)),x43673),f866(f866(f8(f937(x43672,a925),f937(x43672,a925),x43671),f866(f23(f937(x43672,a925)),x43674)),x43675)),f866(f866(f23(f937(x43672,a925)),x43674),f866(f866(f45(x43671,f937(x43672,a925)),x43673),x43675)))
% 157.60/157.51 [4368]E(f866(f866(f44(x43681,f937(x43682,a925)),x43683),f866(f866(f8(f937(x43682,a925),f937(x43682,a925),x43681),f866(f108(f937(x43682,a925)),x43684)),x43685)),f866(f866(f108(f937(x43682,a925)),x43684),f866(f866(f44(x43681,f937(x43682,a925)),x43683),x43685)))
% 157.60/157.51 [4369]E(f866(f866(f45(x43691,f937(x43692,a925)),x43693),f866(f866(f8(f937(x43692,a925),f937(x43692,a925),x43691),f866(f117(f937(x43692,a925)),x43694)),x43695)),f866(f866(f117(f937(x43692,a925)),x43694),f866(f866(f45(x43691,f937(x43692,a925)),x43693),x43695)))
% 157.60/157.51 [4425]E(f192(f931(x44251),f866(f866(f158(x44251),x44252),x44253),f866(f866(f8(f931(x44251),f931(x44251),a930),f866(f158(x44251),x44254)),f866(f866(f7(a930,x44251,f931(x44251)),f166(x44251,x44253)),x44252)),x44255),f866(f866(f166(x44251,f866(f866(f158(x44251),x44254),x44253)),x44255),x44252))
% 157.60/157.51 [4429]E(f866(f866(f44(x44291,f937(f936(x44292,x44293),a925)),x44294),f866(f866(f8(f937(f936(x44293,x44292),a925),f937(f936(x44292,x44293),a925),x44291),f294(x44293,x44292)),x44295)),f866(f294(x44293,x44292),f866(f866(f44(x44291,f937(f936(x44293,x44292),a925)),x44294),x44295)))
% 157.60/157.51 [4430]E(f866(f866(f45(x44301,f937(f936(x44302,x44303),a925)),x44304),f866(f866(f8(f937(f936(x44303,x44302),a925),f937(f936(x44302,x44303),a925),x44301),f294(x44303,x44302)),x44305)),f866(f294(x44303,x44302),f866(f866(f45(x44301,f937(f936(x44303,x44302),a925)),x44304),x44305)))
% 157.60/157.51 [4531]P107(f866(f866(f243(f937(x45311,a925)),f866(f866(f23(f937(x45311,a925)),f866(f317(x45312,x45311,x45313),x45314)),f866(f317(x45312,x45311,x45313),x45315))),f866(f317(x45312,x45311,x45313),f866(f866(f23(f937(x45312,a925)),x45314),x45315))))
% 157.60/157.51 [4678]E(f866(f163(f931(f936(x46781,x46782)),x46781,f120(f936(x46781,x46782)),f866(f866(f7(x46781,f937(f931(x46781),f931(f936(x46781,x46782))),f937(f931(x46781),f931(f936(x46781,x46782)))),f866(f866(f8(f937(f931(f936(x46781,x46782)),f931(f936(x46781,x46782))),f937(f937(f931(x46781),f931(f936(x46781,x46782))),f937(f931(x46781),f931(f936(x46781,x46782)))),x46781),f8(f931(f936(x46781,x46782)),f931(f936(x46781,x46782)),f931(x46781))),f866(f866(f8(f936(x46781,x46782),f937(f931(f936(x46781,x46782)),f931(f936(x46781,x46782))),x46781),f158(f936(x46781,x46782))),f866(f866(f7(x46781,x46782,f936(x46781,x46782)),f260(x46781,x46782)),x46783)))),f866(f866(f7(f931(x46781),f931(x46782),f931(f936(x46781,x46782))),f188(x46781,x46782)),x46784))),x46785),f866(f866(f188(x46781,x46782),x46785),f866(f866(f158(x46782),x46783),x46784)))
% 157.60/157.51 [4394]E(f866(f866(f117(f937(x43941,a925)),f866(f293(x43942,x43941,x43943),x43944)),f866(f293(x43942,x43941,x43945),x43944)),f866(f293(x43942,x43941,f866(f866(f117(f937(f936(x43942,x43941),a925)),x43943),x43945)),x43944))
% 157.60/157.51 [4431]E(f866(f866(f141(f936(x44311,x44312)),f866(f866(f188(x44311,x44312),x44313),f866(f866(f182(x44312),f866(f196(f931(x44311)),x44313)),x44314))),f866(f866(f188(x44311,x44312),x44315),f866(f866(f145(x44312),f866(f196(f931(x44311)),x44313)),x44314))),f866(f866(f188(x44311,x44312),f866(f866(f141(x44311),x44313),x44315)),x44314))
% 157.60/157.51 [4534]E(f866(f866(f262(x45341,x45342),x45343),f866(f866(f18(x45341,f937(x45342,a925),f937(x45342,a925)),f866(f866(f8(f937(x45342,a925),f937(f937(x45342,a925),f937(x45342,a925)),x45341),f23(f937(x45342,a925))),x45344)),x45345)),f866(f866(f23(f937(f936(x45341,x45342),a925)),f866(f866(f262(x45341,x45342),x45343),x45344)),f866(f866(f262(x45341,x45342),x45343),x45345)))
% 157.60/157.51 [4535]E(f866(f866(f262(x45351,x45352),x45353),f866(f866(f18(x45351,f937(x45352,a925),f937(x45352,a925)),f866(f866(f8(f937(x45352,a925),f937(f937(x45352,a925),f937(x45352,a925)),x45351),f117(f937(x45352,a925))),x45354)),x45355)),f866(f866(f117(f937(f936(x45351,x45352),a925)),f866(f866(f262(x45351,x45352),x45353),x45354)),f866(f866(f262(x45351,x45352),x45353),x45355)))
% 157.60/157.51 [4536]E(f866(f866(f262(x45361,x45362),x45363),f866(f866(f18(x45361,f937(x45362,a925),f937(x45362,a925)),f866(f866(f8(f937(x45362,a925),f937(f937(x45362,a925),f937(x45362,a925)),x45361),f108(f937(x45362,a925))),x45364)),x45365)),f866(f866(f108(f937(f936(x45361,x45362),a925)),f866(f866(f262(x45361,x45362),x45363),x45364)),f866(f866(f262(x45361,x45362),x45363),x45365)))
% 157.60/157.51 [4540]E(f866(f866(f44(x45401,f937(x45402,a925)),x45403),f866(f866(f7(x45401,f937(x45402,a925),f937(x45402,a925)),f866(f866(f8(f937(x45402,a925),f937(f937(x45402,a925),f937(x45402,a925)),x45401),f23(f937(x45402,a925))),x45404)),x45405)),f866(f866(f23(f937(x45402,a925)),f866(f866(f44(x45401,f937(x45402,a925)),x45403),x45404)),x45405))
% 157.60/157.51 [4541]E(f866(f866(f44(x45411,f937(x45412,a925)),x45413),f866(f866(f7(x45411,f937(x45412,a925),f937(x45412,a925)),f866(f866(f8(f937(x45412,a925),f937(f937(x45412,a925),f937(x45412,a925)),x45411),f108(f937(x45412,a925))),x45414)),x45415)),f866(f866(f108(f937(x45412,a925)),f866(f866(f44(x45411,f937(x45412,a925)),x45413),x45414)),x45415))
% 157.60/157.51 [4542]E(f866(f866(f45(x45421,f937(x45422,a925)),x45423),f866(f866(f7(x45421,f937(x45422,a925),f937(x45422,a925)),f866(f866(f8(f937(x45422,a925),f937(f937(x45422,a925),f937(x45422,a925)),x45421),f117(f937(x45422,a925))),x45424)),x45425)),f866(f866(f117(f937(x45422,a925)),f866(f866(f45(x45421,f937(x45422,a925)),x45423),x45424)),x45425))
% 157.60/157.51 [4546]E(f866(f866(f44(x45461,f937(x45462,a925)),x45463),f866(f866(f18(x45461,f937(x45462,a925),f937(x45462,a925)),f866(f866(f8(f937(x45462,a925),f937(f937(x45462,a925),f937(x45462,a925)),x45461),f117(f937(x45462,a925))),x45464)),x45465)),f866(f866(f117(f937(x45462,a925)),f866(f866(f44(x45461,f937(x45462,a925)),x45463),x45464)),f866(f866(f44(x45461,f937(x45462,a925)),x45463),x45465)))
% 157.60/157.51 [4547]E(f866(f866(f45(x45471,f937(x45472,a925)),x45473),f866(f866(f18(x45471,f937(x45472,a925),f937(x45472,a925)),f866(f866(f8(f937(x45472,a925),f937(f937(x45472,a925),f937(x45472,a925)),x45471),f108(f937(x45472,a925))),x45474)),x45475)),f866(f866(f108(f937(x45472,a925)),f866(f866(f45(x45471,f937(x45472,a925)),x45473),x45474)),f866(f866(f45(x45471,f937(x45472,a925)),x45473),x45475)))
% 157.60/157.51 [4560]E(f866(f866(f44(x45601,f937(x45602,a925)),x45603),f866(f866(f18(x45601,f937(x45602,a925),f937(x45602,a925)),f866(f866(f8(f937(x45602,a925),f937(f937(x45602,a925),f937(x45602,a925)),x45601),f117(f937(x45602,a925))),x45604)),x45605)),f866(f866(f117(f937(x45602,a925)),f42(f937(x45602,a925),f866(f317(x45601,f937(x45602,a925),x45604),x45603))),f42(f937(x45602,a925),f866(f317(x45601,f937(x45602,a925),x45605),x45603))))
% 157.60/157.51 [4561]E(f866(f866(f45(x45611,f937(x45612,a925)),x45613),f866(f866(f18(x45611,f937(x45612,a925),f937(x45612,a925)),f866(f866(f8(f937(x45612,a925),f937(f937(x45612,a925),f937(x45612,a925)),x45611),f108(f937(x45612,a925))),x45614)),x45615)),f866(f866(f108(f937(x45612,a925)),f43(f937(x45612,a925),f866(f317(x45611,f937(x45612,a925),x45614),x45613))),f43(f937(x45612,a925),f866(f317(x45611,f937(x45612,a925),x45615),x45613))))
% 157.60/157.51 [4597]E(f866(f866(f145(x45971),f866(f196(f931(x45971)),f184(x45971,x45972,f866(f866(f161(x45973,x45971),x45974),x45975)))),f866(f866(f161(x45973,x45971),x45974),x45975)),f866(f866(f161(x45973,x45971),x45974),f866(f866(f145(x45973),f866(f196(f931(x45973)),f184(x45973,f866(f78(x45971,a925,x45973,x45972),x45974),x45975))),x45975)))
% 157.60/157.51 [4473]E(f866(f866(f141(f936(x44731,x44732)),f866(f866(f188(x44731,x44732),f866(f866(f182(x44731),f866(f196(f931(x44732)),x44733)),x44734)),x44733)),f866(f866(f188(x44731,x44732),f866(f866(f145(x44731),f866(f196(f931(x44732)),x44733)),x44734)),x44735)),f866(f866(f188(x44731,x44732),x44734),f866(f866(f141(x44732),x44733),x44735)))
% 157.60/157.51 [4588]E(f91(x45881,f866(f866(f18(x45881,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45881),a333),f866(f866(f7(x45881,f937(x45881,a925),a925),f336(x45881)),x45882))),f866(f866(f7(x45881,x45883,a925),f866(f866(f8(x45883,f937(x45883,a925),x45881),a332),x45884)),x45885))),f866(f83(x45881,x45883,x45882,x45884),x45885))
% 157.60/157.51 [4589]E(f96(x45891,f866(f866(f18(x45891,a925,a925),f866(f866(f8(a925,f937(a925,a925),x45891),a333),f866(f866(f7(x45891,f937(x45891,a925),a925),f336(x45891)),x45892))),f866(f866(f7(x45891,x45893,a925),f866(f866(f8(x45893,f937(x45893,a925),x45891),a332),x45894)),x45895))),f866(f97(x45891,x45893,x45892,x45894),x45895))
% 157.60/157.51 [4637]E(f866(f866(f92(a1,x46371),f866(f110(a1),f866(f866(f86(a1),x46372),a104))),f866(f866(f18(a1,x46371,x46371),f866(f866(f7(a1,x46371,f937(x46371,x46371)),f866(f866(f8(a925,f937(x46371,f937(x46371,x46371)),a1),f103(x46371)),a200)),f192(x46371,x46373,x46374,x46375))),f866(f866(f8(a930,x46371,a1),x46374),f866(f866(f7(a1,a930,a930),f866(f866(f8(a930,f937(a930,a930),a1),f86(a930)),a111)),x46375)))),f192(x46371,x46373,x46374,f866(f866(f86(a930),f866(f110(a930),x46372)),x46375)))
% 157.60/157.51 [4672]E(f866(f866(f92(a1,x46721),f866(f110(a1),f866(f866(f86(a1),x46722),a104))),f866(f866(f18(a1,x46721,x46721),f866(f866(f7(a1,x46721,f937(x46721,x46721)),f866(f866(f8(a925,f937(x46721,f937(x46721,x46721)),a1),f103(x46721)),a200)),f866(f191(x46721,x46723,x46724),x46725))),f866(f866(f18(a1,x46721,x46721),f866(f866(f8(a930,f937(x46721,x46721),a1),x46724),f866(f866(f7(a1,a930,a930),f866(f866(f8(a930,f937(a930,a930),a1),f86(a930)),a111)),x46725))),f866(f866(f8(a930,x46721,a1),f191(x46721,x46723,x46724)),f866(f866(f7(a1,a930,a930),f866(f866(f8(a930,f937(a930,a930),a1),f86(a930)),a111)),x46725))))),f866(f191(x46721,x46723,x46724),f866(f866(f86(a930),f866(f110(a930),x46722)),x46725)))
% 157.60/157.51 [4707]E(f866(f270(f936(x47071,x47072)),f866(f265(x47071,x47072,a925),f866(f866(f8(f937(x47072,f937(x47073,a925)),f937(x47072,a925),x47071),f866(f8(f937(x47073,a925),a925,x47072),f93(x47073))),f866(f866(f7(x47071,f937(x47072,f937(x47073,a925)),f937(x47072,f937(x47073,a925))),f866(f866(f8(f937(f937(x47073,a925),f937(x47073,a925)),f937(f937(x47072,f937(x47073,a925)),f937(x47072,f937(x47073,a925))),x47071),f8(f937(x47073,a925),f937(x47073,a925),x47072)),f866(f866(f8(f937(x47073,f937(a925,a925)),f937(f937(x47073,a925),f937(x47073,a925)),x47071),f18(x47073,a925,a925)),f866(f866(f8(f937(x47073,a925),f937(x47073,f937(a925,a925)),x47071),f866(f8(a925,f937(a925,a925),x47073),a333)),f866(f866(f7(x47071,f937(f936(x47071,x47073),a925),f937(x47073,a925)),f866(f866(f8(f937(x47073,f937(f937(f936(x47071,x47073),a925),a925)),f937(f937(f936(x47071,x47073),a925),f937(x47073,a925)),x47071),f7(x47073,f937(f936(x47071,x47073),a925),a925)),f866(f866(f8(f937(x47073,f936(x47071,x47073)),f937(x47073,f937(f937(f936(x47071,x47073),a925),a925)),x47071),f866(f8(f936(x47071,x47073),f937(f937(f936(x47071,x47073),a925),a925),x47073),f336(f936(x47071,x47073)))),f260(x47071,x47073)))),x47074))))),f866(f866(f7(x47072,f937(f936(x47073,x47072),a925),f937(x47073,a925)),f866(f866(f8(f937(x47073,f937(f937(f936(x47073,x47072),a925),a925)),f937(f937(f936(x47073,x47072),a925),f937(x47073,a925)),x47072),f7(x47073,f937(f936(x47073,x47072),a925),a925)),f866(f866(f8(f937(x47073,f936(x47073,x47072)),f937(x47073,f937(f937(f936(x47073,x47072),a925),a925)),x47072),f866(f8(f936(x47073,x47072),f937(f937(f936(x47073,x47072),a925),a925),x47073),f336(f936(x47073,x47072)))),f866(f7(x47073,x47072,f936(x47073,x47072)),f260(x47073,x47072))))),x47075))))),f866(f866(f296(x47071,x47073,x47072),x47074),x47075))
% 157.60/157.51 [4783]~E(f27(x47831,x47832,x47833),f28(x47834,x47835,x47836))
% 157.60/157.51 [4321]E(f233(x43211,x43212,x43213,x43214,f229(x43211,x43212,x43215,x43216)),f866(f866(x43214,x43215),x43216))
% 157.60/157.51 [4322]E(f234(x43221,x43222,x43223,x43224,f229(x43221,x43222,x43225,x43226)),f866(f866(x43224,x43225),x43226))
% 157.60/157.51 [4449]E(f134(x44491,x44492,x44493,x44494,f133(x44492,x44495,x44496)),f866(f866(f866(x44494,x44495),x44496),f134(x44491,x44492,x44493,x44494,x44496)))
% 157.60/157.51 [4468]E(f80(x44681,x44682,f80(x44681,x44682,x44683,x44684,x44685),x44684,x44686),f80(x44681,x44682,x44683,x44684,x44686))
% 157.60/157.51 [4576]E(f866(f78(f936(x45761,x45762),x45762,f936(x45763,x45764),f264(x45761,x45762)),f266(x45763,x45761,x45764,x45762,x45765,x45766)),f866(f78(x45764,x45762,f936(x45763,x45764),x45766),f264(x45763,x45764)))
% 157.60/157.51 [4577]E(f866(f78(f936(x45771,x45772),x45771,f936(x45773,x45774),f259(x45771,x45772)),f266(x45773,x45771,x45774,x45772,x45775,x45776)),f866(f78(x45773,x45771,f936(x45773,x45774),x45775),f259(x45773,x45774)))
% 157.60/157.51 [4139]E(f101(x41391,x41392,x41393,f98(x41391,x41394,x41395,x41396)),f866(f866(f866(x41393,x41394),x41395),x41396))
% 157.60/157.51 [4140]E(f102(x41401,x41402,x41403,f98(x41401,x41404,x41405,x41406)),f866(f866(f866(x41403,x41404),x41405),x41406))
% 157.60/157.51 [4192]E(f866(f866(f78(x41921,x41922,x41923,x41924),x41925),x41926),f866(x41924,f866(x41925,x41926)))
% 157.60/157.51 [4331]E(f232(x43311,f936(x43312,f932(x43312)),x43313,f866(f265(x43312,f932(x43312),x43311),x43314),f866(f142(x43312),f133(x43312,x43315,x43316))),f866(f866(x43314,x43315),x43316))
% 157.60/157.51 [4381]E(f235(x43811,x43812,x43813,x43814,f229(x43811,x43812,x43815,x43816)),f866(f866(f86(a930),f866(f866(f86(a930),f866(x43813,x43815)),f866(x43814,x43816))),f866(a119,f2(a930))))
% 157.60/157.51 [3988]E(f866(f866(f265(x39881,x39882,x39883),x39884),f866(f866(f260(x39881,x39882),x39885),x39886)),f866(f866(x39884,x39885),x39886))
% 157.60/157.51 [4050]E(f866(f866(f866(f8(x40501,x40502,x40503),x40504),x40505),x40506),f866(x40504,f866(x40505,x40506)))
% 157.60/157.51 [4051]E(f866(f866(f866(f7(x40511,x40512,x40513),x40514),x40515),x40516),f866(f866(x40514,x40516),x40515))
% 157.60/157.51 [4067]E(f866(f866(f866(f18(x40671,x40672,x40673),x40674),x40675),x40676),f866(f866(x40674,x40676),f866(x40675,x40676)))
% 157.60/157.51 [4090]E(f866(f163(x40901,x40902,x40903,x40904),f866(f866(f158(x40902),x40905),x40906)),f866(f866(x40904,x40905),x40906))
% 157.60/157.51 [4128]E(f176(f936(x41281,x41282),f866(f866(f241(a930),x41283),x41284),f866(f866(f260(x41281,x41282),x41285),x41286)),f866(f866(f188(x41281,x41282),f176(x41281,x41283,x41285)),f176(x41282,x41284,x41286)))
% 157.60/157.51 [4196]E(f866(f866(f158(f936(x41961,x41962)),f866(f866(f260(x41961,x41962),x41963),x41964)),f866(f866(f188(x41961,x41962),x41965),x41966)),f866(f866(f188(x41961,x41962),f866(f866(f158(x41961),x41963),x41965)),f866(f866(f158(x41962),x41964),x41966)))
% 157.60/157.51 [4197]E(f866(f866(f161(x41971,x41972),x41973),f866(f866(f166(x41971,x41974),x41975),x41976)),f866(f866(f166(x41972,f866(f866(f161(x41971,x41972),x41973),x41974)),x41975),f866(x41973,x41976)))
% 157.60/157.51 [4221]E(f866(f866(f263(x42211,x42212,x42213,x42214),x42215),x42216),f866(x42214,f866(f866(f260(x42211,x42212),x42215),x42216)))
% 157.60/157.51 [4238]E(f866(f149(x42381,x42382,x42383,x42384),f866(f866(f158(x42382),x42385),x42386)),f866(f149(x42381,x42382,x42383,f866(f866(x42383,x42384),x42385)),x42386))
% 157.60/157.51 [4264]E(f268(x42641,x42642,x42643,x42644,f866(f866(f260(x42641,x42642),x42645),x42646)),f866(f866(x42644,x42645),x42646))
% 157.60/157.51 [4345]E(f866(f866(f44(x43451,f937(x43452,a925)),x43453),f866(f78(x43454,f937(x43452,a925),x43451,x43455),x43456)),f866(f866(f44(x43454,f937(x43452,a925)),f866(f317(x43451,x43454,x43456),x43453)),x43455))
% 157.60/157.51 [4397]E(f866(f866(f161(x43971,x43972),x43973),f866(f866(f161(x43974,x43971),x43975),x43976)),f866(f866(f161(x43974,x43972),f866(f78(x43971,x43972,x43974,x43973),x43975)),x43976))
% 157.60/157.51 [4403]E(f866(f317(x44031,x44032,f866(f78(x44033,x44032,x44031,x44034),x44035)),x44036),f866(f317(x44033,x44032,x44034),f866(f317(x44031,x44033,x44035),x44036)))
% 157.60/157.51 [4404]E(f866(f318(x44041,x44042,f866(f78(x44043,x44042,x44041,x44044),x44045)),x44046),f866(f318(x44041,x44043,x44045),f866(f318(x44043,x44042,x44044),x44046)))
% 157.60/157.51 [4432]E(f866(f149(x44321,x44322,x44323,f866(f149(x44321,x44322,x44323,x44324),x44325)),x44326),f866(f149(x44321,x44322,x44323,x44324),f866(f866(f141(x44322),x44325),x44326)))
% 157.60/157.51 [4566]E(f866(f266(x45661,x45661,x45662,x45663,f32(x45661),x45664),f866(f866(f260(x45661,x45662),x45665),x45666)),f866(f866(f260(x45661,x45663),x45665),f866(x45664,x45666)))
% 157.60/157.51 [4567]E(f866(f266(x45671,x45672,x45673,x45673,x45674,f32(x45673)),f866(f866(f260(x45671,x45673),x45675),x45676)),f866(f866(f260(x45672,x45673),f866(x45674,x45675)),x45676))
% 157.60/157.51 [4655]E(f866(f866(f161(f936(x46551,x46552),f936(x46551,x46553)),f866(f265(x46551,x46552,f936(x46551,x46553)),f866(f866(f7(x46551,f937(x46552,x46553),f937(x46552,f936(x46551,x46553))),f866(f866(f8(f937(x46553,f936(x46551,x46553)),f937(f937(x46552,x46553),f937(x46552,f936(x46551,x46553))),x46551),f8(x46553,f936(x46551,x46553),x46552)),f260(x46551,x46553))),x46554))),f866(f866(f188(x46551,x46552),x46555),x46556)),f866(f866(f188(x46551,x46553),x46555),f866(f866(f161(x46552,x46553),x46554),x46556)))
% 157.60/157.51 [4248]E(f866(f866(f78(x42481,x42482,x42483,f866(f16(x42482,x42481),x42484)),x42485),x42486),x42484)
% 157.60/157.51 [4280]E(f866(f317(x42801,x42802,x42803),f866(f317(x42804,x42801,x42805),x42806)),f866(f317(x42804,x42802,f866(f866(f8(x42801,x42802,x42804),x42803),x42805)),x42806))
% 157.60/157.51 [4286]E(f866(f866(f44(x42861,f937(x42862,a925)),f866(f317(x42863,x42861,x42864),x42865)),x42866),f866(f866(f44(x42863,f937(x42862,a925)),x42865),f866(f866(f8(x42861,f937(x42862,a925),x42863),x42866),x42864)))
% 157.60/157.51 [4287]E(f866(f866(f45(x42871,f937(x42872,a925)),f866(f317(x42873,x42871,x42874),x42875)),x42876),f866(f866(f45(x42873,f937(x42872,a925)),x42875),f866(f866(f8(x42871,f937(x42872,a925),x42873),x42876),x42874)))
% 157.60/157.51 [4288]E(f866(f866(f44(x42881,f937(x42882,a925)),x42883),f866(f866(f8(x42884,f937(x42882,a925),x42881),x42885),x42886)),f866(f866(f44(x42884,f937(x42882,a925)),f866(f317(x42881,x42884,x42886),x42883)),x42885))
% 157.60/157.51 [4289]E(f866(f866(f45(x42891,f937(x42892,a925)),x42893),f866(f866(f8(x42894,f937(x42892,a925),x42891),x42895),x42896)),f866(f866(f45(x42894,f937(x42892,a925)),f866(f317(x42891,x42894,x42896),x42893)),x42895))
% 157.60/157.51 [4347]E(f866(f866(f44(x43471,f937(x43472,a925)),x43473),f866(f866(f8(f937(x43474,a925),f937(x43472,a925),x43471),f317(x43474,x43472,x43475)),x43476)),f866(f317(x43474,x43472,x43475),f866(f866(f44(x43471,f937(x43474,a925)),x43473),x43476)))
% 157.60/157.51 [4348]E(f866(f866(f44(x43481,f937(x43482,a925)),x43483),f866(f866(f8(f937(x43484,a925),f937(x43482,a925),x43481),f293(x43484,x43482,x43485)),x43486)),f866(f293(x43484,x43482,x43485),f866(f866(f44(x43481,f937(x43484,a925)),x43483),x43486)))
% 157.60/157.51 [4349]E(f866(f866(f44(x43491,f937(x43492,a925)),x43493),f866(f866(f8(f937(x43494,a925),f937(x43492,a925),x43491),f318(x43492,x43494,x43495)),x43496)),f866(f318(x43492,x43494,x43495),f866(f866(f44(x43491,f937(x43494,a925)),x43493),x43496)))
% 157.60/157.51 [4350]E(f866(f866(f45(x43501,f937(x43502,a925)),x43503),f866(f866(f8(f937(x43504,a925),f937(x43502,a925),x43501),f318(x43502,x43504,x43505)),x43506)),f866(f318(x43502,x43504,x43505),f866(f866(f45(x43501,f937(x43504,a925)),x43503),x43506)))
% 157.60/157.51 [4437]E(f866(f149(x44371,x44372,f866(f7(x44372,x44371,x44371),x44373),x44374),f866(f175(x44372),f866(f866(f158(x44372),x44375),x44376))),f866(f866(x44373,x44375),f866(f149(x44371,x44372,f866(f7(x44372,x44371,x44371),x44373),x44374),f866(f175(x44372),x44376))))
% 157.60/157.51 [4495]E(f866(f866(f18(f936(x44951,x44952),x44952,x44953),f866(f866(f8(x44954,f937(x44952,x44953),f936(x44951,x44952)),x44955),f866(f866(f8(x44951,x44954,f936(x44951,x44952)),x44956),f259(x44951,x44952)))),f264(x44951,x44952)),f866(f265(x44951,x44952,x44953),f866(f866(f8(x44954,f937(x44952,x44953),x44951),x44955),x44956)))
% 157.60/157.51 [4502]E(f866(f149(x45021,x45022,f866(f7(x45022,x45021,x45021),x45023),f866(f149(x45021,x45022,f866(f7(x45022,x45021,x45021),x45023),x45024),f866(f175(x45022),x45025))),f866(f175(x45022),x45026)),f866(f149(x45021,x45022,f866(f7(x45022,x45021,x45021),x45023),x45024),f866(f175(x45022),f866(f866(f141(x45022),x45026),x45025))))
% 157.60/157.51 [4504]E(f866(f866(f161(f936(x45041,x45042),f936(x45043,x45042)),f866(f265(x45041,x45042,f936(x45043,x45042)),f866(f866(f8(x45043,f937(x45042,f936(x45043,x45042)),x45041),f260(x45043,x45042)),x45044))),f866(f866(f188(x45041,x45042),x45045),x45046)),f866(f866(f188(x45043,x45042),f866(f866(f161(x45041,x45043),x45044),x45045)),x45046))
% 157.60/157.51 [4549]P107(f866(f866(f243(f937(x45491,a925)),f866(f293(x45492,x45491,x45493),f866(f866(f45(x45494,f937(x45492,a925)),x45495),x45496))),f866(f866(f45(x45494,f937(x45491,a925)),x45495),f866(f866(f8(f937(x45492,a925),f937(x45491,a925),x45494),f293(x45492,x45491,x45493)),x45496))))
% 157.60/157.51 [4360]E(f866(f866(f188(x43601,x43602),f866(f866(f166(x43601,x43603),x43604),f866(f259(x43601,x43602),x43605))),f866(f866(f166(x43602,x43606),x43604),f866(f264(x43601,x43602),x43605))),f866(f866(f166(f936(x43601,x43602),f866(f866(f188(x43601,x43602),x43603),x43606)),x43604),x43605))
% 157.60/157.51 [4420]E(f866(f866(f117(f937(f936(x44201,x44202),a925)),f866(f866(f296(x44201,x44203,x44202),x44204),x44205)),f866(f866(f296(x44201,x44203,x44202),x44204),x44206)),f866(f866(f296(x44201,x44203,x44202),x44204),f866(f866(f117(f937(f936(x44203,x44202),a925)),x44205),x44206)))
% 157.60/157.51 [4514]E(f866(f866(f316(f936(x45141,x45142)),f866(f866(f260(x45141,x45142),x45143),x45144)),f866(f866(f117(f937(f936(x45141,x45142),a925)),f866(f866(f262(x45141,x45142),x45145),f866(f16(f937(x45142,a925),x45141),f866(f866(f316(x45142),x45144),x45146)))),f866(f866(f262(x45141,x45142),f866(f866(f316(x45141),x45143),x45145)),f866(f16(f937(x45142,a925),x45141),x45146)))),f866(f866(f262(x45141,x45142),f866(f866(f316(x45141),x45143),x45145)),f866(f16(f937(x45142,a925),x45141),f866(f866(f316(x45142),x45144),x45146))))
% 157.60/157.51 [4593]E(f866(f866(f108(f937(x45931,a925)),f866(f318(x45931,x45932,f866(f78(f936(x45932,x45933),x45932,x45931,f259(x45932,x45933)),x45934)),x45935)),f866(f318(x45931,x45933,f866(f78(f936(x45932,x45933),x45933,x45931,f264(x45932,x45933)),x45934)),x45936)),f866(f318(x45931,f936(x45932,x45933),x45934),f866(f866(f262(x45932,x45933),x45935),f866(f16(f937(x45933,a925),x45932),x45936))))
% 157.60/157.51 [4443]E(f866(f866(f117(f937(f936(x44431,x44432),a925)),f866(f866(f296(x44431,x44433,x44432),x44434),x44435)),f866(f866(f296(x44431,x44433,x44432),x44436),x44435)),f866(f866(f296(x44431,x44433,x44432),f866(f866(f117(f937(f936(x44431,x44433),a925)),x44434),x44436)),x44435))
% 157.60/157.51 [4574]E(f866(f866(f44(x45741,f937(x45742,a925)),x45743),f866(f866(f7(x45741,f937(x45744,f937(x45742,a925)),f937(x45742,a925)),f866(f866(f8(f937(x45744,a925),f937(f937(x45744,f937(x45742,a925)),f937(x45742,a925)),x45741),f44(x45744,f937(x45742,a925))),x45745)),x45746)),f866(f866(f44(x45744,f937(x45742,a925)),f866(f866(f44(x45741,f937(x45744,a925)),x45743),x45745)),x45746))
% 157.60/157.51 [4575]E(f866(f866(f45(x45751,f937(x45752,a925)),x45753),f866(f866(f7(x45751,f937(x45754,f937(x45752,a925)),f937(x45752,a925)),f866(f866(f8(f937(x45754,a925),f937(f937(x45754,f937(x45752,a925)),f937(x45752,a925)),x45751),f45(x45754,f937(x45752,a925))),x45755)),x45756)),f866(f866(f45(x45754,f937(x45752,a925)),f866(f866(f44(x45751,f937(x45754,a925)),x45753),x45755)),x45756))
% 157.60/157.51 [4627]E(f866(f265(x46271,x46272,f936(x46273,x46274)),f866(f866(f7(x46271,f937(x46272,x46274),f937(x46272,f936(x46273,x46274))),f866(f866(f8(f937(x46274,f936(x46273,x46274)),f937(f937(x46272,x46274),f937(x46272,f936(x46273,x46274))),x46271),f8(x46274,f936(x46273,x46274),x46272)),f866(f866(f8(x46273,f937(x46274,f936(x46273,x46274)),x46271),f260(x46273,x46274)),x46275))),x46276)),f266(x46271,x46273,x46272,x46274,x46275,x46276))
% 157.60/157.51 [4650]E(f866(f317(x46501,x46502,f866(f866(f18(x46501,x46502,x46502),f866(f866(f18(x46501,x46502,f937(x46502,x46502)),f866(f866(f8(a925,f937(x46502,f937(x46502,x46502)),x46501),f103(x46502)),x46503)),x46504)),x46505)),x46506),f866(f866(f117(f937(x46502,a925)),f866(f317(x46501,x46502,x46504),f866(f866(f108(f937(x46501,a925)),x46506),f866(f270(x46501),x46503)))),f866(f317(x46501,x46502,x46505),f866(f866(f108(f937(x46501,a925)),x46506),f866(f270(x46501),f866(f866(f8(a925,a925,x46501),a329),x46503))))))
% 157.60/157.51 [4662]E(f866(f317(x46621,f936(x46622,x46623),f866(f866(f18(x46621,x46623,f936(x46622,x46623)),f866(f866(f8(x46622,f937(x46623,f936(x46622,x46623)),x46621),f260(x46622,x46623)),x46624)),x46625)),x46626),f866(f866(f262(x46622,x46623),f866(f317(x46621,x46622,x46624),x46626)),f866(f866(f8(f937(x46621,a925),f937(x46623,a925),x46622),f317(x46621,x46623,x46625)),f866(f866(f7(x46622,f937(x46621,a925),f937(x46621,a925)),f866(f866(f8(f937(x46621,a925),f937(f937(x46621,a925),f937(x46621,a925)),x46622),f108(f937(x46621,a925))),f866(f866(f8(f937(x46622,a925),f937(x46621,a925),x46622),f318(x46621,x46622,x46624)),f866(f866(f7(x46622,f937(x46622,a925),f937(x46622,a925)),f316(x46622)),f195(f937(x46622,a925)))))),x46626))))
% 157.60/157.51 [4689]E(f254(x46891,x46892,x46893,x46894,x46895,x46896),f866(x46894,f866(f270(x46891),f866(f866(f8(f937(f937(x46893,x46891),a925),a925,x46891),f93(f937(x46893,x46891))),f866(f866(f8(f937(f937(x46893,x46891),a925),f937(f937(x46893,x46891),a925),x46891),f866(f18(f937(x46893,x46891),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x46893,x46891)),a333),f866(f866(f7(f937(x46893,x46891),f937(f937(x46893,x46891),a925),a925),f336(f937(x46893,x46891))),x46895)))),f866(f866(f7(x46891,f937(f937(x46893,x46891),x46891),f937(f937(x46893,x46891),a925)),f866(f866(f8(f937(x46891,a925),f937(f937(f937(x46893,x46891),x46891),f937(f937(x46893,x46891),a925)),x46891),f8(x46891,a925,f937(x46893,x46891))),a332)),f866(f866(f7(f937(x46893,x46891),x46893,x46891),f5(f937(x46893,x46891))),x46896)))))))
% 157.60/157.51 [4476]E(f866(f78(x44761,x44762,x44763,x44764),f80(x44763,x44761,x44765,x44766,x44767)),f80(x44763,x44762,f866(f78(x44761,x44762,x44763,x44764),x44765),x44766,f866(x44764,x44767)))
% 157.60/157.51 [4610]E(f866(f264(x46101,x46102),f866(f266(x46103,x46101,x46104,x46102,x46105,x46106),x46107)),f866(x46106,f866(f264(x46103,x46104),x46107)))
% 157.60/157.51 [4611]E(f866(f259(x46111,x46112),f866(f266(x46113,x46111,x46114,x46112,x46115,x46116),x46117)),f866(x46115,f866(f259(x46113,x46114),x46117)))
% 157.60/157.51 [4323]E(f866(f866(f188(x43231,x43232),f866(f866(f166(x43231,x43233),x43234),x43235)),f866(f866(f166(x43232,x43236),x43234),x43237)),f866(f866(f166(f936(x43231,x43232),f866(f866(f188(x43231,x43232),x43233),x43236)),x43234),f866(f866(f260(x43231,x43232),x43235),x43237)))
% 157.60/157.51 [4392]E(f866(f866(f866(f267(x43921,x43922,x43923,x43924),x43925),x43926),x43927),f866(f866(f265(x43922,x43923,x43924),x43926),f866(x43925,x43927)))
% 157.60/157.51 [4402]E(f866(f866(f866(f267(x44021,x44022,x44023,x44024),x44025),x44026),x44027),f866(f866(x44026,f866(f259(x44022,x44023),f866(x44025,x44027))),f866(f264(x44022,x44023),f866(x44025,x44027))))
% 157.60/157.51 [4454]E(f866(f78(x44541,x44542,x44543,x44544),f866(f78(x44545,x44541,x44543,x44546),x44547)),f866(f78(x44545,x44542,x44543,f866(f78(x44541,x44542,x44545,x44544),x44546)),x44547))
% 157.60/157.51 [4631]E(f866(f266(x46311,x46312,x46313,x46313,x46314,f32(x46313)),f866(f266(x46311,x46311,x46315,x46313,f32(x46311),x46316),x46317)),f866(f866(f260(x46312,x46313),f866(x46314,f866(f259(x46311,x46315),x46317))),f866(x46316,f866(f264(x46311,x46315),x46317))))
% 157.60/157.51 [4632]E(f866(f266(x46321,x46321,x46322,x46323,f32(x46321),x46324),f866(f266(x46325,x46321,x46322,x46322,x46326,f32(x46322)),x46327)),f866(f866(f260(x46321,x46323),f866(x46326,f866(f259(x46325,x46322),x46327))),f866(x46324,f866(f264(x46325,x46322),x46327))))
% 157.60/157.51 [4648]E(f866(f266(x46481,x46482,x46483,x46483,x46484,f32(x46483)),f866(f266(x46485,x46481,x46483,x46483,x46486,f32(x46483)),x46487)),f866(f266(x46485,x46482,x46483,x46483,f866(f78(x46481,x46482,x46485,x46484),x46486),f32(x46483)),x46487))
% 157.60/157.51 [4649]E(f866(f266(x46491,x46491,x46492,x46493,f32(x46491),x46494),f866(f266(x46491,x46491,x46495,x46492,f32(x46491),x46496),x46497)),f866(f266(x46491,x46491,x46495,x46493,f32(x46491),f866(f78(x46492,x46493,x46495,x46494),x46496)),x46497))
% 157.60/157.51 [4659]E(f866(f266(x46591,x46592,x46593,x46593,x46594,f32(x46593)),f866(f266(x46591,x46591,x46595,x46593,f32(x46591),x46596),x46597)),f866(f266(x46592,x46592,x46595,x46593,f32(x46592),x46596),f866(f266(x46591,x46592,x46595,x46595,x46594,f32(x46595)),x46597)))
% 157.60/157.51 [4357]E(f866(f866(f296(x43571,x43572,x43573),f866(f866(f296(x43571,x43574,x43572),x43575),x43576)),x43577),f866(f866(f296(x43571,x43574,x43573),x43575),f866(f866(f296(x43574,x43572,x43573),x43576),x43577)))
% 157.60/157.51 [4426]E(f866(f866(f265(x44261,x44262,x44263),f866(f78(x44264,f937(x44262,x44263),x44261,x44265),x44266)),x44267),f866(f866(x44265,f866(x44266,f866(f259(x44261,x44262),x44267))),f866(f264(x44261,x44262),x44267)))
% 157.60/157.51 [4507]E(f866(f149(x45071,x45072,f866(f7(x45072,x45071,x45071),x45073),x45074),f866(f175(x45072),f866(f866(f161(x45075,x45072),x45076),x45077))),f866(f149(x45071,x45075,f866(f7(x45075,x45071,x45071),f866(f78(x45072,f937(x45071,x45071),x45075,x45073),x45076)),x45074),f866(f175(x45075),x45077)))
% 157.60/157.51 [4455]E(f866(f866(f44(x44551,f937(f936(x44552,x44553),a925)),x44554),f866(f866(f8(f937(f936(x44555,x44553),a925),f937(f936(x44552,x44553),a925),x44551),f866(f296(x44552,x44555,x44553),x44556)),x44557)),f866(f866(f296(x44552,x44555,x44553),x44556),f866(f866(f44(x44551,f937(f936(x44555,x44553),a925)),x44554),x44557)))
% 157.60/157.51 [4598]E(f866(f866(f44(x45981,f937(f936(x45982,x45983),a925)),x45984),f866(f866(f7(x45981,f937(f936(x45985,x45983),a925),f937(f936(x45982,x45983),a925)),f866(f866(f8(f937(f936(x45982,x45985),a925),f937(f937(f936(x45985,x45983),a925),f937(f936(x45982,x45983),a925)),x45981),f296(x45982,x45985,x45983)),x45986)),x45987)),f866(f866(f296(x45982,x45985,x45983),f866(f866(f44(x45981,f937(f936(x45982,x45985),a925)),x45984),x45986)),x45987))
% 157.60/157.51 [4599]E(f866(f149(x45991,x45992,f866(f866(f7(x45991,f937(x45992,x45993),f937(x45992,x45991)),f866(f866(f8(f937(x45993,x45991),f937(f937(x45992,x45993),f937(x45992,x45991)),x45991),f8(x45993,x45991,x45992)),x45994)),x45995),x45996),x45997),f866(f149(x45991,x45993,x45994,x45996),f866(f866(f161(x45992,x45993),x45995),x45997)))
% 157.60/157.51 [4660]E(f866(f866(f45(x46601,f937(x46602,a925)),x46603),f866(f866(f8(f937(x46604,f937(x46602,a925)),f937(x46602,a925),x46601),f866(f45(x46604,f937(x46602,a925)),x46605)),f866(f866(f7(x46601,f937(x46604,f937(x46602,a925)),f937(x46604,f937(x46602,a925))),f866(f866(f8(f937(f937(x46602,a925),f937(x46602,a925)),f937(f937(x46604,f937(x46602,a925)),f937(x46604,f937(x46602,a925))),x46601),f8(f937(x46602,a925),f937(x46602,a925),x46604)),f866(f866(f8(f937(x46602,a925),f937(f937(x46602,a925),f937(x46602,a925)),x46601),f117(f937(x46602,a925))),x46606))),x46607))),f866(f866(f117(f937(x46602,a925)),f866(f866(f45(x46601,f937(x46602,a925)),x46603),x46606)),f866(f866(f45(x46604,f937(x46602,a925)),x46605),x46607)))
% 157.60/157.51 [4661]E(f866(f866(f44(x46611,f937(x46612,a925)),x46613),f866(f866(f8(f937(x46614,f937(x46612,a925)),f937(x46612,a925),x46611),f866(f44(x46614,f937(x46612,a925)),x46615)),f866(f866(f7(x46611,f937(x46614,f937(x46612,a925)),f937(x46614,f937(x46612,a925))),f866(f866(f8(f937(f937(x46612,a925),f937(x46612,a925)),f937(f937(x46614,f937(x46612,a925)),f937(x46614,f937(x46612,a925))),x46611),f8(f937(x46612,a925),f937(x46612,a925),x46614)),f866(f866(f8(f937(x46612,a925),f937(f937(x46612,a925),f937(x46612,a925)),x46611),f108(f937(x46612,a925))),x46616))),x46617))),f866(f866(f108(f937(x46612,a925)),f866(f866(f44(x46611,f937(x46612,a925)),x46613),x46616)),f866(f866(f44(x46614,f937(x46612,a925)),x46615),x46617)))
% 157.60/157.51 [4653]E(f206(x46531,x46532,f866(f866(f866(x46533,x46534),x46535),x46536),f866(f866(f7(x46531,f936(a106,a106),f937(a106,f932(x46532))),f866(f866(f7(x46531,a106,f937(f936(a106,a106),f937(a106,f932(x46532)))),f866(f866(f7(x46531,a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(x46532))))),x46537),x46534)),x46535)),x46536)),f866(f866(f866(f218(x46531,x46532,x46533,x46537),x46534),x46535),x46536))
% 157.60/157.51 [4667]E(f207(x46671,x46672,f866(f866(f866(x46673,x46674),x46675),x46676),f866(f866(f7(x46671,f936(a106,a106),f937(a106,f932(x46672))),f866(f866(f7(x46671,a106,f937(f936(a106,a106),f937(a106,f932(x46672)))),f866(f866(f7(x46671,a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(x46672))))),x46677),x46674)),x46675)),x46676)),f220(x46671,x46672,x46673,x46677,x46674,x46675,x46676))
% 157.60/157.51 [4658]E(f202(x46581,x46582,f866(f866(f866(x46583,x46584),x46585),x46586),f866(f866(f7(x46581,f936(a106,a106),f937(a106,f932(f934(x46582)))),f866(f866(f7(x46581,a106,f937(f936(a106,a106),f937(a106,f932(f934(x46582))))),f866(f866(f7(x46581,a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(f934(x46582)))))),x46587),x46584)),x46585)),x46586)),f866(f866(f866(f215(x46581,x46582,x46583,x46587),x46584),x46585),x46586))
% 157.60/157.51 [4669]E(f205(x46691,x46692,f866(f866(f866(x46693,x46694),x46695),x46696),f866(f866(f7(x46691,f936(a106,a106),f937(a106,f932(f934(x46692)))),f866(f866(f7(x46691,a106,f937(f936(a106,a106),f937(a106,f932(f934(x46692))))),f866(f866(f7(x46691,a106,f937(a106,f937(f936(a106,a106),f937(a106,f932(f934(x46692)))))),x46697),x46694)),x46695)),x46696)),f217(x46691,x46692,x46693,x46697,x46694,x46695,x46696))
% 157.60/157.51 [4568]E(f866(f266(x45681,x45682,x45683,x45684,x45685,x45686),f866(f866(f260(x45681,x45683),x45687),x45688)),f866(f866(f260(x45682,x45684),f866(x45685,x45687)),f866(x45686,x45688)))
% 157.60/157.51 [4671]E(f866(f866(f161(f936(x46711,x46712),f936(x46713,x46714)),f866(f265(x46711,x46712,f936(x46713,x46714)),f866(f866(f7(x46711,f937(x46712,x46714),f937(x46712,f936(x46713,x46714))),f866(f866(f8(f937(x46714,f936(x46713,x46714)),f937(f937(x46712,x46714),f937(x46712,f936(x46713,x46714))),x46711),f8(x46714,f936(x46713,x46714),x46712)),f866(f866(f8(x46713,f937(x46714,f936(x46713,x46714)),x46711),f260(x46713,x46714)),x46715))),x46716))),f866(f866(f188(x46711,x46712),x46717),x46718)),f866(f866(f188(x46713,x46714),f866(f866(f161(x46711,x46713),x46715),x46717)),f866(f866(f161(x46712,x46714),x46716),x46718)))
% 157.60/157.51 [4676]E(f866(f866(f161(f936(x46761,x46762),x46763),f866(f265(x46761,x46762,x46763),f866(f866(f8(f937(x46762,f936(x46761,x46764)),f937(x46762,x46763),x46761),f866(f8(f936(x46761,x46764),x46763,x46762),x46765)),f866(f866(f7(x46761,f937(x46762,x46764),f937(x46762,f936(x46761,x46764))),f866(f866(f8(f937(x46764,f936(x46761,x46764)),f937(f937(x46762,x46764),f937(x46762,f936(x46761,x46764))),x46761),f8(x46764,f936(x46761,x46764),x46762)),f260(x46761,x46764))),x46766)))),f866(f866(f188(x46761,x46762),x46767),x46768)),f866(f866(f161(f936(x46761,x46764),x46763),x46765),f866(f866(f188(x46761,x46764),x46767),f866(f866(f161(x46762,x46764),x46766),x46768))))
% 157.60/157.51 [4602]E(f866(f866(f161(f936(x46021,x46022),x46023),f866(f265(x46021,x46022,x46023),f866(f866(f8(f937(x46022,f936(x46024,x46022)),f937(x46022,x46023),x46021),f866(f8(f936(x46024,x46022),x46023,x46022),x46025)),f866(f866(f8(x46024,f937(x46022,f936(x46024,x46022)),x46021),f260(x46024,x46022)),x46026)))),f866(f866(f188(x46021,x46022),x46027),x46028)),f866(f866(f161(f936(x46024,x46022),x46023),x46025),f866(f866(f188(x46024,x46022),f866(f866(f161(x46021,x46024),x46026),x46027)),x46028)))
% 157.60/157.51 [4559]E(f866(f866(f265(x45591,x45592,x45593),f866(f866(f8(f937(x45592,f936(x45594,x45595)),f937(x45592,x45593),x45591),f866(f8(f936(x45594,x45595),x45593,x45592),f866(f265(x45594,x45595,x45593),x45596))),x45597)),x45598),f866(f866(f265(x45594,x45595,x45593),x45596),f866(f866(f265(x45591,x45592,f936(x45594,x45595)),x45597),x45598)))
% 157.60/157.51 [4677]E(f866(f866(f44(f936(x46771,x46772),f937(f936(x46773,x46774),a925)),f866(f866(f262(x46771,x46772),x46775),f866(f16(f937(x46772,a925),x46771),x46776))),f866(f265(x46771,x46772,f937(f936(x46773,x46774),a925)),f866(f866(f7(x46771,f937(x46772,f937(x46773,f937(x46774,a925))),f937(x46772,f937(f936(x46773,x46774),a925))),f866(f866(f8(f937(f937(x46773,f937(x46774,a925)),f937(f936(x46773,x46774),a925)),f937(f937(x46772,f937(x46773,f937(x46774,a925))),f937(x46772,f937(f936(x46773,x46774),a925))),x46771),f8(f937(x46773,f937(x46774,a925)),f937(f936(x46773,x46774),a925),x46772)),f866(f866(f8(f937(x46773,a925),f937(f937(x46773,f937(x46774,a925)),f937(f936(x46773,x46774),a925)),x46771),f262(x46773,x46774)),x46777))),f866(f866(f8(f937(x46774,a925),f937(x46773,f937(x46774,a925)),x46772),f16(f937(x46774,a925),x46773)),x46778)))),f866(f866(f262(x46773,x46774),f866(f866(f44(x46771,f937(x46773,a925)),x46775),x46777)),f866(f16(f937(x46774,a925),x46773),f866(f866(f44(x46772,f937(x46774,a925)),x46776),x46778))))
% 157.60/157.51 [4616]E(f866(f866(f267(x46161,x46162,x46163,x46164),f866(f866(f267(x46161,x46165,x46166,f936(x46162,x46163)),x46167),x46168)),x46169),f866(f866(f267(x46161,x46165,x46166,x46164),x46167),f866(f866(f7(x46165,f937(x46162,f937(x46163,x46164)),f937(x46166,x46164)),f866(f866(f8(f937(x46166,f936(x46162,x46163)),f937(f937(x46162,f937(x46163,x46164)),f937(x46166,x46164)),x46165),f267(x46166,x46162,x46163,x46164)),x46168)),x46169)))
% 157.60/157.51 [4645]E(f866(f78(f936(x46451,x46452),f936(x46453,x46454),f936(x46455,x46456),f266(x46451,x46453,x46452,x46454,x46457,x46458)),f266(x46455,x46451,x46456,x46452,x46459,x464510)),f266(x46455,x46453,x46456,x46454,f866(f78(x46451,x46453,x46455,x46457),x46459),f866(f78(x46452,x46454,x46456,x46458),x464510)))
% 157.60/157.51 [4651]E(f866(f266(x46511,x46512,x46513,x46514,x46515,x46516),f866(f266(x46517,x46511,x46518,x46513,x46519,x465110),x465111)),f866(f266(x46517,x46512,x46518,x46514,f866(f78(x46511,x46512,x46517,x46515),x46519),f866(f78(x46513,x46514,x46518,x46516),x465110)),x465111))
% 157.60/157.51 [4813]~P4(x48131)+P4(f934(x48131))
% 157.60/157.51 [4814]~P64(x48141)+P64(f934(x48141))
% 157.60/157.51 [4815]~P105(x48151)+P105(f931(x48151))
% 157.60/157.51 [4818]~P146(x48181)+~E(f84(x48181),f2(x48181))
% 157.60/157.51 [4820]~E(x48201,f2(a106))+E(f866(a22,x48201),f2(a1))
% 157.60/157.51 [4821]~E(x48211,f2(a1))+E(f88(a1,x48211),f2(a1))
% 157.60/157.51 [4827]~P148(x48271)+P28(x48271,f2(x48271))
% 157.60/157.51 [4829]~P110(x48291)+P13(x48291,f120(x48291))
% 157.60/157.51 [4838]P107(x48381)+P107(f866(a329,x48381))
% 157.60/157.51 [4892]~P148(x48921)+~P28(x48921,f84(x48921))
% 157.60/157.51 [4935]~P107(x49351)+~P107(f866(a329,x49351))
% 157.60/157.51 [4956]E(f866(a111,x49561),f2(a930))+~P107(f866(a200,x49561))
% 157.60/157.51 [5022]~P99(x50221)+P14(x50221,x50221,f87(x50221))
% 157.60/157.51 [5023]~P102(x50231)+P14(x50231,x50231,f117(x50231))
% 157.60/157.51 [5024]~P103(x50241)+P14(x50241,x50241,f108(x50241))
% 157.60/157.51 [5025]~P110(x50251)+P14(x50251,x50251,f241(x50251))
% 157.60/157.51 [5026]~P110(x50261)+P14(x50261,x50261,f242(x50261))
% 157.60/157.51 [5027]~P69(x50271)+P16(x50271,x50271,f87(x50271))
% 157.60/157.51 [4824]~E(x48241,f2(a930))+E(f866(f107(a1),x48241),f2(a1))
% 157.60/157.51 [4831]~P96(x48311)+E(f866(f110(x48311),a89),f2(x48311))
% 157.60/157.51 [4834]~E(f553(x48341),f2(a930))+E(f866(f172(a930),x48341),f2(a930))
% 157.60/157.51 [4835]~P109(x48351)+E(f245(x48351,f243(x48351)),f241(x48351))
% 157.60/157.51 [4836]~P109(x48361)+E(f246(x48361,f243(x48361)),f242(x48361))
% 157.60/157.51 [4837]~P93(x48371)+E(f88(x48371,f2(x48371)),f2(x48371))
% 157.60/157.51 [4846]~P148(x48461)+E(f866(f107(x48461),f84(a930)),f84(x48461))
% 157.60/157.51 [4847]~P148(x48471)+E(f866(f107(x48471),f2(a930)),f2(x48471))
% 157.60/157.51 [4848]~P142(x48481)+E(f866(f109(x48481),f84(a1)),f84(x48481))
% 157.60/157.51 [4849]~P142(x48491)+E(f866(f109(x48491),f2(a1)),f2(x48491))
% 157.60/157.51 [4850]E(x48501,f2(a930))+~E(f866(f107(a1),x48501),f2(a1))
% 157.60/157.51 [4886]~P128(x48861)+E(f866(f81(x48861),f84(x48861)),f84(x48861))
% 157.60/157.51 [4887]~P89(x48871)+E(f866(f81(x48871),f2(x48871)),f2(x48871))
% 157.60/157.51 [4888]~P98(x48881)+E(f866(f85(x48881),f195(x48881)),f250(x48881))
% 157.60/157.51 [4889]~P98(x48891)+E(f866(f85(x48891),f250(x48891)),f195(x48891))
% 157.60/157.51 [4890]~P77(x48901)+E(f866(f85(x48901),f2(x48901)),f2(x48901))
% 157.60/157.51 [4891]~P82(x48911)+E(f866(f172(x48911),f120(x48911)),f2(x48911))
% 157.60/157.51 [4909]~P36(x49091)+P40(f866(f179(a1),x49091))
% 157.60/157.51 [4940]~P96(x49401)+E(f866(f85(x49401),f84(x49401)),f866(f110(x49401),a104))
% 157.60/157.51 [4955]~P96(x49551)+P28(x49551,f866(f110(x49551),a89))
% 157.60/157.51 [4981]P36(x49811)+~P40(f866(f179(a1),x49811))
% 157.60/157.51 [5029]E(f866(f107(a1),f866(a111,x50291)),x50291)+P107(f866(a200,x50291))
% 157.60/157.51 [5099]~P116(x50991)+E(f253(x50991,f84(x50991),f87(x50991)),f252(x50991))
% 157.60/157.51 [5132]~P96(x51321)+~P28(x51321,f866(f110(x51321),a104))
% 157.60/157.51 [5279]E(f866(f81(a1),x52791),x52791)+P107(f866(f866(f244(a1),x52791),f2(a1)))
% 157.60/157.51 [5297]~E(f866(a111,x52971),f2(a930))+P107(f866(f866(f243(a1),x52971),f2(a1)))
% 157.60/157.51 [5361]~P107(f866(a200,x53611))+P107(f866(f866(f244(a1),x53611),f2(a1)))
% 157.60/157.51 [5402]~P113(x54021)+P107(f866(f866(f243(x54021),f2(x54021)),f84(x54021)))
% 157.60/157.51 [5403]~P142(x54031)+P107(f866(f866(f336(x54031),f84(x54031)),f116(x54031)))
% 157.60/157.51 [5404]~P148(x54041)+P107(f866(f866(f336(x54041),f84(x54041)),f193(x54041)))
% 157.60/157.51 [5405]~P142(x54051)+P107(f866(f866(f336(x54051),f2(x54051)),f116(x54051)))
% 157.60/157.51 [5406]~P148(x54061)+P107(f866(f866(f336(x54061),f2(x54061)),f193(x54061)))
% 157.60/157.51 [5407]~P113(x54071)+P107(f866(f866(f244(x54071),f2(x54071)),f84(x54071)))
% 157.60/157.51 [5460]E(x54601,f2(a930))+~P107(f866(f866(f243(a930),x54601),f2(a930)))
% 157.60/157.51 [5504]E(f866(a111,x55041),f2(a930))+~P107(f866(f866(f243(a1),x55041),f2(a1)))
% 157.60/157.51 [5565]P107(f866(a200,x55651))+~P107(f866(f866(f244(a1),x55651),f2(a1)))
% 157.60/157.51 [5572]~P110(x55721)+P16(x55721,f931(x55721),f155(x55721,x55721,f5(x55721)))
% 157.60/157.51 [5590]P40(x55901)+~P107(f866(f866(f243(a1),f2(a1)),f373(x55901)))
% 157.60/157.51 [5595]E(f866(f81(a1),x55951),f866(f85(a1),x55951))+~P107(f866(f866(f244(a1),x55951),f2(a1)))
% 157.60/157.51 [5765]~P113(x57651)+~P107(f866(f866(f243(x57651),f84(x57651)),f2(x57651)))
% 157.60/157.51 [5766]~P113(x57661)+~P107(f866(f866(f244(x57661),f84(x57661)),f2(x57661)))
% 157.60/157.51 [5780]~E(x57801,f2(a930))+P107(f866(f866(f243(a1),f866(f107(a1),x57801)),f2(a1)))
% 157.60/157.51 [5781]~E(x57811,f2(a1))+P107(f866(f866(f244(a1),f866(f81(a1),x57811)),f84(a1)))
% 157.60/157.51 [5909]~P82(x59091)+E(f149(x59091,x59091,f86(x59091),f2(x59091)),f172(x59091))
% 157.60/157.51 [6085]~P104(x60851)+P25(a930,x60851,f107(x60851),f250(f937(a930,a925)))
% 157.60/157.51 [6289]E(x62891,f2(a930))+~P107(f866(f866(f243(a1),f866(f107(a1),x62891)),f2(a1)))
% 157.60/157.51 [6290]E(x62901,f2(a1))+~P107(f866(f866(f244(a1),f866(f81(a1),x62901)),f84(a1)))
% 157.60/157.51 [7088]~P107(f866(f866(f244(a1),x70881),f2(a1)))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x70881),x70881)),f2(a1)))
% 157.60/157.51 [7637]P107(f866(f866(f244(a1),x76371),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x76371),x76371)),f2(a1)))
% 157.60/157.51 [8179]E(x81791,f866(a3,f2(a930)))+P107(f866(f866(f244(a930),f866(f866(f23(a930),f866(a20,x81791)),f866(a119,f2(a930)))),f866(a20,x81791)))
% 157.60/157.51 [8938]~P107(f866(f866(f244(a1),x89381),f2(a1)))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89381),x89381)),a104)),f2(a1)))
% 157.60/157.51 [9035]~P107(f866(f866(f244(a1),x90351),f2(a1)))+P107(f866(f866(f244(a1),f866(f866(f86(a1),f866(f866(f86(a1),f84(a1)),x90351)),x90351)),f2(a1)))
% 157.60/157.51 [9360]P107(f866(f866(f244(a1),x93601),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93601),x93601)),a104)),f2(a1)))
% 157.60/157.51 [9421]P107(f866(f866(f244(a1),x94211),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),f866(f866(f86(a1),f84(a1)),x94211)),x94211)),f2(a1)))
% 157.60/157.51 [4929]~E(a89,x49291)+E(f866(f866(f86(a1),x49291),x49291),a89)
% 157.60/157.51 [4930]~E(x49301,a89)+E(f866(f866(f86(a1),x49301),x49301),a89)
% 157.60/157.51 [4941]E(x49411,f2(a1))+E(f866(f866(f41(a1),x49411),x49411),f84(a1))
% 157.60/157.51 [5076]E(x50761,a89)+~E(f866(f866(f86(a1),x50761),x50761),a89)
% 157.60/157.51 [5077]E(a89,x50771)+~E(f866(f866(f86(a1),x50771),x50771),a89)
% 157.60/157.51 [5089]~P5(x50891)+E(f43(x50891,f195(f937(x50891,a925))),f250(x50891))
% 157.60/157.51 [5090]~P5(x50901)+E(f43(x50901,f250(f937(x50901,a925))),f195(x50901))
% 157.60/157.51 [5091]~P5(x50911)+E(f42(x50911,f195(f937(x50911,a925))),f195(x50911))
% 157.60/157.51 [5092]~P5(x50921)+E(f42(x50921,f250(f937(x50921,a925))),f250(x50921))
% 157.60/157.51 [5093]~P110(x50931)+E(f146(x50931,f195(f937(x50931,a925))),f120(x50931))
% 157.60/157.51 [5235]E(x52351,f2(a930))+P107(f866(f866(f244(a930),f2(a930)),x52351))
% 157.60/157.51 [5254]~P6(x52541)+P107(f866(f866(f243(a1),f2(a1)),x52541))
% 157.60/157.51 [5288]~E(f866(f110(a930),x52881),f2(a930))+P107(f866(f866(f243(a1),x52881),a89))
% 157.60/157.51 [5293]P40(x52931)+P107(f866(f866(f336(a1),f373(x52931)),x52931))
% 157.60/157.51 [5294]E(x52941,f866(a3,f2(a930)))+P107(f866(f866(f243(a106),f84(a106)),x52941))
% 157.60/157.51 [5334]P107(f866(a200,x53341))+P107(f866(f866(f243(a1),f2(a1)),x53341))
% 157.60/157.51 [5384]E(f866(f107(a1),f866(a111,x53841)),f2(a1))+P107(f866(f866(f243(a1),f2(a1)),x53841))
% 157.60/157.51 [5441]E(f866(f107(a1),f866(f110(a930),x54411)),f866(f110(a1),x54411))+P107(f866(a200,f866(f110(a1),x54411)))
% 157.60/157.51 [5466]E(f866(f110(a930),x54661),f2(a930))+~P107(f866(a200,f866(f110(a1),x54661)))
% 157.60/157.51 [5467]E(f866(f110(a930),x54671),f2(a930))+~P107(f866(f866(f243(a1),x54671),a89))
% 157.60/157.51 [5501]P6(x55011)+~P107(f866(f866(f243(a1),f2(a1)),x55011))
% 157.60/157.51 [5575]E(f866(a119,f868(x55751)),x55751)+~P107(f866(f866(f244(a930),f2(a930)),x55751))
% 157.60/157.51 [5584]E(f866(a119,f866(f110(a930),x55841)),f84(a930))+~P107(f866(a200,f866(f110(a1),x55841)))
% 157.60/157.51 [5591]E(f866(f107(a1),f452(x55911)),x55911)+~P107(f866(f866(f244(a1),f2(a1)),x55911))
% 157.60/157.51 [5598]~E(x55981,f866(a3,f2(a930)))+~P107(f866(f866(f243(a106),f84(a106)),x55981))
% 157.60/157.51 [5605]E(f866(f107(a1),f866(f110(a930),x56051)),f2(a1))+~P107(f866(a200,f866(f110(a1),x56051)))
% 157.60/157.51 [5630]E(f866(f172(a930),x56301),f2(a930))+P107(f866(f866(f336(a930),f553(x56301)),f866(f179(a930),x56301)))
% 157.60/157.51 [5650]E(f866(f107(a1),f866(a111,x56501)),x56501)+~P107(f866(f866(f243(a1),f2(a1)),x56501))
% 157.60/157.51 [5658]~P107(f866(a200,x56581))+~P107(f866(f866(f243(a1),f2(a1)),x56581))
% 157.60/157.51 [5758]E(f866(f866(f86(a930),f84(a930)),f866(f110(a930),x57581)),f84(a930))+~P107(f866(f866(f244(a1),x57581),a89))
% 157.60/157.51 [5826]E(x58261,f2(a930))+~P107(f866(f866(f244(a930),x58261),f866(a119,f2(a930))))
% 157.60/157.51 [5868]E(f866(f866(f23(a930),f866(f110(a930),x58681)),f84(a930)),f2(a930))+~P107(f866(f866(f243(a1),x58681),a89))
% 157.60/157.51 [5869]E(f866(f866(f86(a930),f866(f110(a930),x58691)),f84(a930)),f84(a930))+~P107(f866(f866(f244(a1),x58691),a89))
% 157.60/157.51 [5881]~P40(x58811)+E(f866(f40(a930),f866(f317(a1,a930,a111),x58811)),f866(f40(a1),x58811))
% 157.60/157.51 [5910]~P110(x59101)+E(f245(x59101,f866(f7(x59101,x59101,a925),f243(x59101))),f242(x59101))
% 157.60/157.51 [5911]~P110(x59111)+E(f246(x59111,f866(f7(x59111,x59111,a925),f243(x59111))),f241(x59111))
% 157.60/157.51 [5921]E(f50(a930,f866(a119,f2(a930)),f866(f110(a930),x59211)),f866(a119,f2(a930)))+~P107(f866(a200,f866(f110(a1),x59211)))
% 157.60/157.51 [5930]~P107(f866(f866(f244(a1),f2(a1)),x59301))+P107(f866(f866(f243(a1),f84(a1)),x59301))
% 157.60/157.51 [5931]P107(f866(f866(f244(a1),f2(a1)),x59311))+~P107(f866(f866(f243(a1),f84(a1)),x59311))
% 157.60/157.51 [5944]E(f866(a119,f866(f866(f23(a930),x59441),f84(a930))),x59441)+~P107(f866(f866(f244(a930),f2(a930)),x59441))
% 157.60/157.51 [6000]P107(f866(f866(f244(a930),f2(a930)),f452(x60001)))+~P107(f866(f866(f244(a1),f2(a1)),x60001))
% 157.60/157.51 [6061]E(f50(a1,f866(f110(a1),a104),x60611),f866(f866(f23(a1),x60611),f84(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x60611))
% 157.60/157.51 [6100]~P107(f866(f866(f244(a1),a89),x61001))+P107(f866(f866(f244(a930),f2(a930)),f866(f110(a930),x61001)))
% 157.60/157.51 [6105]E(f866(a20,f819(x61051)),x61051)+~P107(f866(f866(f336(a930),x61051),f250(f937(a930,a925))))
% 157.60/157.51 [6155]P107(f866(f866(f244(a930),f2(a930)),f866(a111,x61551)))+~P107(f866(f866(f244(a1),f2(a1)),x61551))
% 157.60/157.51 [6204]~P107(f866(f866(f244(a930),f2(a930)),x62041))+P107(f866(f866(f244(a1),f2(a1)),f866(f107(a1),x62041)))
% 157.60/157.51 [6240]~P107(f866(f866(f244(a930),f2(a930)),f866(a111,x62401)))+P107(f866(f866(f244(a1),f2(a1)),x62401))
% 157.60/157.51 [6254]~P40(x62541)+E(f866(f317(a930,a1,f107(a1)),f866(f317(a1,a930,a111),x62541)),x62541)
% 157.60/157.51 [6270]P107(f866(f866(f244(a1),a89),x62701))+~P107(f866(f866(f244(a930),f2(a930)),f866(f110(a930),x62701)))
% 157.60/157.51 [6325]P107(f866(f866(f244(a930),f2(a930)),x63251))+~P107(f866(f866(f244(a1),f2(a1)),f866(f107(a1),x63251)))
% 157.60/157.51 [6438]E(f866(f317(a930,a1,f107(a1)),f866(f290(a930),f866(a111,x64381))),f866(f309(a1,f2(a1)),x64381))+~P107(f866(f866(f243(a1),f2(a1)),x64381))
% 157.60/157.51 [6454]~P113(x64541)+P107(f866(f866(f244(x64541),f2(x64541)),f866(f866(f86(x64541),f84(x64541)),f84(x64541))))
% 157.60/157.51 [6504]P107(f866(f866(f244(a930),f866(a119,f2(a930))),f866(a111,x65041)))+~P107(f866(f866(f244(a1),f84(a1)),x65041))
% 157.60/157.51 [6603]E(x66031,f2(a1))+P107(f866(f54(f2(a1),x66031),f866(f866(f260(a1,a1),f2(a1)),f2(a1))))
% 157.60/157.51 [6775]~P107(f866(f866(f244(a930),f866(a119,f2(a930))),f866(a111,x67751)))+P107(f866(f866(f244(a1),f84(a1)),x67751))
% 157.60/157.51 [7198]~P117(x71981)+P37(x71981,f866(f270(f936(x71981,x71981)),f866(f265(x71981,x71981,a925),f244(x71981))))
% 157.60/157.51 [5813]E(f866(f110(a930),f866(f866(f23(a1),x58131),a104)),f866(a119,f866(f110(a930),x58131)))+P107(f866(a200,f866(f110(a1),x58131)))
% 157.60/157.51 [5829]~P36(x58291)+E(f866(f866(f161(a930,a1),f107(a1)),f866(f866(f161(a1,a930),a111),x58291)),x58291)
% 157.60/157.51 [5950]E(f866(f85(a1),f866(f107(a1),f866(a119,f469(x59501)))),x59501)+~P107(f866(f866(f244(a1),x59501),f2(a1)))
% 157.60/157.51 [5960]E(f866(f866(f86(a930),f84(a930)),f866(f110(a930),x59601)),f866(f110(a930),f866(f866(f23(a1),x59601),a104)))+P107(f866(f866(f244(a1),x59601),a89))
% 157.60/157.51 [6002]E(f866(f866(f41(a1),f866(f110(a1),a104)),x60021),f866(f110(a1),a104))+~P107(f866(f866(f244(a1),f2(a1)),x60021))
% 157.60/157.51 [6094]E(f866(f866(f23(a930),f866(f110(a930),x60941)),f84(a930)),f866(f110(a930),f866(f866(f86(a1),x60941),a104)))+P107(f866(f866(f243(a1),x60941),a89))
% 157.60/157.51 [6095]E(f866(f866(f86(a930),f866(f110(a930),x60951)),f84(a930)),f866(f110(a930),f866(f866(f23(a1),x60951),a104)))+P107(f866(f866(f244(a1),x60951),a89))
% 157.60/157.51 [6142]E(f866(a111,f866(f866(f86(a1),f84(a1)),x61421)),f866(a119,f866(a111,x61421)))+~P107(f866(f866(f243(a1),f2(a1)),x61421))
% 157.60/157.51 [6176]E(f866(a119,f866(f866(f23(a930),x61761),f866(a119,f2(a930)))),x61761)+~P107(f866(f866(f244(a930),f2(a930)),x61761))
% 157.60/157.51 [6389]E(f50(a930,f866(a119,f2(a930)),f866(f110(a930),x63891)),f866(a111,f50(a1,f84(a1),f866(f110(a1),x63891))))+P107(f866(a200,f866(f110(a1),x63891)))
% 157.60/157.51 [6431]~P107(f866(f866(f243(a1),a89),x64311))+P107(f866(f866(f243(a1),a89),f866(f866(f86(a1),x64311),x64311)))
% 157.60/157.51 [6432]~P107(f866(f866(f244(a1),a104),x64321))+P107(f866(f866(f243(a1),a104),f866(f866(f86(a1),x64321),x64321)))
% 157.60/157.51 [6433]~P107(f866(f866(f244(a1),a89),x64331))+P107(f866(f866(f244(a1),a89),f866(f866(f86(a1),x64331),x64331)))
% 157.60/157.51 [6434]~P107(f866(f866(f244(a1),a104),x64341))+P107(f866(f866(f244(a1),a104),f866(f866(f86(a1),x64341),x64341)))
% 157.60/157.51 [6616]~P107(f866(f66(x66161),f250(f937(x66161,a925))))+P107(f866(f66(f934(x66161)),f250(f937(f934(x66161),a925))))
% 157.60/157.51 [6706]~P107(f866(f866(f243(a1),f2(a1)),x67061))+P107(f866(f866(f244(a1),f2(a1)),f866(f866(f86(a1),f84(a1)),x67061)))
% 157.60/157.51 [6713]E(f866(f259(a1,a1),f52(f84(a1),f866(f110(a1),x67131))),f866(f866(f41(a1),f84(a1)),f866(f110(a1),x67131)))+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x67131)))
% 157.60/157.51 [6733]E(f866(f264(a1,a1),f52(f84(a1),f866(f110(a1),x67331))),f50(a1,f84(a1),f866(f110(a1),x67331)))+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x67331)))
% 157.60/157.51 [6745]P107(f866(f66(x67451),f250(f937(x67451,a925))))+~P107(f866(f66(f934(x67451)),f250(f937(f934(x67451),a925))))
% 157.60/157.51 [6776]P107(f866(f866(f243(a1),a89),x67761))+~P107(f866(f866(f243(a1),a89),f866(f866(f86(a1),x67761),x67761)))
% 157.60/157.51 [6777]P107(f866(f866(f244(a1),a89),x67771))+~P107(f866(f866(f244(a1),a89),f866(f866(f86(a1),x67771),x67771)))
% 157.60/157.51 [6778]P107(f866(f866(f244(a1),a104),x67781))+~P107(f866(f866(f243(a1),a104),f866(f866(f86(a1),x67781),x67781)))
% 157.60/157.51 [6779]P107(f866(f866(f244(a1),a104),x67791))+~P107(f866(f866(f244(a1),a104),f866(f866(f86(a1),x67791),x67791)))
% 157.60/157.51 [7092]~P107(f866(f66(x70921),f250(f937(x70921,a925))))+P107(f866(f866(f244(a930),f2(a930)),f866(f40(x70921),f250(f937(x70921,a925)))))
% 157.60/157.51 [7676]P107(f866(f66(a930),x76761))+~P107(f866(f66(a1),f866(f317(a930,a1,f107(a1)),x76761)))
% 157.60/157.51 [5733]~E(a104,x57331)+E(f866(f866(f23(a1),f866(f866(f86(a1),x57331),x57331)),a104),a104)
% 157.60/157.51 [5734]~E(x57341,a104)+E(f866(f866(f23(a1),f866(f866(f86(a1),x57341),x57341)),a104),a104)
% 157.60/157.51 [6265]E(x62651,a104)+~E(f866(f866(f23(a1),f866(f866(f86(a1),x62651),x62651)),a104),a104)
% 157.60/157.51 [6266]E(a104,x62661)+~E(f866(f866(f23(a1),f866(f866(f86(a1),x62661),x62661)),a104),a104)
% 157.60/157.51 [6672]~E(f866(f110(a930),x66721),f2(a930))+P107(f866(a200,f866(f110(a1),f866(f866(f86(a1),x66721),a104))))
% 157.60/157.51 [7021]~P107(f866(a200,f866(f110(a1),x70211)))+P107(f866(a200,f866(f110(a1),f866(f866(f86(a1),x70211),x70211))))
% 157.60/157.51 [7022]~P107(f866(f866(f243(a1),x70221),a89))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x70221),x70221)),a89))
% 157.60/157.51 [7023]~P107(f866(f866(f243(a1),x70231),a104))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x70231),x70231)),a104))
% 157.60/157.51 [7024]~P107(f866(f866(f244(a1),x70241),a89))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x70241),x70241)),a89))
% 157.60/157.51 [7025]~P107(f866(f866(f243(a1),x70251),a104))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x70251),x70251)),a104))
% 157.60/157.51 [7342]E(f866(f110(a930),x73421),f2(a930))+~P107(f866(a200,f866(f110(a1),f866(f866(f86(a1),x73421),a104))))
% 157.60/157.51 [7592]~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x75921)))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),f866(f866(f86(a1),x75921),x75921))))
% 157.60/157.51 [7593]P107(f866(a200,f866(f110(a1),x75931)))+~P107(f866(a200,f866(f110(a1),f866(f866(f86(a1),x75931),x75931))))
% 157.60/157.51 [7594]P107(f866(f866(f243(a1),x75941),a89))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x75941),x75941)),a89))
% 157.60/157.51 [7595]P107(f866(f866(f243(a1),x75951),a104))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x75951),x75951)),a104))
% 157.60/157.51 [7596]P107(f866(f866(f243(a1),x75961),a104))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x75961),x75961)),a104))
% 157.60/157.51 [7597]P107(f866(f866(f244(a1),x75971),a89))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x75971),x75971)),a89))
% 157.60/157.51 [7951]E(f866(a114,f543(x79511)),x79511)+~P107(f866(f866(f336(f937(f936(a930,a930),a925)),x79511),a105))
% 157.60/157.51 [6590]~P96(x65901)+E(f866(f110(x65901),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f84(x65901))
% 157.60/157.51 [7072]~P107(f866(a200,f866(f110(a1),x70721)))+E(f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x70721),x70721)),a104)),f2(a930))
% 157.60/157.51 [8125]~P107(f866(f866(f244(a1),f866(f110(a1),x81251)),f2(a1)))+E(f866(f259(a1,a1),f866(a56,f55(f866(f85(a1),f84(a1)),f866(f85(a1),f866(f110(a1),x81251))))),f866(f866(f41(a1),f84(a1)),f866(f110(a1),x81251)))
% 157.60/157.51 [8138]~P107(f866(f866(f244(a1),f866(f110(a1),x81381)),f2(a1)))+E(f866(f264(a1,a1),f866(a56,f55(f866(f85(a1),f84(a1)),f866(f85(a1),f866(f110(a1),x81381))))),f50(a1,f84(a1),f866(f110(a1),x81381)))
% 157.60/157.51 [8186]~P107(f866(f866(f243(a1),a89),x81861))+P107(f866(f866(f243(a1),a89),f866(f866(f23(a1),f866(f866(f86(a1),x81861),x81861)),a104)))
% 157.60/157.51 [8187]~P107(f866(f866(f243(a1),a104),x81871))+P107(f866(f866(f243(a1),a104),f866(f866(f23(a1),f866(f866(f86(a1),x81871),x81871)),a104)))
% 157.60/157.51 [8188]~P107(f866(f866(f243(a1),a89),x81881))+P107(f866(f866(f244(a1),a89),f866(f866(f23(a1),f866(f866(f86(a1),x81881),x81881)),a104)))
% 157.60/157.51 [8189]~P107(f866(f866(f244(a1),a104),x81891))+P107(f866(f866(f244(a1),a104),f866(f866(f23(a1),f866(f866(f86(a1),x81891),x81891)),a104)))
% 157.60/157.51 [8480]~P96(x84801)+~P28(x84801,f866(f110(x84801),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))
% 157.60/157.51 [8662]P107(f866(f866(f243(a1),a89),x86621))+~P107(f866(f866(f243(a1),a89),f866(f866(f23(a1),f866(f866(f86(a1),x86621),x86621)),a104)))
% 157.60/157.51 [8663]P107(f866(f866(f243(a1),a89),x86631))+~P107(f866(f866(f244(a1),a89),f866(f866(f23(a1),f866(f866(f86(a1),x86631),x86631)),a104)))
% 157.60/157.51 [8664]P107(f866(f866(f243(a1),a104),x86641))+~P107(f866(f866(f243(a1),a104),f866(f866(f23(a1),f866(f866(f86(a1),x86641),x86641)),a104)))
% 157.60/157.51 [8665]P107(f866(f866(f244(a1),a104),x86651))+~P107(f866(f866(f244(a1),a104),f866(f866(f23(a1),f866(f866(f86(a1),x86651),x86651)),a104)))
% 157.60/157.51 [8985]E(f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x89851),x89851)),a104)),f866(f866(f92(a930,a930),f866(f110(a930),x89851)),f866(f866(f8(a930,a930,a930),a119),f866(f866(f18(a930,a930,a930),f86(a930)),f5(a930)))))+P107(f866(a200,f866(f110(a1),x89851)))
% 157.60/157.51 [9842]E(x98421,f195(f937(f936(a930,a930),a925)))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x98421),f195(f937(f936(a930,a930),a925)))),a74))
% 157.60/157.51 [8912]~P107(f866(a200,f866(f110(a1),x89121)))+P107(f866(a200,f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89121),x89121)),a104))))
% 157.60/157.51 [8913]~P107(f866(f866(f244(a1),x89131),a89))+P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89131),x89131)),a104)),a89))
% 157.60/157.51 [8914]~P107(f866(f866(f243(a1),x89141),a104))+P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89141),x89141)),a104)),a104))
% 157.60/157.51 [8915]~P107(f866(f866(f244(a1),x89151),a89))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89151),x89151)),a104)),a89))
% 157.60/157.51 [8916]~P107(f866(f866(f244(a1),x89161),a104))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x89161),x89161)),a104)),a104))
% 157.60/157.51 [9026]~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x90261)))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x90261),x90261)),a104))))
% 157.60/157.51 [9190]~P96(x91901)+E(f866(f866(f86(x91901),f84(x91901)),f84(x91901)),f866(f110(x91901),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))
% 157.60/157.51 [9344]P107(f866(a200,f866(f110(a1),x93441)))+~P107(f866(a200,f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93441),x93441)),a104))))
% 157.60/157.51 [9345]P107(f866(f866(f243(a1),x93451),a104))+~P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93451),x93451)),a104)),a104))
% 157.60/157.51 [9346]P107(f866(f866(f244(a1),x93461),a89))+~P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93461),x93461)),a104)),a89))
% 157.60/157.51 [9347]P107(f866(f866(f244(a1),x93471),a89))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93471),x93471)),a104)),a89))
% 157.60/157.51 [9348]P107(f866(f866(f244(a1),x93481),a104))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93481),x93481)),a104)),a104))
% 157.60/157.51 [9887]~P107(f866(f66(f936(a930,a930)),x98871))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f195(f937(f936(a930,a930),a925))),x98871)),a75))
% 157.60/157.51 [9672]~P148(x96721)+E(f866(f866(f252(x96721),f84(x96721)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(x96721))
% 157.60/157.51 [9673]~P148(x96731)+E(f866(f866(f252(x96731),f2(x96731)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f2(x96731))
% 157.60/157.51 [10113]~P107(f866(f866(f244(a930),f84(a930)),x101131))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f41(a930),x101131),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.51 [10119]~P107(f866(f866(f244(a930),f2(a930)),x101191))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f41(a930),f866(f866(f86(a930),x101191),f84(a930))),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.51 [10158]~E(f50(a930,x101581,f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(a930))+P107(f866(f866(f244(a930),f2(a930)),f50(a930,x101581,f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.51 [10178]E(f50(a930,x101781,f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(a930))+~P107(f866(f866(f244(a930),f2(a930)),f50(a930,x101781,f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.51 [4854]~P37(x48541,x48542)+P59(x48541,x48542)
% 157.60/157.51 [4855]~P43(x48551,x48552)+P59(x48551,x48552)
% 157.60/157.51 [4857]~P7(x48571,x48572)+P48(x48571,x48572)
% 157.60/157.51 [4859]~P7(x48591,x48592)+P50(x48591,x48592)
% 157.60/157.51 [4861]~P15(x48611,x48612)+P50(x48611,x48612)
% 157.60/157.51 [4863]~P7(x48631,x48632)+P51(x48631,x48632)
% 157.60/157.51 [4865]~P15(x48651,x48652)+P51(x48651,x48652)
% 157.60/157.51 [4866]~P7(x48661,x48662)+P15(x48661,x48662)
% 157.60/157.51 [4811]E(x48111,x48112)+~E(f33(x48111),f33(x48112))
% 157.60/157.51 [4812]E(x48121,x48122)+~E(f34(x48121),f34(x48122))
% 157.60/157.51 [4816]~E(x48161,x48162)+E(f277(x48161,x48162),f84(a106))
% 157.60/157.51 [4819]E(f225(x48191,x48192),x48191)+~E(x48192,f2(a930))
% 157.60/157.51 [4826]~E(x48262,f120(x48261))+E(f159(x48261,x48262),f120(x48261))
% 157.60/157.51 [4845]~E(f159(x48452,x48451),f120(x48452))+E(x48451,f120(x48452))
% 157.60/157.51 [4870]~P1(x48702)+P1(f937(x48701,x48702))
% 157.60/157.51 [4871]~P108(x48712)+P108(f937(x48711,x48712))
% 157.60/157.51 [4872]~P109(x48722)+P109(f937(x48721,x48722))
% 157.60/157.51 [4873]~P111(x48732)+P111(f937(x48731,x48732))
% 157.60/157.51 [4874]~P2(x48742)+P2(f937(x48741,x48742))
% 157.60/157.51 [4875]~P112(x48752)+P112(f937(x48751,x48752))
% 157.60/157.51 [4876]~P83(x48762)+P83(f937(x48761,x48762))
% 157.60/157.51 [4877]~P83(x48772)+P102(f937(x48771,x48772))
% 157.60/157.51 [4878]~P100(x48782)+P84(f937(x48781,x48782))
% 157.60/157.51 [4879]~P100(x48792)+P85(f937(x48791,x48792))
% 157.60/157.51 [4880]~P5(x48802)+P5(f937(x48801,x48802))
% 157.60/157.51 [4881]~P83(x48812)+P103(f937(x48811,x48812))
% 157.60/157.51 [4882]~P101(x48822)+P101(f937(x48821,x48822))
% 157.60/157.51 [4883]~P98(x48832)+P98(f937(x48831,x48832))
% 157.60/157.51 [4884]~P92(x48842)+P92(f937(x48841,x48842))
% 157.60/157.51 [4885]~P100(x48852)+P100(f937(x48851,x48852))
% 157.60/157.51 [4898]E(x48981,x48982)+~E(f866(a119,x48981),f866(a119,x48982))
% 157.60/157.51 [4899]E(x48991,x48992)+~E(f866(a114,x48991),f866(a114,x48992))
% 157.60/157.51 [4900]E(x49001,x49002)+~E(f866(a3,x49001),f866(a3,x49002))
% 157.60/157.51 [4902]E(x49021,x49022)+~E(f866(a20,x49021),f866(a20,x49022))
% 157.60/157.51 [4957]P39(x49571,x49572)+~E(f713(x49572,x49571),f714(x49572,x49571))
% 157.60/157.51 [4987]~P59(x49871,x49872)+P39(x49871,f314(x49871,x49872))
% 157.60/157.51 [4988]~P52(x49881,x49882)+P52(x49881,f314(x49881,x49882))
% 157.60/157.51 [5001]~P62(x50011)+E(f50(x50011,x50012,x50012),f2(x50011))
% 157.60/157.51 [5028]~P114(x50281)+P57(x50281,x50282,f2(x50281))
% 157.60/157.51 [5036]~P37(x50361,x50362)+P37(f931(x50361),f153(x50361,x50362))
% 157.60/157.51 [5037]~P37(x50371,x50372)+P37(f931(x50371),f152(x50371,x50372))
% 157.60/157.51 [5038]~P38(x50381,x50382)+P38(f931(x50381),f154(x50381,x50382))
% 157.60/157.51 [5039]~P38(x50391,x50392)+P38(f931(x50391),f165(x50391,x50392))
% 157.60/157.51 [5040]~P52(x50401,x50402)+P52(f931(x50401),f165(x50401,x50402))
% 157.60/157.51 [5137]~P37(x51371,x51372)+P37(f937(x51371,a925),f327(x51371,x51372))
% 157.60/157.51 [5138]~P37(x51381,x51382)+P37(f937(x51381,a925),f325(x51381,x51382))
% 157.60/157.51 [5263]~P6(x52631)+P40(f310(a1,x52631,x52632))
% 157.60/157.51 [5364]~P37(x53641,x53642)+P61(x53641,f72(x53641,x53641,x53642))
% 157.60/157.51 [5875]~P79(x58751)+P25(x58751,x58751,f85(x58751),x58752)
% 157.60/157.51 [4840]~E(x48402,f120(x48401))+E(f866(f174(x48401),x48402),f120(x48401))
% 157.60/157.51 [4841]~E(x48412,f120(x48411))+E(f866(f175(x48411),x48412),f120(x48411))
% 157.60/157.51 [4904]E(x49041,f866(a111,x49042))+~E(f866(f107(a1),x49041),x49042)
% 157.60/157.51 [4907]E(x49071,f120(x49072))+~E(f866(f174(x49072),x49071),f120(x49072))
% 157.60/157.51 [4908]E(x49081,f120(x49082))+~E(f866(f175(x49082),x49081),f120(x49082))
% 157.60/157.51 [4926]~P96(x49261)+E(f866(f110(x49261),x49262),f866(f109(x49261),x49262))
% 157.60/157.51 [4934]~P4(x49341)+P107(f866(f66(x49341),x49342))
% 157.60/157.51 [4942]~E(f674(x49422,x49421),f120(x49421))+E(f186(x49421,x49422),f120(f931(x49421)))
% 157.60/157.51 [4951]~E(x49512,f120(x49511))+E(f866(f179(x49511),x49512),f195(f937(x49511,a925)))
% 157.60/157.51 [4952]~E(x49522,f120(x49521))+E(f195(f937(x49521,a925)),f866(f179(x49521),x49522))
% 157.60/157.51 [4954]E(x49541,x49542)+~E(f866(f107(a1),x49541),f866(f107(a1),x49542))
% 157.60/157.51 [4958]E(f223(x49581,x49582),f2(a930))+P107(f866(f66(x49581),x49582))
% 157.60/157.51 [4976]~P128(x49761)+E(f88(x49761,f88(x49761,x49762)),f88(x49761,x49762))
% 157.60/157.51 [4990]~P81(x49901)+E(f866(f866(f252(x49901),x49902),f84(a930)),x49902)
% 157.60/157.51 [4991]~P114(x49911)+E(f866(f866(f252(x49911),x49912),f84(a930)),x49912)
% 157.60/157.51 [4992]~P52(x49921,x49922)+E(f866(f294(x49921,x49921),x49922),x49922)
% 157.60/157.51 [4996]E(x49961,x49962)+E(f277(x49961,x49962),f866(f866(f86(a106),x49962),f84(a106)))
% 157.60/157.51 [4999]E(f866(f40(x49991),x49992),f2(a930))+P107(f866(f66(x49991),x49992))
% 157.60/157.51 [5002]~E(f159(x50021,x50022),x50022)+P107(f866(f144(x50021),x50022))
% 157.60/157.51 [5005]~P77(x50051)+E(f866(f866(f23(x50051),x50052),f2(x50051)),x50052)
% 157.60/157.51 [5006]~P71(x50061)+E(f866(f866(f87(x50061),x50062),f84(x50061)),x50062)
% 157.60/157.51 [5007]~P81(x50071)+E(f866(f866(f87(x50071),x50072),f84(x50071)),x50072)
% 157.60/157.51 [5008]~P114(x50081)+E(f866(f866(f87(x50081),x50082),f84(x50081)),x50082)
% 157.60/157.51 [5009]~P85(x50091)+E(f866(f866(f117(x50091),x50092),f195(x50091)),x50092)
% 157.60/157.51 [5010]~P114(x50101)+E(f866(f866(f86(x50101),x50102),f2(x50101)),x50102)
% 157.60/157.51 [5011]~P82(x50111)+E(f866(f866(f86(x50111),x50112),f2(x50111)),x50112)
% 157.60/157.51 [5012]~P72(x50121)+E(f866(f866(f86(x50121),x50122),f2(x50121)),x50122)
% 157.60/157.51 [5013]~P84(x50131)+E(f866(f866(f108(x50131),x50132),f250(x50131)),x50132)
% 157.60/157.51 [5014]~P62(x50141)+E(f866(f866(f41(x50141),x50142),f84(x50141)),x50142)
% 157.60/157.51 [5015]~P125(x50151)+E(f866(f866(f297(x50151),x50152),f84(x50151)),x50152)
% 157.60/157.51 [5016]~P114(x50161)+E(f866(f866(f252(x50161),x50162),f2(a930)),f84(x50161))
% 157.60/157.51 [5017]~P116(x50171)+E(f866(f866(f252(x50171),x50172),f2(a930)),f84(x50171))
% 157.60/157.51 [5018]~E(x50182,f195(f937(x50181,a925)))+E(f866(f40(x50181),x50182),f2(a930))
% 157.60/157.51 [5030]~P62(x50301)+E(f50(x50301,x50302,f2(x50301)),x50302)
% 157.60/157.51 [5041]~P114(x50411)+E(f866(f866(f87(x50411),x50412),f2(x50411)),f2(x50411))
% 157.60/157.51 [5042]~P129(x50421)+E(f866(f866(f87(x50421),x50422),f2(x50421)),f2(x50421))
% 157.60/157.51 [5043]~P84(x50431)+E(f866(f866(f117(x50431),x50432),f250(x50431)),f250(x50431))
% 157.60/157.51 [5044]~P85(x50441)+E(f866(f866(f108(x50441),x50442),f195(x50441)),f195(x50441))
% 157.60/157.51 [5045]~P62(x50451)+E(f866(f866(f41(x50451),x50452),f2(x50451)),f2(x50451))
% 157.60/157.51 [5046]~P126(x50461)+E(f866(f866(f297(x50461),x50462),f2(x50461)),f2(x50461))
% 157.60/157.51 [5048]~P62(x50481)+E(f50(x50481,x50482,f84(x50481)),f2(x50481))
% 157.60/157.51 [5049]~P62(x50491)+E(f50(x50491,f2(x50491),x50492),f2(x50491))
% 157.60/157.51 [5078]E(x50781,f2(a930))+E(f60(x50782,x50781,f120(x50782)),f120(f931(x50782)))
% 157.60/157.51 [5101]P52(x51011,x51012)+~E(f866(f294(x51011,x51011),x51012),x51012)
% 157.60/157.51 [5102]P37(x51021,x51022)+~E(f554(x51022,x51021),f195(f937(x51021,a925)))
% 157.60/157.51 [5103]E(x51031,f120(x51032))+~E(f866(f179(x51032),x51031),f195(f937(x51032,a925)))
% 157.60/157.51 [5104]E(x51041,f120(x51042))+~E(f195(f937(x51042,a925)),f866(f179(x51042),x51041))
% 157.60/157.51 [5107]~E(x51071,x51072)+P107(f866(f866(a332,x51071),x51072))
% 157.60/157.51 [5117]P107(x51171)+P107(f866(f866(a337,x51171),x51172))
% 157.60/157.51 [5118]E(x51181,f120(x51182))+E(f866(f866(f171(x51182),x51181),f2(a930)),f866(f148(x51182),x51181))
% 157.60/157.51 [5121]E(f159(x51211,x51212),x51212)+~P107(f866(f144(x51211),x51212))
% 157.60/157.51 [5128]~P107(x51282)+P107(f866(f866(a337,x51281),x51282))
% 157.60/157.51 [5129]~P107(x51292)+P107(f866(f866(a334,x51291),x51292))
% 157.60/157.51 [5130]~P107(x51301)+P107(f866(f866(a334,x51301),x51302))
% 157.60/157.51 [5140]~E(f675(x51402,x51401),f679(x51402,x51401))+P107(f866(f144(x51401),x51402))
% 157.60/157.51 [5147]E(f866(f270(x51471),x51472),f195(f937(x51471,a925)))+P107(f866(x51472,f340(x51472)))
% 157.60/157.51 [5148]E(f195(f937(x51481,a925)),f866(f270(x51481),x51482))+P107(f866(x51482,f341(x51482)))
% 157.60/157.51 [5217]~P128(x52171)+E(f866(f866(f87(x52171),x52172),f88(x52171,x52172)),f866(f81(x52171),x52172))
% 157.60/157.51 [5228]~E(x52281,f2(a1))+E(f51(x52281,x52282),f866(f866(f260(a1,a1),f2(a1)),f2(a1)))
% 157.60/157.51 [5259]~P59(x52591,x52592)+P59(x52591,f866(f294(x52591,x52591),x52592))
% 157.60/157.51 [5260]~P38(x52601,x52602)+P38(x52601,f866(f294(x52601,x52601),x52602))
% 157.60/157.51 [5261]~P39(x52611,x52612)+P39(x52611,f866(f294(x52611,x52611),x52612))
% 157.60/157.51 [5262]~P52(x52621,x52622)+P52(x52621,f866(f294(x52621,x52621),x52622))
% 157.60/157.51 [5284]E(x52841,x52842)+~P107(f866(f866(a332,x52841),x52842))
% 157.60/157.51 [5295]P107(x52951)+~P107(f866(f866(a333,x52952),x52951))
% 157.60/157.51 [5296]P107(x52961)+~P107(f866(f866(a333,x52961),x52962))
% 157.60/157.51 [5301]~P112(x53011)+P107(f866(f866(f243(x53011),x53012),f250(x53011)))
% 157.60/157.51 [5305]E(x53051,x53052)+~E(f866(x53051,f444(x53052,x53051)),f866(x53052,f444(x53052,x53051)))
% 157.60/157.51 [5336]E(x53361,f2(a930))+E(f225(x53361,f50(a930,x53362,x53361)),f225(x53362,x53361))
% 157.60/157.51 [5341]~P110(x53411)+P13(x53411,f866(f866(f158(x53411),x53412),f120(x53411)))
% 157.60/157.51 [5343]E(x53431,f2(a1))+P107(f866(f54(x53432,x53431),f51(x53432,x53431)))
% 157.60/157.51 [5359]~P15(x53592,x53591)+P107(f866(f866(x53591,f811(x53591)),f811(x53591)))
% 157.60/157.51 [5362]~E(x53621,x53622)+P107(f866(f866(f244(a930),x53621),f866(a119,x53622)))
% 157.60/157.51 [5373]~E(x53731,f2(a930))+P107(f866(f866(f244(a930),x53731),f866(a119,x53732)))
% 157.60/157.51 [5383]P107(f866(x53831,x53832))+P107(f866(f866(f243(a1),f2(a1)),f426(x53831)))
% 157.60/157.51 [5446]E(f866(f866(f316(x54462),f515(x54462,x54461)),f530(x54462,x54461)),x54461)+E(x54461,f195(f937(x54462,a925)))
% 157.60/157.51 [5447]P59(x54471,x54472)+~P59(x54471,f866(f294(x54471,x54471),x54472))
% 157.60/157.51 [5448]P38(x54481,x54482)+~P38(x54481,f866(f294(x54481,x54481),x54482))
% 157.60/157.51 [5449]P39(x54491,x54492)+~P39(x54491,f866(f294(x54491,x54491),x54492))
% 157.60/157.51 [5450]P52(x54501,x54502)+~P52(x54501,f866(f294(x54501,x54501),x54502))
% 157.60/157.51 [5453]~E(f50(a930,x54532,x54531),f2(a930))+E(f866(f866(f87(a930),x54531),f363(x54531,x54532)),x54532)
% 157.60/157.51 [5454]~E(f50(a1,x54542,x54541),f2(a1))+E(f866(f866(f87(a1),x54541),f342(x54541,x54542)),x54542)
% 157.60/157.51 [5482]~P107(f866(x54821,x54822))+P107(f866(f866(f243(a1),f2(a1)),f374(x54821)))
% 157.60/157.51 [5493]E(f866(f866(f23(a930),f866(a111,x54931)),f866(a111,x54932)),f866(a111,x54931))+~P107(f866(a200,x54932))
% 157.60/157.51 [5522]E(f280(x55221,x55222),f84(a106))+~P107(f866(f866(f243(a106),x55221),f84(a106)))
% 157.60/157.51 [5616]E(f866(f866(f171(x56161),x56162),f675(x56162,x56161)),f866(f866(f171(x56161),x56162),f679(x56162,x56161)))+P107(f866(f144(x56161),x56162))
% 157.60/157.51 [5659]~P107(f866(x56591,f96(x56592,x56591)))+P107(f866(x56591,f567(x56592,x56591)))
% 157.60/157.51 [5723]P61(x57231,x57232)+~P107(f866(f322(x57231,x57232),f527(x57232,x57231)))
% 157.60/157.51 [5872]~P15(x58722,x58721)+P107(f866(f866(x58721,f813(x58721,x58722)),f813(x58721,x58722)))
% 157.60/157.51 [5873]~P15(x58732,x58731)+P107(f866(f866(x58731,f816(x58731,x58732)),f816(x58731,x58732)))
% 157.60/157.51 [5882]~E(f866(a119,f50(a930,x58821,x58822)),x58822)+E(f50(a930,f866(a119,x58821),x58822),f2(a930))
% 157.60/157.51 [5939]P37(x59391,x59392)+P107(f866(f866(f336(x59391),f589(x59392,x59391)),f590(x59392,x59391)))
% 157.60/157.51 [5946]~P142(x59461)+P107(f866(f866(f336(x59461),f866(f107(x59461),x59462)),f116(x59461)))
% 157.60/157.51 [5947]~P148(x59471)+P107(f866(f866(f336(x59471),f866(f107(x59471),x59472)),f193(x59471)))
% 157.60/157.51 [5948]~P142(x59481)+P107(f866(f866(f336(x59481),f866(f109(x59481),x59482)),f116(x59481)))
% 157.60/157.51 [5949]~P96(x59491)+P107(f866(f866(f336(x59491),f866(f110(x59491),x59492)),f116(x59491)))
% 157.60/157.51 [6083]~P38(x60831,x60832)+E(f866(f866(f296(x60831,x60831,x60831),x60832),f314(x60831,x60832)),x60832)
% 157.60/157.51 [6099]E(f866(a119,f50(a930,x60991,x60992)),x60992)+E(f50(a930,f866(a119,x60991),x60992),f866(a119,f50(a930,x60991,x60992)))
% 157.60/157.51 [6516]P37(x65161,x65162)+~P107(f866(f866(f336(x65161),f516(x65162,x65161)),f323(x65161,x65162)))
% 157.60/157.51 [6553]~P113(x65531)+~P107(f866(f866(f244(x65531),f866(f107(x65531),x65532)),f2(x65531)))
% 157.60/157.51 [6554]~P89(x65541)+~P107(f866(f866(f244(x65541),f866(f81(x65541),x65542)),f2(x65541)))
% 157.60/157.51 [6586]E(x65861,f195(f937(x65862,a925)))+~P107(f866(f866(f336(x65862),f515(x65862,x65861)),f530(x65862,x65861)))
% 157.60/157.51 [6646]P107(f866(f866(f244(a1),x66461),f50(a1,x66462,x66461)))+~P107(f866(f866(f244(a1),x66461),f2(a1)))
% 157.60/157.51 [6747]E(f866(f866(f316(a930),f866(a119,x67471)),f310(a930,x67472,x67471)),f310(a930,x67472,f866(a119,x67471)))+~P107(f866(f866(f243(a930),x67472),f866(a119,x67471)))
% 157.60/157.51 [6839]~P110(x68391)+P13(x68391,f157(x68391,x68391,f5(x68391),x68392))
% 157.60/157.51 [6967]E(f866(f174(x69671),x69672),x69672)+~P107(f866(f866(f243(a930),f866(f196(f931(x69671)),x69672)),f84(a930)))
% 157.60/157.51 [6986]~P89(x69861)+P107(f866(f866(f243(x69861),f866(f85(x69861),f866(f81(x69861),x69862))),f2(x69861)))
% 157.60/157.51 [7017]~P37(x70171,x70172)+P37(x70171,f866(f866(f296(x70171,x70171,x70171),x70172),f314(x70171,x70172)))
% 157.60/157.51 [7018]~P52(x70181,x70182)+P52(x70181,f866(f866(f296(x70181,x70181,x70181),x70182),f314(x70181,x70182)))
% 157.60/157.51 [7237]~P107(f866(f866(f244(a1),x72372),f2(a1)))+P107(f866(f866(f243(a1),f50(a1,x72371,x72372)),f2(a1)))
% 157.60/157.51 [7633]~P148(x76331)+E(f197(x76331,f866(f866(f7(x76331,x76331,x76331),f86(x76331)),f84(x76331)),x76332,f2(x76331)),f866(f107(x76331),x76332))
% 157.60/157.51 [7662]~P121(x76621)+~P107(f866(f866(f244(x76621),f866(f866(f87(x76621),x76622),x76622)),f2(x76621)))
% 157.60/157.51 [10266]~P128(x102661)+~P107(f866(f866(f244(x102661),f866(f866(f252(x102661),x102662),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f2(x102661)))
% 157.60/157.51 [4905]~E(x49052,f120(x49051))+E(f866(f196(f931(x49051)),x49052),f2(a930))
% 157.60/157.51 [4943]~E(x49431,f2(a930))+E(f866(f866(f86(a930),x49431),x49432),x49432)
% 157.60/157.51 [4944]~E(x49442,f2(a930))+E(f866(f866(f87(a930),x49441),x49442),f2(a930))
% 157.60/157.51 [4946]~E(x49461,f2(a930))+E(f866(f866(f87(a930),x49461),x49462),f2(a930))
% 157.60/157.51 [4947]~E(x49472,f2(a930))+E(f866(f866(f252(a930),x49471),x49472),f84(a930))
% 157.60/157.51 [4948]~E(x49482,f2(a1))+E(f866(f866(f41(a1),x49481),x49482),f2(a1))
% 157.60/157.51 [4959]E(x49591,f120(x49592))+~E(f866(f196(f931(x49592)),x49591),f2(a930))
% 157.60/157.51 [4961]~P99(x49611)+E(f866(f866(f87(x49611),x49612),x49612),x49612)
% 157.60/157.51 [4962]~P83(x49621)+E(f866(f866(f117(x49621),x49622),x49622),x49622)
% 157.60/157.51 [4964]~P102(x49641)+E(f866(f866(f117(x49641),x49642),x49642),x49642)
% 157.60/157.51 [4965]~P83(x49651)+E(f866(f866(f108(x49651),x49652),x49652),x49652)
% 157.60/157.51 [4967]~P103(x49671)+E(f866(f866(f108(x49671),x49672),x49672),x49672)
% 157.60/157.51 [4969]~P110(x49691)+E(f866(f866(f241(x49691),x49692),x49692),x49692)
% 157.60/157.51 [4971]~P110(x49711)+E(f866(f866(f242(x49711),x49712),x49712),x49712)
% 157.60/157.51 [4989]~P77(x49891)+E(f866(f866(f23(x49891),x49892),x49892),f2(x49891))
% 157.60/157.51 [5003]~P77(x50031)+E(f866(f85(x50031),f866(f85(x50031),x50032)),x50032)
% 157.60/157.51 [5004]~P98(x50041)+E(f866(f85(x50041),f866(f85(x50041),x50042)),x50042)
% 157.60/157.51 [5021]~E(x50212,f2(a930))+E(f866(f866(f252(a930),x50211),x50212),f866(a119,f2(a930)))
% 157.60/157.51 [5057]~P71(x50571)+E(f866(f866(f87(x50571),f84(x50571)),x50572),x50572)
% 157.60/157.51 [5058]~P81(x50581)+E(f866(f866(f87(x50581),f84(x50581)),x50582),x50582)
% 157.60/157.51 [5059]~P114(x50591)+E(f866(f866(f87(x50591),f84(x50591)),x50592),x50592)
% 157.60/157.51 [5060]~P85(x50601)+E(f866(f866(f117(x50601),f195(x50601)),x50602),x50602)
% 157.60/157.51 [5061]~P114(x50611)+E(f866(f866(f86(x50611),f2(x50611)),x50612),x50612)
% 157.60/157.51 [5062]~P82(x50621)+E(f866(f866(f86(x50621),f2(x50621)),x50622),x50622)
% 157.60/157.51 [5063]~P72(x50631)+E(f866(f866(f86(x50631),f2(x50631)),x50632),x50632)
% 157.60/157.51 [5064]~P84(x50641)+E(f866(f866(f108(x50641),f250(x50641)),x50642),x50642)
% 157.60/157.51 [5082]~P114(x50821)+E(f866(f866(f87(x50821),f2(x50821)),x50822),f2(x50821))
% 157.60/157.51 [5083]~P129(x50831)+E(f866(f866(f87(x50831),f2(x50831)),x50832),f2(x50831))
% 157.60/157.51 [5084]~P84(x50841)+E(f866(f866(f117(x50841),f250(x50841)),x50842),f250(x50841))
% 157.60/157.51 [5085]~P81(x50851)+E(f866(f866(f252(x50851),f84(x50851)),x50852),f84(x50851))
% 157.60/157.51 [5086]~P85(x50861)+E(f866(f866(f108(x50861),f195(x50861)),x50862),f195(x50861))
% 157.60/157.51 [5087]~P62(x50871)+E(f866(f866(f41(x50871),f2(x50871)),x50872),f2(x50871))
% 157.60/157.51 [5088]~P125(x50881)+E(f866(f866(f297(x50881),f2(x50881)),x50882),f2(x50881))
% 157.60/157.51 [5096]E(x50961,f120(x50962))+E(f151(x50962,f866(f175(x50962),x50961)),f866(f148(x50962),x50961))
% 157.60/157.51 [5097]E(x50971,f120(x50972))+E(f866(f148(x50972),f866(f175(x50972),x50971)),f151(x50972,x50971))
% 157.60/157.51 [5098]E(x50981,f2(a930))+~E(f866(f866(f86(a930),x50982),x50981),x50982)
% 157.60/157.51 [5105]~P142(x51051)+E(f866(f109(x51051),f866(f107(a1),x51052)),f866(f107(x51051),x51052))
% 157.60/157.51 [5106]~P96(x51061)+E(f866(f109(x51061),f866(f110(a1),x51062)),f866(f110(x51061),x51062))
% 157.60/157.51 [5113]E(x51131,f84(a930))+~E(f866(f866(f87(a930),x51132),x51131),f84(a930))
% 157.60/157.51 [5114]E(x51141,f84(a930))+~E(f866(f866(f87(a930),x51141),x51142),f84(a930))
% 157.60/157.51 [5115]E(x51151,f2(a930))+~E(f866(f866(f86(a930),x51152),x51151),f2(a930))
% 157.60/157.51 [5116]E(x51161,f2(a930))+~E(f866(f866(f86(a930),x51161),x51162),f2(a930))
% 157.60/157.51 [5133]~P128(x51331)+E(f866(f81(x51331),f866(f107(x51331),x51332)),f866(f107(x51331),x51332))
% 157.60/157.51 [5134]~P89(x51341)+E(f866(f81(x51341),f866(f81(x51341),x51342)),f866(f81(x51341),x51342))
% 157.60/157.51 [5135]~P89(x51351)+E(f866(f81(x51351),f866(f85(x51351),x51352)),f866(f81(x51351),x51352))
% 157.60/157.51 [5136]~P72(x51361)+E(f866(f172(x51361),f866(f175(x51361),x51362)),f866(f172(x51361),x51362))
% 157.60/157.51 [5141]~E(x51411,f866(a119,f2(a930)))+E(f866(f866(f252(a930),x51411),x51412),f866(a119,f2(a930)))
% 157.60/157.51 [5150]~P77(x51501)+E(f866(f866(f23(x51501),f2(x51501)),x51502),f866(f85(x51501),x51502))
% 157.60/157.51 [5151]~E(x51512,f2(a930))+E(f146(a930,f866(f309(a930,x51511),x51512)),f120(a930))
% 157.60/157.51 [5160]~P96(x51601)+E(f866(f866(f86(x51601),x51602),f866(f110(x51601),a89)),x51602)
% 157.60/157.51 [5161]E(x51611,f2(a1))+E(f52(f866(f81(a1),x51612),f866(f81(a1),x51611)),f58(x51612,x51611))
% 157.60/157.51 [5177]~E(x51771,x51772)+P107(f866(f866(f243(a930),x51771),x51772))
% 157.60/157.51 [5184]~E(x51841,f2(a106))+E(f866(f866(f86(a930),f866(a20,x51841)),x51842),x51842)
% 157.60/157.51 [5185]~E(f866(f110(a1),x51852),f866(f107(a1),x51851))+E(x51851,f866(a111,f866(f110(a1),x51852)))
% 157.60/157.51 [5198]~P6(x51981)+P6(f866(f866(f252(a1),x51981),x51982))
% 157.60/157.51 [5199]~P98(x51991)+E(f866(f866(f117(x51991),x51992),f866(f85(x51991),x51992)),f250(x51991))
% 157.60/157.51 [5200]~P77(x52001)+E(f866(f866(f86(x52001),x52002),f866(f85(x52001),x52002)),f2(x52001))
% 157.60/157.51 [5201]~P98(x52011)+E(f866(f866(f108(x52011),x52012),f866(f85(x52011),x52012)),f195(x52011))
% 157.60/157.51 [5225]E(x52251,f2(a930))+~E(f866(f85(a1),f866(f107(a1),x52252)),f866(f107(a1),x52251))
% 157.60/157.51 [5226]E(x52261,f2(a930))+~E(f866(f85(a1),f866(f107(a1),x52261)),f866(f107(a1),x52262))
% 157.60/157.51 [5236]E(f201(x52361,x52362),f2(a1))+P107(f866(f866(f243(a1),x52362),x52361))
% 157.60/157.51 [5237]E(f185(x52371,x52372),f120(a1))+P107(f866(f866(f243(a1),x52371),x52372))
% 157.60/157.51 [5238]E(f249(x52381,x52382),f2(a106))+P107(f866(f866(f244(a106),x52381),x52382))
% 157.60/157.51 [5251]E(x52511,f866(a119,f2(a930)))+~E(f866(f866(f87(a930),x52512),x52511),f866(a119,f2(a930)))
% 157.60/157.51 [5252]E(x52521,f866(a119,f2(a930)))+~E(f866(f866(f87(a930),x52521),x52522),f866(a119,f2(a930)))
% 157.60/157.51 [5253]~P108(x52531)+P107(f866(f866(f243(x52531),x52532),x52532))
% 157.60/157.51 [5256]~P96(x52561)+E(f866(f866(f87(x52561),x52562),f866(f110(x52561),a104)),f866(f85(x52561),x52562))
% 157.60/157.51 [5276]~P142(x52761)+E(f866(f85(x52761),f866(f109(x52761),x52762)),f866(f109(x52761),f866(f85(a1),x52762)))
% 157.60/157.51 [5277]~P96(x52771)+E(f866(f85(x52771),f866(f110(x52771),x52772)),f866(f110(x52771),f866(f85(a1),x52772)))
% 157.60/157.51 [5306]~E(x53061,f866(a119,x53062))+P107(f866(f866(f244(a930),f2(a930)),x53061))
% 157.60/157.51 [5324]~P110(x53241)+E(f866(f85(f937(x53241,a925)),f866(f290(x53241),x53242)),f866(f291(x53241),x53242))
% 157.60/157.51 [5325]~P110(x53251)+E(f866(f85(f937(x53251,a925)),f866(f311(x53251),x53252)),f866(f308(x53251),x53252))
% 157.60/157.51 [5326]~P110(x53261)+E(f866(f85(f937(x53261,a925)),f866(f308(x53261),x53262)),f866(f311(x53261),x53262))
% 157.60/157.51 [5327]~P110(x53271)+E(f866(f85(f937(x53271,a925)),f866(f291(x53271),x53272)),f866(f290(x53271),x53272))
% 157.60/157.51 [5335]~E(f866(f107(a1),x53352),x53351)+P107(f866(f866(f243(a1),f2(a1)),x53351))
% 157.60/157.51 [5342]~E(x53422,f2(a1))+E(f58(x53421,x53422),f866(f866(f260(a1,a1),f2(a1)),f866(f81(a1),x53421)))
% 157.60/157.51 [5344]~P1(x53441)+P107(f866(f866(f243(x53441),f195(x53441)),x53442))
% 157.60/157.51 [5378]E(x53781,x53782)+~E(f866(f866(f86(a1),x53781),x53781),f866(f866(f86(a1),x53782),x53782))
% 157.60/157.51 [5382]~P107(f866(x53821,x53822))+P107(f866(x53821,f866(a111,f374(x53821))))
% 157.60/157.51 [5408]~P128(x54081)+E(f866(f866(f87(x54081),f88(x54081,x54082)),f866(f81(x54081),x54082)),x54082)
% 157.60/157.51 [5415]~E(x54152,f2(a930))+E(f91(f936(a930,a930),f53(x54151,x54152)),f866(f866(f260(a930,a930),f2(a930)),x54151))
% 157.60/157.51 [5420]~E(x54201,x54202)+~P107(f866(f866(f244(a930),x54201),x54202))
% 157.60/157.51 [5421]~E(x54211,x54212)+~P107(f866(f866(f244(a1),x54211),x54212))
% 157.60/157.51 [5424]~P148(x54241)+E(f866(f866(f86(x54241),f84(x54241)),f866(f107(x54241),x54242)),f866(f107(x54241),f866(a119,x54242)))
% 157.60/157.51 [5428]~E(x54281,f2(a930))+~P107(f866(f866(f244(a930),x54282),x54281))
% 157.60/157.51 [5442]E(f159(x54421,x54422),x54422)+~E(f866(f196(f931(x54421)),f159(x54421,x54422)),f866(f196(f931(x54421)),x54422))
% 157.60/157.51 [5443]E(f866(f40(x54431),f866(f179(x54431),x54432)),f866(f196(f931(x54431)),x54432))+~P107(f866(f144(x54431),x54432))
% 157.60/157.51 [5458]~P107(f866(x54581,f375(x54581)))+P107(f866(x54581,f866(f107(a1),x54582)))
% 157.60/157.51 [5468]E(f249(x54681,x54682),x54682)+~P107(f866(f866(f244(a106),x54681),x54682))
% 157.60/157.51 [5472]E(f280(x54721,x54722),f84(a106))+~P107(f866(f866(f244(a106),x54722),x54721))
% 157.60/157.51 [5473]E(f185(x54731,x54732),f120(a1))+~P107(f866(f866(f244(a1),x54732),x54731))
% 157.60/157.51 [5474]E(f135(x54741,x54742),f122(a1))+~P107(f866(f866(f244(a1),x54741),x54742))
% 157.60/157.51 [5476]~P111(x54761)+E(f310(x54761,x54762,x54762),f866(f866(f316(x54761),x54762),f195(f937(x54761,a925))))
% 157.60/157.51 [5496]~E(f866(f866(f23(a930),x54961),x54962),f2(a930))+P107(f866(f866(f243(a930),x54961),x54962))
% 157.60/157.51 [5519]~E(x55192,f2(a930))+E(f60(x55191,x55192,f120(x55191)),f866(f866(f158(f931(x55191)),f120(x55191)),f120(f931(x55191))))
% 157.60/157.51 [5523]~P108(x55231)+~P107(f866(f866(f244(x55231),x55232),x55232))
% 157.60/157.51 [5525]~E(f50(a1,x55251,x55252),f2(a1))+E(f50(a1,x55251,f866(f85(a1),x55252)),f2(a1))
% 157.60/157.51 [5527]~E(f50(a1,x55271,x55272),f2(a1))+E(f50(a1,f866(f85(a1),x55271),x55272),f2(a1))
% 157.60/157.51 [5534]E(f866(f309(a930,x55341),f866(a119,x55342)),f195(f937(a930,a925)))+P107(f866(f866(f243(a930),x55341),x55342))
% 157.60/157.51 [5557]E(f146(a930,f866(f309(a930,x55571),x55572)),f120(a930))+P107(f866(f866(f244(a930),x55571),x55572))
% 157.60/157.51 [5562]~E(f866(f40(x55621),f866(f179(x55621),x55622)),f866(f196(f931(x55621)),x55622))+P107(f866(f144(x55621),x55622))
% 157.60/157.51 [5566]~P107(f866(f144(x55661),x55662))+P107(f866(f144(x55661),f866(f174(x55661),x55662)))
% 157.60/157.51 [5567]~P107(f866(f144(x55671),x55672))+P107(f866(f144(x55671),f866(f178(x55671),x55672)))
% 157.60/157.51 [5568]~P107(f866(f144(x55681),x55682))+P107(f866(f144(x55681),f866(f175(x55681),x55682)))
% 157.60/157.51 [5576]P107(f866(x55761,x55762))+~P107(f866(x55761,f866(a111,f426(x55761))))
% 157.60/157.51 [5577]P107(f866(f866(f243(a930),x55772),x55771))+P107(f866(f866(f243(a930),x55771),x55772))
% 157.60/157.51 [5578]P107(f866(f866(f243(a1),x55782),x55781))+P107(f866(f866(f243(a1),x55781),x55782))
% 157.60/157.51 [5582]~P89(x55821)+P107(f866(f866(f243(x55821),x55822),f866(f81(x55821),x55822)))
% 157.60/157.51 [5585]P107(f866(x55851,f376(x55851)))+~P107(f866(x55851,f866(f107(a1),x55852)))
% 157.60/157.51 [5609]E(f866(f866(f23(a930),x56091),x56092),f2(a930))+~P107(f866(f866(f243(a930),x56091),x56092))
% 157.60/157.51 [5610]E(f866(f866(f41(a930),x56101),x56102),f2(a930))+~P107(f866(f866(f244(a930),x56101),x56102))
% 157.60/157.51 [5628]E(f50(a930,x56281,x56282),x56281)+~P107(f866(f866(f244(a930),x56281),x56282))
% 157.60/157.51 [5636]E(f50(a1,x56361,f866(f85(a1),x56362)),f298(x56361,x56362))+P107(f866(f866(f243(a1),f2(a1)),x56362))
% 157.60/157.51 [5648]E(f866(f866(f23(a1),x56481),x56482),f201(x56481,x56482))+~P107(f866(f866(f243(a1),x56482),x56481))
% 157.60/157.51 [5668]P107(f866(f866(f243(a1),f2(a1)),f375(x56681)))+P107(f866(x56681,f866(f107(a1),x56682)))
% 157.60/157.51 [5681]~P113(x56811)+P107(f866(f866(f243(x56811),f2(x56811)),f866(f107(x56811),x56812)))
% 157.60/157.51 [5682]~P89(x56821)+P107(f866(f866(f243(x56821),f2(x56821)),f866(f81(x56821),x56822)))
% 157.60/157.51 [5709]E(f866(f866(f86(a930),x57091),f869(x57092,x57091)),x57092)+~P107(f866(f866(f243(a930),x57091),x57092))
% 157.60/157.51 [5721]~E(f866(f110(a1),x57211),f866(f107(a1),x57212))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x57211)))
% 157.60/157.51 [5724]E(f310(a1,x57241,x57242),f195(f937(a1,a925)))+~P107(f866(f866(f244(a1),x57242),x57241))
% 157.60/157.51 [5726]~P128(x57261)+E(f866(f866(f87(x57261),f866(f81(x57261),x57262)),f866(f81(x57261),x57262)),f866(f866(f87(x57261),x57262),x57262))
% 157.60/157.51 [5732]E(f146(a930,f866(f309(a930,x57321),f866(a119,x57322))),f120(a930))+P107(f866(f866(f243(a930),x57321),x57322))
% 157.60/157.51 [5736]E(f866(f866(f41(a1),x57361),x57362),f299(x57361,x57362))+~P107(f866(f866(f243(a1),f2(a1)),x57362))
% 157.60/157.51 [5756]P107(f866(f144(x57561),x57562))+~P107(f866(f144(x57561),f866(f174(x57561),x57562)))
% 157.60/157.51 [5757]P107(f866(f144(x57571),x57572))+~P107(f866(f144(x57571),f866(f175(x57571),x57572)))
% 157.60/157.51 [5782]P107(f866(f66(a930),x57821))+P107(f866(f866(f336(a930),f758(x57821,x57822)),x57821))
% 157.60/157.51 [5783]P107(f866(f66(a930),x57831))+P107(f866(f866(f336(a930),f812(x57831,x57832)),x57831))
% 157.60/157.51 [5786]P107(f866(f866(f244(a930),x57862),f866(a119,x57861)))+P107(f866(f866(f244(a930),x57861),x57862))
% 157.60/157.51 [5787]E(f50(a1,x57871,x57872),f298(x57871,x57872))+~P107(f866(f866(f243(a1),f2(a1)),x57872))
% 157.60/157.51 [5791]E(f146(a930,f866(f309(a930,x57911),x57912)),f120(a930))+~P107(f866(f866(f243(a930),x57912),x57911))
% 157.60/157.51 [5794]~P79(x57941)+E(f866(f317(x57941,x57941,f85(x57941)),f866(f290(x57941),x57942)),f866(f311(x57941),f866(f85(x57941),x57942)))
% 157.60/157.51 [5795]~P79(x57951)+E(f866(f317(x57951,x57951,f85(x57951)),f866(f311(x57951),x57952)),f866(f290(x57951),f866(f85(x57951),x57952)))
% 157.60/157.51 [5796]~P79(x57961)+E(f866(f317(x57961,x57961,f85(x57961)),f866(f308(x57961),x57962)),f866(f291(x57961),f866(f85(x57961),x57962)))
% 157.60/157.51 [5797]~P79(x57971)+E(f866(f317(x57971,x57971,f85(x57971)),f866(f291(x57971),x57972)),f866(f308(x57971),f866(f85(x57971),x57972)))
% 157.60/157.51 [5808]E(x58081,f195(f937(x58082,a925)))+P107(f866(f866(f336(x58082),f377(x58081,x58082)),x58081))
% 157.60/157.51 [5809]E(x58091,f195(f937(x58092,a925)))+P107(f866(f866(f336(x58092),f378(x58091,x58092)),x58091))
% 157.60/157.51 [5821]~P107(f866(f866(f244(a930),x58211),x58212))+P107(f866(f866(f243(a930),x58211),x58212))
% 157.60/157.51 [5822]~P107(f866(f866(f244(a1),x58221),x58222))+P107(f866(f866(f243(a1),x58221),x58222))
% 157.60/157.51 [5838]E(f52(x58381,x58382),f866(f866(f260(a1,a1),f2(a1)),x58381))+~P107(f866(f866(f244(a1),x58381),x58382))
% 157.60/157.51 [5841]E(f224(f866(f85(a1),x58411),f866(f85(a1),x58412)),f224(x58411,x58412))+~P107(f866(f866(f244(a1),x58412),f2(a1)))
% 157.60/157.51 [5854]E(x58541,x58542)+~E(f866(a3,f866(a119,f866(a20,x58541))),f866(a3,f866(a119,f866(a20,x58542))))
% 157.60/157.51 [5859]E(f52(x58591,x58592),f866(f866(f260(a1,a1),f2(a1)),x58591))+~P107(f866(f866(f243(a1),x58592),f2(a1)))
% 157.60/157.51 [5888]E(f50(a930,f866(f110(a930),x58881),f866(f110(a930),x58882)),f2(a930))+~P107(f866(a200,f866(f110(a1),x58881)))
% 157.60/157.51 [5902]P107(f866(f866(f243(a1),f2(a1)),f376(x59021)))+~P107(f866(x59021,f866(f107(a1),x59022)))
% 157.60/157.51 [5937]P40(f310(a1,x59371,x59372))+~P107(f866(f866(f243(a1),f2(a1)),x59371))
% 157.60/157.51 [5942]~P107(f866(f66(x59421),x59422))+P107(f866(f66(f937(x59421,a925)),f866(f315(x59421),x59422)))
% 157.60/157.51 [5955]E(f866(f866(f86(a1),x59551),f866(f107(a1),f408(x59552,x59551))),x59552)+~P107(f866(f866(f243(a1),x59551),x59552))
% 157.60/157.51 [5963]P107(f866(f866(f243(a930),x59631),x59632))+P107(f866(f866(f243(a930),f866(a119,x59632)),x59631))
% 157.60/157.51 [6007]E(f866(f866(f41(a930),f866(f110(a930),x60071)),f866(f110(a930),x60072)),f2(a930))+~P107(f866(a200,f866(f110(a1),x60071)))
% 157.60/157.51 [6008]E(f866(f866(f87(a930),f866(f110(a930),x60081)),f866(f110(a930),x60082)),f2(a930))+~P107(f866(f866(f244(a1),x60081),a89))
% 157.60/157.51 [6010]P107(f866(f866(f243(a930),x60101),f866(a119,x60102)))+~P107(f866(f866(f243(a930),x60101),x60102))
% 157.60/157.51 [6012]P107(f866(f866(f244(a930),x60121),f866(a119,x60122)))+~P107(f866(f866(f243(a930),x60121),x60122))
% 157.60/157.51 [6014]P107(f866(f866(f244(a930),x60141),f866(a119,x60142)))+~P107(f866(f866(f244(a930),x60141),x60142))
% 157.60/157.51 [6017]~E(x60171,x60172)+P107(f866(f866(f244(a1),x60171),f866(f866(f86(a1),x60172),f84(a1))))
% 157.60/157.51 [6020]E(f50(a1,x60201,x60202),f2(a1))+E(f866(f866(f23(a1),x60202),f50(a1,x60201,x60202)),f50(a1,f866(f85(a1),x60201),x60202))
% 157.60/157.51 [6029]E(x60291,f120(x60292))+P107(f866(f866(f336(x60292),f151(x60292,x60291)),f866(f179(x60292),x60291)))
% 157.60/157.51 [6041]E(f91(f936(a930,a930),f53(x60411,x60412)),f866(f866(f260(a930,a930),f2(a930)),x60411))+~P107(f866(f866(f244(a930),x60411),x60412))
% 157.60/157.51 [6076]E(f866(f866(f23(a930),f866(f110(a930),x60761)),f866(f110(a930),x60762)),f866(f110(a930),x60761))+~P107(f866(f866(f244(a1),x60762),a89))
% 157.60/157.51 [6077]E(f866(f866(f86(a930),f866(f110(a930),x60771)),f866(f110(a930),x60772)),f866(f110(a930),x60772))+~P107(f866(f866(f244(a1),x60771),a89))
% 157.60/157.51 [6084]E(f866(a119,f866(f866(f86(a930),x60841),f902(x60842,x60841))),x60842)+~P107(f866(f866(f244(a930),x60841),x60842))
% 157.60/157.51 [6110]P107(f866(x61101,x61102))+~P107(f866(x61101,f866(a95,f555(x61102,x61101))))
% 157.60/157.51 [6111]P107(f866(x61111,x61112))+~P107(f866(x61111,f866(a3,f825(x61112,x61111))))
% 157.60/157.51 [6120]~P107(f866(f866(f244(a930),x61201),f866(a119,x61202)))+P107(f866(f866(f243(a930),x61201),x61202))
% 157.60/157.51 [6167]E(f866(f866(f316(a930),x61671),f866(f309(a930,x61672),x61671)),f866(f309(a930,x61672),f866(a119,x61671)))+~P107(f866(f866(f243(a930),x61672),x61671))
% 157.60/157.51 [6169]E(x61691,f120(x61692))+E(f866(f866(f141(x61692),f121(x61692,x61691)),f866(f866(f158(x61692),f151(x61692,x61691)),f120(x61692))),x61691)
% 157.60/157.51 [6186]P107(f866(f66(x61861),x61862))+~P107(f866(f866(f244(a930),f2(a930)),f866(f40(x61861),x61862)))
% 157.60/157.51 [6189]~E(x61891,f195(f937(x61892,a925)))+~P107(f866(f866(f244(a930),f2(a930)),f866(f40(x61892),x61891)))
% 157.60/157.51 [6201]~P107(f866(f866(f244(a930),x62011),x62012))+P107(f866(f866(f243(a930),f866(a119,x62011)),x62012))
% 157.60/157.51 [6205]~P110(x62051)+E(f157(x62051,x62051,f5(x62051),f159(x62051,x62052)),f146(x62051,f866(f179(x62051),x62052)))
% 157.60/157.51 [6208]E(x62081,f120(x62082))+P107(f866(f866(f336(x62082),f866(f148(x62082),x62081)),f866(f179(x62082),x62081)))
% 157.60/157.51 [6214]~P113(x62141)+P107(f866(f866(f244(x62141),x62142),f866(f866(f86(x62141),x62142),f84(x62141))))
% 157.60/157.51 [6216]~P89(x62161)+P107(f866(f866(f243(x62161),f866(f85(x62161),x62162)),f866(f81(x62161),x62162)))
% 157.60/157.51 [6247]P107(f866(f66(a930),x62471))+~P107(f866(f866(f243(a930),f758(x62471,x62472)),x62472))
% 157.60/157.51 [6248]P107(f866(f66(a930),x62481))+~P107(f866(f866(f244(a930),f812(x62481,x62482)),x62482))
% 157.60/157.51 [6251]~P107(f866(f66(f936(x62511,x62511)),x62512))+P107(f866(f66(x62511),f866(f289(x62511),x62512)))
% 157.60/157.51 [6309]~P107(f866(f866(f244(a930),x63092),f866(a119,x63091)))+~P107(f866(f866(f244(a930),x63091),x63092))
% 157.60/157.51 [6310]~P111(x63101)+E(f866(f866(f108(f937(x63101,a925)),f866(f308(x63101),x63102)),f866(f291(x63101),x63102)),f866(f866(f316(x63101),x63102),f195(f937(x63101,a925))))
% 157.60/157.51 [6322]P107(f866(f66(x63221),x63222))+~P107(f866(f66(f937(x63221,a925)),f866(f315(x63221),x63222)))
% 157.60/157.51 [6344]P107(f866(f866(f243(a930),f866(a119,x63441)),f866(a119,x63442)))+~P107(f866(f866(f243(a930),x63441),x63442))
% 157.60/157.51 [6345]P107(f866(f866(f243(a930),f866(a20,x63451)),f866(a20,x63452)))+~P107(f866(f866(f243(a106),x63451),x63452))
% 157.60/157.51 [6346]P107(f866(f866(f243(a106),f866(a3,x63461)),f866(a3,x63462)))+~P107(f866(f866(f243(a930),x63461),x63462))
% 157.60/157.51 [6348]P107(f866(f866(f244(a930),f866(a119,x63481)),f866(a119,x63482)))+~P107(f866(f866(f244(a930),x63481),x63482))
% 157.60/157.51 [6349]P107(f866(f866(f244(a930),f866(a20,x63491)),f866(a20,x63492)))+~P107(f866(f866(f244(a106),x63491),x63492))
% 157.60/157.51 [6350]P107(f866(f866(f244(a106),f866(a3,x63501)),f866(a3,x63502)))+~P107(f866(f866(f244(a930),x63501),x63502))
% 157.60/157.51 [6355]E(x63551,x63552)+~E(f866(f317(a930,a1,f107(a1)),x63551),f866(f317(a930,a1,f107(a1)),x63552))
% 157.60/157.51 [6371]P107(f866(f866(f243(a930),x63711),x63712))+~P107(f866(f866(f243(a930),f866(a119,x63711)),x63712))
% 157.60/157.51 [6374]P107(f866(f866(f244(a930),x63741),x63742))+~P107(f866(f866(f243(a930),f866(a119,x63741)),x63742))
% 157.60/157.51 [6375]P107(f866(f866(f244(a930),x63751),x63752))+~P107(f866(f866(f244(a930),f866(a119,x63751)),x63752))
% 157.60/157.51 [6392]E(f50(a1,x63921,x63922),f2(a1))+E(f866(f866(f23(a1),f50(a1,x63921,x63922)),x63922),f50(a1,x63921,f866(f85(a1),x63922)))
% 157.60/157.51 [6457]E(f866(f40(f937(x64571,a925)),f866(f315(x64571),x64572)),f866(f866(f252(a930),f866(a119,f866(a119,f2(a930)))),f866(f40(x64571),x64572)))+~P107(f866(f66(x64571),x64572))
% 157.60/157.51 [6460]E(x64601,f120(x64602))+E(f866(f866(f171(x64602),x64601),f866(f866(f23(a930),f866(f196(f931(x64602)),x64601)),f84(a930))),f151(x64602,x64601))
% 157.60/157.51 [6482]E(x64821,f120(x64822))+E(f866(f866(f141(x64822),f866(f178(x64822),x64821)),f866(f866(f158(x64822),f866(f148(x64822),x64821)),f120(x64822))),f866(f174(x64822),x64821))
% 157.60/157.51 [6513]~P107(f866(f66(x65131),f42(f937(x65131,a925),x65132)))+P107(f866(f66(f937(x65131,a925)),x65132))
% 157.60/157.51 [6535]P107(f866(f866(f243(a930),f866(f110(a930),x65351)),f866(f110(a930),x65352)))+~P107(f866(f866(f243(a1),x65351),a89))
% 157.60/157.51 [6555]~P107(f866(f866(f244(a1),x65551),x65552))+P107(f866(f866(f243(a1),x65551),f866(f866(f23(a1),x65552),f84(a1))))
% 157.60/157.51 [6556]~P107(f866(f866(f243(a1),x65561),x65562))+P107(f866(f866(f244(a1),x65561),f866(f866(f86(a1),x65562),f84(a1))))
% 157.60/157.51 [6557]~P107(f866(f866(f244(a1),x65571),x65572))+P107(f866(f866(f244(a1),x65571),f866(f866(f86(a1),x65572),f84(a1))))
% 157.60/157.51 [6559]~P107(f866(f866(f243(a1),x65591),x65592))+P107(f866(f866(f243(a930),f866(f110(a930),x65591)),f866(f110(a930),x65592)))
% 157.60/157.51 [6561]~P107(f866(f866(f243(a930),x65611),x65612))+P107(f866(f866(f243(a1),f866(f107(a1),x65611)),f866(f107(a1),x65612)))
% 157.60/157.51 [6562]~P107(f866(f866(f243(a1),x65621),x65622))+P107(f866(f866(f243(a1),f866(f110(a1),x65621)),f866(f110(a1),x65622)))
% 157.60/157.51 [6564]~P107(f866(f866(f244(a930),x65641),x65642))+P107(f866(f866(f244(a1),f866(f107(a1),x65641)),f866(f107(a1),x65642)))
% 157.60/157.51 [6565]~P107(f866(f866(f244(a1),x65651),x65652))+P107(f866(f866(f244(a1),f866(f110(a1),x65651)),f866(f110(a1),x65652)))
% 157.60/157.51 [6587]~P107(f866(f866(f243(a930),x65871),x65872))+~P107(f866(f866(f243(a930),f866(a119,x65872)),x65871))
% 157.60/157.51 [6629]~P107(f866(f866(f243(a930),f866(a119,x66291)),f866(a119,x66292)))+P107(f866(f866(f243(a930),x66291),x66292))
% 157.60/157.51 [6630]~P107(f866(f866(f243(a106),f866(a3,x66301)),f866(a3,x66302)))+P107(f866(f866(f243(a930),x66301),x66302))
% 157.60/157.51 [6631]~P107(f866(f866(f243(a930),f866(a20,x66311)),f866(a20,x66312)))+P107(f866(f866(f243(a106),x66311),x66312))
% 157.60/157.51 [6633]~P107(f866(f866(f244(a930),f866(a119,x66331)),f866(a119,x66332)))+P107(f866(f866(f244(a930),x66331),x66332))
% 157.60/157.51 [6634]~P107(f866(f866(f244(a106),f866(a3,x66341)),f866(a3,x66342)))+P107(f866(f866(f244(a930),x66341),x66342))
% 157.60/157.51 [6635]~P107(f866(f866(f244(a930),f866(a111,x66351)),f866(a111,x66352)))+P107(f866(f866(f244(a1),x66351),x66352))
% 157.60/157.51 [6636]~P107(f866(f866(f244(a930),f866(a20,x66361)),f866(a20,x66362)))+P107(f866(f866(f244(a106),x66361),x66362))
% 157.60/157.51 [6678]~P107(f866(f866(f244(a930),f866(a111,x66782)),f866(a111,x66781)))+P107(f866(f866(f244(a1),f2(a1)),x66781))
% 157.60/157.51 [6712]P107(f866(f866(f243(a1),f2(a1)),f50(a1,x67121,x67122)))+~P107(f866(f866(f244(a1),f2(a1)),x67122))
% 157.60/157.51 [6873]P37(x68731,x68732)+~E(f866(f866(f296(x68731,x68731,x68731),x68732),x68732),f195(f937(f936(x68731,x68731),a925)))
% 157.60/157.51 [6885]~P37(x68851,x68852)+P37(x68851,f866(f866(f296(x68851,x68851,x68851),x68852),x68852))
% 157.60/157.51 [6896]P107(f866(f866(f243(a1),x68961),x68962))+~P107(f866(f866(f244(a1),x68961),f866(f866(f86(a1),x68962),f84(a1))))
% 157.60/157.51 [6897]P107(f866(f866(f244(a1),x68971),x68972))+~P107(f866(f866(f243(a1),x68971),f866(f866(f23(a1),x68972),f84(a1))))
% 157.60/157.51 [6900]P107(f866(f866(f243(a930),x69001),x69002))+~P107(f866(f866(f243(a1),f866(f107(a1),x69001)),f866(f107(a1),x69002)))
% 157.60/157.51 [6901]P107(f866(f866(f243(a1),x69011),x69012))+~P107(f866(f866(f243(a1),f866(f110(a1),x69011)),f866(f110(a1),x69012)))
% 157.60/157.51 [6903]P107(f866(f866(f244(a930),x69031),x69032))+~P107(f866(f866(f244(a1),f866(f107(a1),x69031)),f866(f107(a1),x69032)))
% 157.60/157.51 [6904]P107(f866(f866(f244(a1),x69041),x69042))+~P107(f866(f866(f244(a930),f866(f110(a930),x69041)),f866(f110(a930),x69042)))
% 157.60/157.51 [6905]P107(f866(f866(f244(a1),x69051),x69052))+~P107(f866(f866(f244(a1),f866(f110(a1),x69051)),f866(f110(a1),x69052)))
% 157.60/157.51 [6999]~E(f704(x69992,x69991),f120(x69991))+E(f866(f149(f931(x69991),f931(x69991),f141(x69991),f120(x69991)),x69992),f120(x69991))
% 157.60/157.51 [7000]~E(f705(x70002,x70001),f120(x70001))+E(f866(f149(f931(x70001),f931(x70001),f141(x70001),f120(x70001)),x70002),f120(x70001))
% 157.60/157.51 [7004]~P5(x70041)+E(f866(f149(x70041,x70041,f108(x70041),f250(x70041)),x70042),f43(x70041,f866(f179(x70041),x70042)))
% 157.60/157.51 [7005]~P5(x70051)+E(f866(f149(x70051,x70051,f117(x70051),f195(x70051)),x70052),f42(x70051,f866(f179(x70051),x70052)))
% 157.60/157.51 [7019]E(x70191,f2(a106))+E(f866(f866(f86(a930),f866(a20,f866(f866(f23(a106),x70191),f84(a106)))),f866(a119,x70192)),f866(f866(f86(a930),f866(a20,x70191)),x70192))
% 157.60/157.51 [7069]P107(f866(f866(f244(a1),f866(f866(f23(a1),x70691),x70692)),f2(a1)))+~P107(f866(f866(f244(a1),x70691),x70692))
% 157.60/157.51 [7094]~P110(x70941)+E(f866(f866(f117(f937(x70941,a925)),f866(f866(f316(x70941),x70942),f195(f937(x70941,a925)))),f866(f311(x70941),x70942)),f866(f291(x70941),x70942))
% 157.60/157.51 [7168]~P61(x71681,x71682)+P37(x71681,f866(f270(f936(x71681,x71681)),f866(f265(x71681,x71681,a925),x71682)))
% 157.60/157.51 [7169]~P61(x71691,x71692)+P59(x71691,f866(f270(f936(x71691,x71691)),f866(f265(x71691,x71691,a925),x71692)))
% 157.60/157.51 [7170]~P50(x71701,x71702)+P38(x71701,f866(f270(f936(x71701,x71701)),f866(f265(x71701,x71701,a925),x71702)))
% 157.60/157.51 [7171]~P51(x71711,x71712)+P52(x71711,f866(f270(f936(x71711,x71711)),f866(f265(x71711,x71711,a925),x71712)))
% 157.60/157.51 [7172]E(x71721,f195(f937(x71722,a925)))+~P107(f866(f866(f243(f937(x71722,a925)),x71721),f195(f937(x71722,a925))))
% 157.60/157.51 [7252]~P107(f866(f866(f244(a930),f2(a930)),x72522))+P107(f866(f866(f243(a930),f50(a930,x72521,x72522)),x72522))
% 157.60/157.51 [7253]~P107(f866(f866(f243(a1),f2(a1)),x72531))+P107(f866(f866(f243(a1),f50(a1,x72531,x72532)),x72531))
% 157.60/157.51 [7254]~P107(f866(f866(f244(a930),f2(a930)),x72542))+P107(f866(f866(f244(a930),f50(a930,x72541,x72542)),x72542))
% 157.60/157.51 [7256]~P107(f866(f866(f244(a1),f2(a1)),x72562))+P107(f866(f866(f244(a1),f50(a1,x72561,x72562)),x72562))
% 157.60/157.51 [7332]~P111(x73321)+E(f866(f866(f23(f937(x73321,a925)),f866(f866(f316(x73321),x73322),f195(f937(x73321,a925)))),f866(f290(x73321),x73322)),f866(f866(f316(x73321),x73322),f195(f937(x73321,a925))))
% 157.60/157.51 [7405]~P48(x74051,x74052)+P53(x74051,f250(f937(x74051,a925)),f866(f270(f936(x74051,x74051)),f866(f265(x74051,x74051,a925),x74052)))
% 157.60/157.51 [7406]P107(f866(x74061,x74062))+P107(f866(f866(f336(f937(f936(a930,a930),a925)),f555(x74062,x74061)),a105))
% 157.60/157.51 [7450]E(f866(f866(f141(a930),f146(a930,f866(f309(a930,x74501),x74502))),f866(f866(f158(a930),x74502),f120(a930))),f146(a930,f866(f309(a930,x74501),f866(a119,x74502))))+~P107(f866(f866(f243(a930),x74501),x74502))
% 157.60/157.51 [7601]E(x76011,f2(a930))+~E(f866(f149(a930,a930,f86(a930),x76011),x76012),f2(a930))
% 157.60/157.51 [7625]~P107(f866(f866(f244(a1),f866(f866(f23(a1),x76251),x76252)),f2(a1)))+P107(f866(f866(f244(a1),x76251),x76252))
% 157.60/157.51 [7653]P37(x76531,x76532)+~P37(x76531,f866(f866(f296(x76531,x76531,x76531),x76532),x76532))
% 157.60/157.51 [7679]~P107(f866(f866(f243(a930),f866(a119,x76791)),x76792))+P107(f192(a925,a247,f866(f243(a930),x76791),x76792))
% 157.60/157.51 [7831]P25(a930,a930,f866(f866(f7(a930,a930,a930),f23(a930)),x78311),x78312)+P107(f866(f866(f336(a930),f359(x78311,x78312)),x78312))
% 157.60/157.51 [7887]E(f866(f866(f866(f70(a930,x78871,f86(a930)),f866(f16(a930,x78871),f84(a930))),f2(a930)),x78872),f866(f40(x78871),x78872))+~P107(f866(f66(x78871),x78872))
% 157.60/157.51 [7928]P25(a930,a930,f866(f866(f7(a930,a930,a930),f23(a930)),x79281),x79282)+~P107(f866(f866(f243(a930),x79281),f359(x79281,x79282)))
% 157.60/157.51 [7985]P37(x79851,x79852)+P107(f866(f866(f243(f937(x79851,a925)),f554(x79852,x79851)),f866(f293(x79851,x79851,x79852),f554(x79852,x79851))))
% 157.60/157.51 [7990]P61(x79901,x79902)+~P37(x79901,f866(f270(f936(x79901,x79901)),f866(f265(x79901,x79901,a925),x79902)))
% 157.60/157.51 [7991]P50(x79911,x79912)+~P38(x79911,f866(f270(f936(x79911,x79911)),f866(f265(x79911,x79911,a925),x79912)))
% 157.60/157.51 [7992]P51(x79921,x79922)+~P52(x79921,f866(f270(f936(x79921,x79921)),f866(f265(x79921,x79921,a925),x79922)))
% 157.60/157.51 [8058]P107(f866(f866(f243(a930),f866(a119,x80581)),x80582))+~P107(f192(a925,a247,f866(f243(a930),x80581),x80582))
% 157.60/157.51 [8113]P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x81131),x81132)),f314(a930,a324)))+~P107(f866(f866(f243(a930),x81131),x81132))
% 157.60/157.51 [8209]P48(x82091,x82092)+~P53(x82091,f250(f937(x82091,a925)),f866(f270(f936(x82091,x82091)),f866(f265(x82091,x82091,a925),x82092)))
% 157.60/157.51 [8264]~P107(f866(f144(x82641),x82642))+P107(f866(f144(f937(x82641,a925)),f866(f866(f161(f931(x82641),f937(x82641,a925)),f179(x82641)),f59(x82641,x82642))))
% 157.60/157.51 [8458]~P37(x84581,f866(f294(x84581,x84581),x84582))+P37(x84581,f866(f294(x84581,x84581),f866(f866(f296(x84581,x84581,x84581),x84582),f314(x84581,x84582))))
% 157.60/157.51 [8557]P26(x85571,a930,f829(x85572,x85571),x85572,f866(f309(a930,f2(a930)),f866(f40(x85571),x85572)))+~P107(f866(f66(x85571),x85572))
% 157.60/157.51 [8558]P26(a930,x85581,f830(x85582,x85581),f866(f309(a930,f2(a930)),f866(f40(x85581),x85582)),x85582)+~P107(f866(f66(x85581),x85582))
% 157.60/157.51 [8575]P26(a930,x85751,f831(x85752,x85751),f310(a930,f84(a930),f866(f40(x85751),x85752)),x85752)+~P107(f866(f66(x85751),x85752))
% 157.60/157.51 [8584]P107(f866(f66(f936(x85841,x85841)),f866(f866(f296(x85841,x85841,x85841),x85842),f314(x85841,x85842))))+~P107(f866(f66(f936(x85841,x85841)),x85842))
% 157.60/157.51 [8611]E(x86111,f2(a1))+P107(f866(f54(x86112,x86111),f866(f866(f260(a1,a1),f866(f866(f41(a1),x86112),x86111)),f50(a1,x86112,x86111))))
% 157.60/157.51 [8625]~P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x86251),x86252)),f314(a930,a324)))+P107(f866(f866(f243(a930),x86251),x86252))
% 157.60/157.51 [8640]~P82(x86401)+E(f866(f149(x86401,x86401,f866(f7(x86401,x86401,x86401),f86(x86401)),f2(x86401)),f866(f175(x86401),x86402)),f866(f149(x86401,x86401,f86(x86401),f2(x86401)),x86402))
% 157.60/157.51 [8812]~P110(x88121)+E(f866(f149(f931(x88121),x88121,f866(f7(x88121,f931(x88121),f931(x88121)),f155(x88121,x88121,f5(x88121))),f120(x88121)),x88122),f157(x88121,x88121,f5(x88121),x88122))
% 157.60/157.51 [8923]~P59(x89231,f866(f270(f936(x89231,x89231)),f866(f265(x89231,x89231,a925),x89232)))+P59(x89231,f866(f270(f936(x89231,x89231)),f866(f265(x89231,x89231,a925),f251(x89231,x89231,x89232))))
% 157.60/157.51 [8937]P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x89371),x89372)),f866(f866(f296(a930,a930,a930),a324),f314(a930,a324))))+~P107(f866(f866(f244(a930),x89371),x89372))
% 157.60/157.51 [8983]~P107(f866(f66(f936(x89831,x89831)),f866(f866(f296(x89831,x89831,x89831),x89832),f314(x89831,x89832))))+P107(f866(f66(f936(x89831,x89831)),x89832))
% 157.60/157.51 [9041]~P59(x90411,f866(f270(f936(x90411,x90411)),f866(f265(x90411,x90411,a925),f251(x90411,x90411,x90412))))+P59(x90411,f866(f270(f936(x90411,x90411)),f866(f265(x90411,x90411,a925),x90412)))
% 157.60/157.51 [9244]P59(x92441,x92442)+P107(f866(f866(f336(f936(x92441,x92441)),f866(f866(f260(x92441,x92441),f581(x92442,x92441)),f581(x92442,x92441))),f866(f866(f296(x92441,x92441,x92441),x92442),f314(x92441,x92442))))
% 157.60/157.51 [9245]P59(x92451,x92452)+P107(f866(f866(f336(f936(x92451,x92451)),f866(f866(f260(x92451,x92451),f587(x92452,x92451)),f587(x92452,x92451))),f866(f866(f296(x92451,x92451,x92451),x92452),f314(x92451,x92452))))
% 157.60/157.51 [9363]~P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x93631),x93632)),f866(f866(f296(a930,a930,a930),a324),f314(a930,a324))))+P107(f866(f866(f244(a930),x93631),x93632))
% 157.60/157.51 [5320]~P96(x53201)+E(f866(f866(f86(x53201),f866(f110(x53201),a89)),x53202),x53202)
% 157.60/157.51 [5349]~P98(x53491)+E(f866(f866(f117(x53491),f866(f85(x53491),x53492)),x53492),f250(x53491))
% 157.60/157.51 [5350]~P3(x53501)+E(f866(f866(f86(x53501),f866(f85(x53501),x53502)),x53502),f2(x53501))
% 157.60/157.51 [5351]~P77(x53511)+E(f866(f866(f86(x53511),f866(f85(x53511),x53512)),x53512),f2(x53511))
% 157.60/157.51 [5352]~P98(x53521)+E(f866(f866(f108(x53521),f866(f85(x53521),x53522)),x53522),f195(x53521))
% 157.60/157.51 [5386]~P96(x53861)+E(f866(f866(f87(x53861),f866(f110(x53861),a104)),x53862),f866(f85(x53861),x53862))
% 157.60/157.51 [5549]~P118(x55491)+E(f866(f866(f87(x55491),f866(f85(x55491),f84(x55491))),x55492),f866(f85(x55491),x55492))
% 157.60/157.51 [5594]E(f866(f81(a1),x55941),f84(a1))+~E(f866(f81(a1),f866(f866(f87(a1),x55941),x55942)),f84(a1))
% 157.60/157.51 [5684]~P96(x56841)+E(f866(f866(f86(x56841),f84(x56841)),f866(f110(x56841),x56842)),f866(f110(x56841),f866(f866(f23(a1),x56842),a104)))
% 157.60/157.51 [5737]~P83(x57371)+E(f13(x57371,f866(f866(f316(x57371),x57372),f195(f937(x57371,a925)))),x57372)
% 157.60/157.51 [5738]~P83(x57381)+E(f10(x57381,f866(f866(f316(x57381),x57382),f195(f937(x57381,a925)))),x57382)
% 157.60/157.51 [5739]~P110(x57391)+E(f14(x57391,f866(f866(f316(x57391),x57392),f195(f937(x57391,a925)))),x57392)
% 157.60/157.51 [5740]~P110(x57401)+E(f15(x57401,f866(f866(f316(x57401),x57402),f195(f937(x57401,a925)))),x57402)
% 157.60/157.51 [5741]~P5(x57411)+E(f43(x57411,f866(f866(f316(x57411),x57412),f195(f937(x57411,a925)))),x57412)
% 157.60/157.51 [5742]~P5(x57421)+E(f42(x57421,f866(f866(f316(x57421),x57422),f195(f937(x57421,a925)))),x57422)
% 157.60/157.51 [5764]E(f866(f866(f86(a930),x57641),f866(f866(f23(a930),x57642),x57641)),x57642)+P107(f866(f866(f244(a930),x57642),x57641))
% 157.60/157.51 [5803]E(x58031,f120(x58032))+P107(f866(f866(f244(a930),f2(a930)),f866(f196(f931(x58032)),x58031)))
% 157.60/157.51 [5932]~P110(x59321)+E(f11(x59321,f241(x59321),f866(f866(f316(x59321),x59322),f195(f937(x59321,a925)))),x59322)
% 157.60/157.51 [5933]~P110(x59331)+E(f12(x59331,f242(x59331),f866(f866(f316(x59331),x59332),f195(f937(x59331,a925)))),x59332)
% 157.60/157.51 [5996]E(f866(f866(f23(a930),x59961),f866(f866(f23(a930),x59961),x59962)),x59962)+~P107(f866(f866(f243(a930),x59962),x59961))
% 157.60/157.51 [5997]E(f866(f866(f86(a930),x59971),f866(f866(f23(a930),x59972),x59971)),x59972)+~P107(f866(f866(f243(a930),x59971),x59972))
% 157.60/157.51 [6019]E(f50(a930,f866(f866(f23(a930),x60191),x60192),x60192),f50(a930,x60191,x60192))+P107(f866(f866(f244(a930),x60191),x60192))
% 157.60/157.51 [6030]E(f866(f85(a1),f866(f866(f41(a1),x60301),f866(f85(a1),x60302))),f299(x60301,x60302))+P107(f866(f866(f243(a1),f2(a1)),x60302))
% 157.60/157.51 [6032]~E(x60322,f2(a930))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f252(a930),x60321),x60322)))
% 157.60/157.51 [6086]~P96(x60861)+E(f866(f866(f86(x60861),f866(f85(x60861),f84(x60861))),f866(f110(x60861),x60862)),f866(f110(x60861),f866(f866(f86(a1),x60862),a104)))
% 157.60/157.51 [6088]E(f866(f866(f252(a930),f866(f110(a930),x60881)),x60882),f866(f866(f252(a930),f2(a930)),x60882))+~P107(f866(a200,f866(f110(a1),x60881)))
% 157.60/157.51 [6193]E(f866(f148(a930),f146(a930,f866(f309(a930,x61931),x61932))),x61931)+~P107(f866(f866(f244(a930),x61931),x61932))
% 157.60/157.51 [6209]E(f866(f866(f87(a930),f866(f110(a930),x62091)),f866(f110(a930),x62092)),f866(f110(a930),f866(f866(f87(a1),x62091),x62092)))+P107(f866(f866(f244(a1),x62091),a89))
% 157.60/157.51 [6215]~P121(x62151)+P107(f866(f866(f243(x62151),f2(x62151)),f866(f866(f87(x62151),x62152),x62152)))
% 157.60/157.51 [6227]E(f866(f866(f23(a930),f866(a119,x62271)),x62272),f866(a119,f866(f866(f23(a930),x62271),x62272)))+~P107(f866(f866(f243(a930),x62272),x62271))
% 157.60/157.51 [6230]E(f50(a930,f866(f866(f23(a930),x62301),x62302),x62302),f50(a930,x62301,x62302))+~P107(f866(f866(f243(a930),x62302),x62301))
% 157.60/157.51 [6285]E(f866(f866(f252(a930),f866(a111,x62851)),x62852),f866(a111,f866(f866(f252(a1),x62851),x62852)))+~P107(f866(f866(f243(a1),f2(a1)),x62851))
% 157.60/157.51 [6303]P107(f866(f144(x63031),x63032))+P107(f866(f866(f244(a930),f675(x63032,x63031)),f866(f196(f931(x63031)),x63032)))
% 157.60/157.51 [6304]P107(f866(f144(x63041),x63042))+P107(f866(f866(f244(a930),f679(x63042,x63041)),f866(f196(f931(x63041)),x63042)))
% 157.60/157.51 [6316]~E(x63161,f120(x63162))+~P107(f866(f866(f244(a930),f2(a930)),f866(f196(f931(x63162)),x63161)))
% 157.60/157.51 [6327]E(f151(a930,f146(a930,f866(f309(a930,x63271),x63272))),f866(f866(f23(a930),x63272),f84(a930)))+~P107(f866(f866(f244(a930),x63271),x63272))
% 157.60/157.51 [6330]E(f866(f866(f86(a1),x63301),f866(f107(a1),f866(a119,f411(x63302,x63301)))),x63302)+~P107(f866(f866(f244(a1),x63301),x63302))
% 157.60/157.51 [6337]E(x63371,f2(a930))+E(f866(f866(f87(a930),x63372),f866(f866(f252(a930),x63372),f866(f866(f23(a930),x63371),f84(a930)))),f866(f866(f252(a930),x63372),x63371))
% 157.60/157.51 [6365]E(f866(f866(f87(a930),f866(a111,x63651)),f866(a111,x63652)),f866(a111,f866(f866(f87(a1),x63651),x63652)))+~P107(f866(f866(f243(a1),f2(a1)),x63651))
% 157.60/157.51 [6366]E(f866(f866(f41(a930),f866(a111,x63661)),f866(a111,x63662)),f866(a111,f866(f866(f41(a1),x63661),x63662)))+~P107(f866(f866(f243(a1),f2(a1)),x63661))
% 157.60/157.51 [6380]~P114(x63801)+E(f866(f866(f86(x63801),x63802),x63802),f866(f866(f87(x63801),f866(f866(f86(x63801),f84(x63801)),f84(x63801))),x63802))
% 157.60/157.51 [6401]E(f866(f866(f23(a1),f866(f107(a1),x64011)),f866(f107(a1),x64012)),f866(f107(a1),f866(f866(f23(a930),x64011),x64012)))+~P107(f866(f866(f243(a930),x64012),x64011))
% 157.60/157.51 [6403]E(f866(f866(f260(a1,a1),f866(f110(a1),a104)),f866(f866(f86(a1),x64031),x64032)),f55(x64031,x64032))+~P107(f866(f866(f243(a1),x64032),f2(a1)))
% 157.60/157.51 [6435]E(f186(x64351,x64352),f120(f931(x64351)))+P107(f866(f866(f336(f931(x64351)),f674(x64352,x64351)),f866(f179(f931(x64351)),x64352)))
% 157.60/157.51 [6444]E(f123(a1,f866(f136(a1),x64441),f135(x64442,f866(f866(f86(a1),x64441),f84(a1)))),f135(x64442,x64441))+P107(f866(f866(f244(a1),x64442),x64441))
% 157.60/157.51 [6519]E(f866(f866(f158(a1),x65191),f185(f866(f866(f86(a1),x65191),f84(a1)),x65192)),f185(x65191,x65192))+~P107(f866(f866(f243(a1),x65191),x65192))
% 157.60/157.51 [6558]~P107(f866(f866(f244(a930),x65582),x65581))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f23(a930),x65581),x65582)))
% 157.60/157.51 [6592]~P107(f866(f866(f244(a930),x65921),f866(a111,x65922)))+P107(f866(f866(f244(a1),f866(f107(a1),x65921)),x65922))
% 157.60/157.51 [6620]~P110(x66201)+E(f866(f866(f117(f937(x66201,a925)),f866(f290(x66201),x66202)),f866(f866(f316(x66201),x66202),f195(f937(x66201,a925)))),f866(f308(x66201),x66202))
% 157.60/157.51 [6621]~P107(f866(f866(f243(a1),f2(a1)),x66211))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f252(a1),x66211),x66212)))
% 157.60/157.51 [6624]~P107(f866(f866(f244(a930),f2(a930)),x66241))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f252(a930),x66241),x66242)))
% 157.60/157.51 [6654]~E(f866(x66541,f2(a930)),f2(a930))+E(f866(f866(f6(a930,a930),x66541),f310(a930,f866(a119,f2(a930)),x66542)),f866(f866(f6(a930,a930),x66541),f310(a930,f2(a930),x66542)))
% 157.60/157.51 [6720]~P96(x67201)+E(f866(f866(f87(x67201),f866(f866(f86(x67201),f84(x67201)),f84(x67201))),f866(f110(x67201),x67202)),f866(f110(x67201),f866(f866(f86(a1),x67202),x67202)))
% 157.60/157.51 [6735]E(f866(f866(f316(a1),x67351),f310(a1,f866(f866(f86(a1),x67351),f84(a1)),x67352)),f310(a1,x67351,x67352))+P107(f866(f866(f244(a1),x67352),x67351))
% 157.60/157.51 [6736]P107(f866(f866(f244(a930),x67361),f866(a111,x67362)))+~P107(f866(f866(f244(a1),f866(f107(a1),x67361)),x67362))
% 157.60/157.51 [6842]E(f866(a111,f866(f866(f41(a1),f866(f110(a1),x68421)),f866(f110(a1),x68422))),f866(f866(f41(a930),f866(f110(a930),x68421)),f866(f110(a930),x68422)))+P107(f866(a200,f866(f110(a1),x68421)))
% 157.60/157.51 [6898]P107(f866(f866(f244(a930),x68981),x68982))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f23(a930),x68982),x68981)))
% 157.60/157.51 [6942]P107(f866(f866(f244(a930),f2(a930)),x69421))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f87(a930),x69422),x69421)))
% 157.60/157.51 [6943]P107(f866(f866(f244(a930),f2(a930)),x69431))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f87(a930),x69431),x69432)))
% 157.60/157.51 [6962]~P107(f866(f866(f243(a1),x69621),f2(a1)))+E(f866(f866(f87(a930),f866(a111,f866(f85(a1),x69621))),f866(a111,f866(f85(a1),x69622))),f866(a111,f866(f866(f87(a1),x69621),x69622)))
% 157.60/157.51 [7016]~E(x70162,f195(f937(x70161,a925)))+P107(f866(f866(f243(f937(x70161,a925)),x70162),f866(f85(f937(x70161,a925)),x70162)))
% 157.60/157.51 [7079]~P96(x70791)+E(f866(f866(f86(x70791),f866(f866(f86(x70791),f2(x70791)),f866(f110(x70791),x70792))),f866(f110(x70791),x70792)),f866(f110(x70791),f866(f866(f86(a1),x70792),x70792)))
% 157.60/157.51 [7133]~P107(f866(f866(f244(a1),x71331),x71332))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x71331),f84(a1))),x71332))
% 157.60/157.51 [7199]E(x71991,f2(a930))+~P107(f866(f866(f243(a1),f866(f107(a1),x71992)),f866(f85(a1),f866(f107(a1),x71991))))
% 157.60/157.51 [7200]E(x72001,f2(a930))+~P107(f866(f866(f243(a1),f866(f107(a1),x72001)),f866(f85(a1),f866(f107(a1),x72002))))
% 157.60/157.51 [7300]E(f866(f866(f260(a1,a1),f866(f110(a1),a104)),f866(f866(f86(a1),x73001),x73002)),f55(x73001,x73002))+~P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),x73001),x73002)))
% 157.60/157.51 [7344]~P27(x73441,x73442)+P37(x73441,f866(f259(f937(f936(x73441,x73441),a925),f937(f936(x73441,x73441),a925)),x73442))
% 157.60/157.51 [7363]~P107(f866(f866(f243(a930),f866(a119,f2(a930))),x73631))+P107(f866(f866(f243(a930),f866(a119,f2(a930))),f866(f866(f252(a930),x73631),x73632)))
% 157.60/157.51 [7543]~P107(f866(f866(f243(a1),x75431),x75432))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x75431),x75431)),f866(f866(f86(a1),x75432),x75432)))
% 157.60/157.51 [7548]~P107(f866(f866(f244(a1),x75481),x75482))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x75481),x75481)),f866(f866(f86(a1),x75482),x75482)))
% 157.60/157.51 [7602]~P107(f866(f866(f244(a930),f2(a930)),x76021))+P107(f866(f866(f244(a930),f866(f866(f23(a930),x76021),f866(a119,x76022))),x76021))
% 157.60/157.51 [7635]P107(f866(f866(f243(a930),f866(a119,f2(a930))),x76351))+~P107(f866(f866(f243(a930),f866(a119,f2(a930))),f866(f866(f87(a930),x76352),x76351)))
% 157.60/157.51 [7636]P107(f866(f866(f243(a930),f866(a119,f2(a930))),x76361))+~P107(f866(f866(f243(a930),f866(a119,f2(a930))),f866(f866(f87(a930),x76361),x76362)))
% 157.60/157.51 [7640]P107(f866(f866(f243(a930),f866(f866(f171(a930),x76401),x76402)),f866(f172(a930),x76401)))+~P107(f866(f866(f244(a930),x76402),f866(f196(f931(a930)),x76401)))
% 157.60/157.51 [7678]P107(f866(f866(f244(a1),x76781),x76782))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x76781),f84(a1))),x76782))
% 157.60/157.51 [7720]P107(f866(f66(x77201),f250(f937(x77201,a925))))+~P107(f866(f66(f937(x77202,x77201)),f250(f937(f937(x77202,x77201),a925))))
% 157.60/157.51 [7721]P107(f866(f66(x77211),f250(f937(x77211,a925))))+~P107(f866(f66(f938(x77212,x77211)),f250(f937(f938(x77212,x77211),a925))))
% 157.60/157.51 [7722]P107(f866(f66(x77221),f250(f937(x77221,a925))))+~P107(f866(f66(f938(x77221,x77222)),f250(f937(f938(x77221,x77222),a925))))
% 157.60/157.51 [7760]E(x77601,f195(f937(x77602,a925)))+~P107(f866(f866(f243(f937(x77602,a925)),x77601),f866(f85(f937(x77602,a925)),x77601)))
% 157.60/157.51 [7897]E(f866(f149(f931(x78971),f931(x78971),f141(x78971),f120(x78971)),x78972),f120(x78971))+P107(f866(f866(f336(f931(x78971)),f704(x78972,x78971)),f866(f179(f931(x78971)),x78972)))
% 157.60/157.51 [7898]E(f866(f149(f931(x78981),f931(x78981),f141(x78981),f120(x78981)),x78982),f120(x78981))+P107(f866(f866(f336(f931(x78981)),f705(x78982,x78981)),f866(f179(f931(x78981)),x78982)))
% 157.60/157.51 [8131]P107(f866(f866(f243(a1),x81311),x81312))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x81311),x81311)),f866(f866(f86(a1),x81312),x81312)))
% 157.60/157.51 [8136]P107(f866(f866(f244(a1),x81361),x81362))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x81361),x81361)),f866(f866(f86(a1),x81362),x81362)))
% 157.60/157.51 [8229]~P114(x82291)+E(f866(f866(f87(x82291),f866(f866(f86(x82291),f84(x82291)),f84(x82291))),f866(f866(f6(a930,x82291),f107(x82291)),f310(a930,f84(a930),x82292))),f866(f866(f87(x82291),f866(f107(x82291),x82292)),f866(f866(f86(x82291),f866(f107(x82291),x82292)),f84(x82291))))
% 157.60/157.51 [8278]P107(f866(f866(f336(a930),x82781),x82782))+~P107(f866(f866(f336(a1),f866(f107(a1),x82781)),f866(f317(a930,a1,f107(a1)),x82782)))
% 157.60/157.51 [8430]~P107(f866(f66(x84301),x84302))+E(f866(f317(a930,x84301,f885(x84302,x84301)),f866(f270(a930),f866(f866(f7(a930,a930,a925),f244(a930)),f886(x84302,x84301)))),x84302)
% 157.60/157.51 [8708]P54(x87081,x87082)+P107(f866(f866(f336(f936(x87081,x87081)),f866(f866(f260(x87081,x87081),f501(x87082,x87081)),f501(x87082,x87081))),x87082))
% 157.60/157.51 [8709]P38(x87091,x87092)+P107(f866(f866(f336(f936(x87091,x87091)),f866(f866(f260(x87091,x87091),f799(x87092,x87091)),f802(x87092,x87091))),x87092))
% 157.60/157.51 [8710]P38(x87101,x87102)+P107(f866(f866(f336(f936(x87101,x87101)),f866(f866(f260(x87101,x87101),f802(x87102,x87101)),f803(x87102,x87101))),x87102))
% 157.60/157.51 [8711]P39(x87111,x87112)+P107(f866(f866(f336(f936(x87111,x87111)),f866(f866(f260(x87111,x87111),f714(x87112,x87111)),f713(x87112,x87111))),x87112))
% 157.60/157.51 [8712]P39(x87121,x87122)+P107(f866(f866(f336(f936(x87121,x87121)),f866(f866(f260(x87121,x87121),f713(x87122,x87121)),f714(x87122,x87121))),x87122))
% 157.60/157.51 [8713]P52(x87131,x87132)+P107(f866(f866(f336(f936(x87131,x87131)),f866(f866(f260(x87131,x87131),f814(x87132,x87131)),f815(x87132,x87131))),x87132))
% 157.60/157.51 [8855]~P96(x88551)+E(f866(f866(f23(x88551),f84(x88551)),f866(f110(x88551),x88552)),f866(f110(x88551),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f85(a1),x88552))))
% 157.60/157.51 [8980]~P107(f866(f866(f244(f937(a930,a925)),x89801),x89802))+P107(f866(f866(f244(f937(a1,a925)),f866(f317(a930,a1,f107(a1)),x89801)),f866(f317(a930,a1,f107(a1)),x89802)))
% 157.60/157.51 [9014]~P107(f866(f866(f244(a1),x90141),x90142))+P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x90141),x90141)),a104)),f866(f866(f86(a1),x90142),x90142)))
% 157.60/157.51 [9016]~P107(f866(f866(f244(a1),x90161),x90162))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x90161),x90161)),a104)),f866(f866(f86(a1),x90162),x90162)))
% 157.60/157.51 [9089]~P107(f866(f866(f336(a930),x90891),f866(f179(a930),x90892)))+P107(f866(f866(f243(a930),x90891),f866(f149(a930,a930,f86(a930),f2(a930)),x90892)))
% 157.60/157.51 [9184]P45(x91841,x91842)+~P107(f866(f866(f336(f936(x91841,x91841)),f866(f866(f260(x91841,x91841),f493(x91842,x91841)),f493(x91842,x91841))),x91842))
% 157.60/157.51 [9185]P38(x91851,x91852)+~P107(f866(f866(f336(f936(x91851,x91851)),f866(f866(f260(x91851,x91851),f799(x91852,x91851)),f803(x91852,x91851))),x91852))
% 157.60/157.51 [9186]P52(x91861,x91862)+~P107(f866(f866(f336(f936(x91861,x91861)),f866(f866(f260(x91861,x91861),f815(x91862,x91861)),f814(x91862,x91861))),x91862))
% 157.60/157.51 [9325]~P107(f866(f866(f243(f937(a1,a925)),f866(f317(a930,a1,f107(a1)),x93251)),f866(f317(a930,a1,f107(a1)),x93252)))+P107(f866(f866(f243(f937(a930,a925)),x93251),x93252))
% 157.60/157.51 [9326]~P107(f866(f866(f244(f937(a1,a925)),f866(f317(a930,a1,f107(a1)),x93261)),f866(f317(a930,a1,f107(a1)),x93262)))+P107(f866(f866(f244(f937(a930,a925)),x93261),x93262))
% 157.60/157.51 [9411]P107(f866(f866(f244(a1),x94111),x94112))+~P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x94111),x94111)),a104)),f866(f866(f86(a1),x94112),x94112)))
% 157.60/157.51 [9413]P107(f866(f866(f244(a1),x94131),x94132))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x94131),x94131)),a104)),f866(f866(f86(a1),x94132),x94132)))
% 157.60/157.51 [9484]~P24(a924,a940,f866(f866(f316(f929(a924)),f98(a924,x94841,a941,x94842)),f195(f937(f929(a924),a925))))+~P107(f866(f939(a331),f874(x94841,x94842)))
% 157.60/157.51 [9992]~P151(x99922,x99921)+P24(a924,a940,f866(f866(f316(f929(a924)),f98(a924,f866(f16(f937(a926,a925),a924),f866(f866(f7(a926,a926,a925),a332),x99921)),a941,f866(f16(f937(a926,a925),a924),f939(x99922)))),f195(f937(f929(a924),a925))))
% 157.60/157.51 [10286]~P105(x102861)+E(f123(f931(x102861),f866(f136(f931(x102861)),f120(x102861)),f866(f866(f866(f103(f932(f931(x102861))),f866(f866(f244(a1),f2(a1)),x102862)),f866(f125(f936(x102861,f931(x102861)),f931(x102861),f138(x102861,f931(x102861),f139(x102861,f866(f866(f23(a1),x102862),f84(a1))),f139(f931(x102861),f866(f866(f23(a1),x102862),f84(a1))))),f866(f265(x102861,f931(x102861),f932(f931(x102861))),f866(f866(f8(f937(f931(x102861),f931(x102861)),f937(f931(x102861),f932(f931(x102861))),x102861),f866(f8(f931(x102861),f932(f931(x102861)),f931(x102861)),f136(f931(x102861)))),f158(x102861))))),f122(f931(x102861)))),f139(f931(x102861),x102862))
% 157.60/157.51 [10308]~P107(f866(f66(x103081),x103082))+E(f866(f196(f931(x103081)),f96(f931(x103081),f866(f866(f18(f931(x103081),a925,a925),f866(f866(f8(a925,f937(a925,a925),f931(x103081)),a333),f866(f866(f7(f931(x103081),f937(x103081,a925),a925),f866(f866(f8(f937(x103081,a925),f937(f937(x103081,a925),a925),f931(x103081)),a332),f179(x103081))),x103082))),f144(x103081)))),f223(x103081,x103082))
% 157.60/157.51 [6326]E(f866(f866(f86(a930),f866(f866(f23(a930),x63261),x63262)),x63262),x63261)+~P107(f866(f866(f243(a930),x63262),x63261))
% 157.60/157.51 [6397]E(f866(f866(f41(a930),f866(f866(f87(a930),x63971),x63972)),x63972),x63971)+~P107(f866(f866(f244(a930),f2(a930)),x63972))
% 157.60/157.51 [6398]E(f866(f866(f41(a930),f866(f866(f87(a930),x63981),x63982)),x63981),x63982)+~P107(f866(f866(f244(a930),f2(a930)),x63981))
% 157.60/157.51 [6402]~P72(x64021)+E(f866(f866(f6(a930,x64021),f866(f171(x64021),x64022)),f866(f309(a930,f2(a930)),f866(f196(f931(x64021)),x64022))),f866(f172(x64021),x64022))
% 157.60/157.51 [6511]E(f50(a930,f866(a119,f866(f866(f87(a930),x65111),x65112)),x65111),f84(a930))+~P107(f866(f866(f244(a930),f84(a930)),x65111))
% 157.60/157.51 [6517]E(f866(a119,f866(f866(f86(a930),f866(f110(a930),x65171)),x65172)),f866(f866(f86(a930),f84(a930)),x65172))+~P107(f866(a200,f866(f110(a1),x65171)))
% 157.60/157.51 [6546]E(f866(a111,f866(f866(f252(a1),f866(f110(a1),x65461)),x65462)),f866(f866(f252(a930),f866(f110(a930),x65461)),x65462))+P107(f866(a200,f866(f110(a1),x65461)))
% 157.60/157.51 [6793]E(f866(f866(f23(a930),x67931),f866(f110(a930),f866(f866(f86(a1),x67932),a104))),f866(f866(f23(a930),f866(a119,x67931)),f866(f110(a930),x67932)))+~P107(f866(f866(f244(a1),a89),x67932))
% 157.60/157.51 [6872]E(x68721,f2(a930))+E(f866(a119,f866(f866(f86(a930),f866(f866(f23(a930),x68721),f84(a930))),x68722)),f866(f866(f86(a930),x68721),x68722))
% 157.60/157.51 [6911]E(x69111,f2(a1))+P107(f866(f866(f244(a1),f2(a1)),f866(f866(f252(a1),f866(f81(a1),x69111)),x69112)))
% 157.60/157.51 [6926]~E(x69262,f2(a930))+P107(f866(f866(f244(a1),f2(a1)),f866(f866(f252(a1),f866(f81(a1),x69261)),x69262)))
% 157.60/157.51 [6965]E(x69651,f2(a930))+E(f866(f866(f86(a930),x69652),f866(f866(f87(a930),f866(f866(f23(a930),x69651),f84(a930))),x69652)),f866(f866(f87(a930),x69651),x69652))
% 157.60/157.51 [7009]~P107(f866(f866(f243(a1),x70091),x70092))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x70091),a104)),x70092))
% 157.60/157.51 [7137]E(f866(f866(f158(a930),x71371),f146(a930,f866(f309(a930,f866(a119,x71371)),x71372))),f146(a930,f866(f309(a930,x71371),x71372)))+~P107(f866(f866(f244(a930),x71371),x71372))
% 157.60/157.51 [7335]E(x73351,x73352)+~E(f866(f866(f23(a1),f866(f866(f86(a1),x73351),x73351)),a104),f866(f866(f23(a1),f866(f866(f86(a1),x73352),x73352)),a104))
% 157.60/157.51 [7338]E(x73381,f120(x73382))+E(f274(x73382,f866(f866(f161(x73382,f936(a106,x73382)),f866(f260(a106,x73382),f84(a106))),x73381)),f283(x73382,x73381))
% 157.60/157.51 [7573]P107(f866(f866(f243(a1),x75731),x75732))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x75731),a104)),x75732))
% 157.60/157.51 [8038]~P107(f866(f866(f244(a930),x80381),x80382))+P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x80381),x80382)),a248))
% 157.60/157.51 [8255]~P107(f866(f866(f244(a106),f2(a106)),x82551))+P107(f866(f866(f244(a106),f866(f259(a106,f936(a106,a106)),f866(f275(x82551),x82552))),x82551))
% 157.60/157.51 [8511]~P38(x85111,x85112)+P38(x85111,f866(f866(f117(f937(f936(x85111,x85111),a925)),x85112),f314(x85111,f195(f937(f936(x85111,x85111),a925)))))
% 157.60/157.51 [8512]~P39(x85121,x85122)+P39(x85121,f866(f866(f117(f937(f936(x85121,x85121),a925)),x85122),f314(x85121,f195(f937(f936(x85121,x85121),a925)))))
% 157.60/157.51 [8561]~P89(x85611)+P107(f866(f866(f243(x85611),f866(f81(x85611),f866(f172(x85611),x85612))),f866(f172(x85611),f866(f866(f161(x85611,x85611),f81(x85611)),x85612))))
% 157.60/157.51 [8586]P107(f866(f866(f244(a930),x85861),x85862))+~P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),x85861),x85862)),a248))
% 157.60/157.51 [8732]E(f866(f866(f260(x87321,x87321),f595(x87322,x87321)),f595(x87322,x87321)),x87322)+~P107(f866(f866(f336(f936(x87321,x87321)),x87322),f314(x87321,f195(f937(f936(x87321,x87321),a925)))))
% 157.60/157.51 [8777]E(f866(f309(a930,x87771),f866(f866(f86(a930),x87771),f866(f40(a930),x87772))),x87772)+~P107(f866(f866(f243(f937(a930,a925)),x87772),f866(f309(a930,x87771),f866(f866(f86(a930),x87771),f866(f40(a930),x87772)))))
% 157.60/157.51 [9007]P39(x90071,x90072)+~P39(x90071,f866(f866(f117(f937(f936(x90071,x90071),a925)),x90072),f314(x90071,f195(f937(f936(x90071,x90071),a925)))))
% 157.60/157.51 [9135]E(f866(f866(f41(a1),f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x91351),x91351)),a104))),f866(f110(a1),f866(f866(f86(a1),x91352),x91352))),f866(f866(f41(a1),f866(f110(a1),x91351)),f866(f110(a1),x91352)))+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x91352)))
% 157.60/157.51 [9229]~P38(x92291,x92292)+P107(f866(f866(f243(f937(f936(x92291,x92291),a925)),f866(f866(f296(x92291,x92291,x92291),x92292),x92292)),x92292))
% 157.60/157.51 [9255]E(f184(f931(x92551),f866(f866(f8(a925,a925,f931(x92551)),a329),f866(f866(f7(f931(x92551),f931(x92551),a925),a332),f120(x92551))),x92552),f186(x92551,f186(x92551,x92552)))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x92551),a930),f196(f931(x92551))),x92552)))
% 157.60/157.51 [9258]E(f866(f866(f41(a1),f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x92581),x92581)),a104))),f866(f110(a1),f866(f866(f86(a1),x92582),x92582))),f866(f866(f41(a1),f866(f866(f86(a1),f866(f110(a1),x92581)),f84(a1))),f866(f110(a1),x92582)))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x92582)))
% 157.60/157.51 [10094]P107(f866(a200,x100942))+E(f866(f866(f92(a1,a930),f866(f866(f23(a1),x100941),x100942)),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f2(a930))),a111)),f866(f866(f23(a930),f866(a111,x100941)),f866(a111,x100942)))
% 157.60/157.51 [10102]E(f866(f866(f92(a1,a930),f866(f110(a1),f866(f866(f86(a1),x101021),f866(f85(a1),x101022)))),f866(f866(f18(a1,a930,a930),f866(f866(f7(a1,a930,f937(a930,a930)),f866(f866(f8(a925,f937(a930,f937(a930,a930)),a1),f103(a930)),a200)),f2(a930))),a111)),f866(f866(f23(a930),f866(f110(a930),x101021)),f866(f110(a930),x101022)))+P107(f866(f866(f244(a1),x101022),a89))
% 157.60/157.51 [10103]~P27(x101031,x101032)+P107(f866(f866(f243(f937(f936(x101031,x101031),a925)),f866(f866(f296(x101031,x101031,x101031),f866(f259(f937(f936(x101031,x101031),a925),f937(f936(x101031,x101031),a925)),x101032)),f866(f264(f937(f936(x101031,x101031),a925),f937(f936(x101031,x101031),a925)),x101032))),f866(f259(f937(f936(x101031,x101031),a925),f937(f936(x101031,x101031),a925)),x101032)))
% 157.60/157.51 [10159]~E(f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,f937(a930,a925),a925),f336(a930)),x101591))),f866(f866(f7(a930,a930,a925),f244(a930)),f866(a119,x101592))))),f2(a930))+~P107(f866(f866(f336(a930),f2(a930)),x101591))
% 157.60/157.51 [10216]E(f50(a1,f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x102161),x102161)),a104)),f866(f110(a1),f866(f866(f86(a1),x102162),x102162))),f866(f866(f86(a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a1,f866(f110(a1),x102161),f866(f110(a1),x102162)))),f84(a1)))+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x102162)))
% 157.60/157.51 [10225]E(f50(a1,f866(f110(a1),f866(f866(f23(a1),f866(f866(f86(a1),x102251),x102251)),a104)),f866(f110(a1),f866(f866(f86(a1),x102252),x102252))),f866(f866(f23(a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a1,f866(f866(f86(a1),f866(f110(a1),x102251)),f84(a1)),f866(f110(a1),x102252)))),f84(a1)))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x102252)))
% 157.60/157.51 [10275]~P5(x102751)+E(f42(x102751,f866(f270(x102751),f866(f866(f8(f937(x102751,a925),a925,x102751),f94(x102751)),f866(f866(f8(f937(x102751,a925),f937(x102751,a925),x102751),f866(f18(x102751,a925,a925),f866(f866(f8(a925,f937(a925,a925),x102751),a337),f866(f866(f7(x102751,f937(x102751,a925),a925),f336(x102751)),x102752)))),f243(x102751))))),f43(x102751,x102752))
% 157.60/157.51 [10301]~P37(x103011,x103012)+P61(x103011,f866(f866(f7(x103011,f937(f936(x103011,x103011),a925),f937(x103011,a925)),f866(f866(f8(f937(x103011,f937(f937(f936(x103011,x103011),a925),a925)),f937(f937(f936(x103011,x103011),a925),f937(x103011,a925)),x103011),f7(x103011,f937(f936(x103011,x103011),a925),a925)),f866(f866(f8(f937(x103011,f936(x103011,x103011)),f937(x103011,f937(f937(f936(x103011,x103011),a925),a925)),x103011),f866(f8(f936(x103011,x103011),f937(f937(f936(x103011,x103011),a925),a925),x103011),f336(f936(x103011,x103011)))),f260(x103011,x103011)))),x103012))
% 157.60/157.51 [10302]~P8(x103021,f250(f937(x103021,a925)),x103022)+P7(x103021,f866(f866(f7(x103021,f937(f936(x103021,x103021),a925),f937(x103021,a925)),f866(f866(f8(f937(x103021,f937(f937(f936(x103021,x103021),a925),a925)),f937(f937(f936(x103021,x103021),a925),f937(x103021,a925)),x103021),f7(x103021,f937(f936(x103021,x103021),a925),a925)),f866(f866(f8(f937(x103021,f936(x103021,x103021)),f937(x103021,f937(f937(f936(x103021,x103021),a925),a925)),x103021),f866(f8(f936(x103021,x103021),f937(f937(f936(x103021,x103021),a925),a925),x103021),f336(f936(x103021,x103021)))),f260(x103021,x103021)))),x103022))
% 157.60/157.51 [10345]P37(x103451,x103452)+~P61(x103451,f866(f866(f7(x103451,f937(f936(x103451,x103451),a925),f937(x103451,a925)),f866(f866(f8(f937(x103451,f937(f937(f936(x103451,x103451),a925),a925)),f937(f937(f936(x103451,x103451),a925),f937(x103451,a925)),x103451),f7(x103451,f937(f936(x103451,x103451),a925),a925)),f866(f866(f8(f937(x103451,f936(x103451,x103451)),f937(x103451,f937(f937(f936(x103451,x103451),a925),a925)),x103451),f866(f8(f936(x103451,x103451),f937(f937(f936(x103451,x103451),a925),a925),x103451),f336(f936(x103451,x103451)))),f260(x103451,x103451)))),x103452))
% 157.60/157.51 [10346]P8(x103461,f250(f937(x103461,a925)),x103462)+~P7(x103461,f866(f866(f7(x103461,f937(f936(x103461,x103461),a925),f937(x103461,a925)),f866(f866(f8(f937(x103461,f937(f937(f936(x103461,x103461),a925),a925)),f937(f937(f936(x103461,x103461),a925),f937(x103461,a925)),x103461),f7(x103461,f937(f936(x103461,x103461),a925),a925)),f866(f866(f8(f937(x103461,f936(x103461,x103461)),f937(x103461,f937(f937(f936(x103461,x103461),a925),a925)),x103461),f866(f8(f936(x103461,x103461),f937(f937(f936(x103461,x103461),a925),a925),x103461),f336(f936(x103461,x103461)))),f260(x103461,x103461)))),x103462))
% 157.60/157.51 [7523]E(f866(f866(f86(a930),f866(f110(a930),f866(f866(f23(a1),x75231),a104))),x75232),f866(a119,f866(f866(f86(a930),f866(f110(a930),x75231)),x75232)))+P107(f866(a200,f866(f110(a1),x75231)))
% 157.60/157.51 [7954]~P96(x79541)+E(f866(f866(f86(x79541),f866(f866(f86(x79541),f84(x79541)),f866(f110(x79541),x79542))),f866(f110(x79541),x79542)),f866(f110(x79541),f866(f866(f23(a1),f866(f866(f86(a1),x79542),x79542)),a104)))
% 157.60/157.51 [8588]~P107(f866(f866(f243(a1),x85881),x85882))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x85881),x85881)),f866(f866(f23(a1),f866(f866(f86(a1),x85882),x85882)),a104)))
% 157.60/157.51 [8590]~P107(f866(f866(f243(a1),x85901),x85902))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x85901),x85901)),f866(f866(f23(a1),f866(f866(f86(a1),x85902),x85902)),a104)))
% 157.60/157.51 [9018]P107(f866(f866(f243(a1),x90181),x90182))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x90181),x90181)),f866(f866(f23(a1),f866(f866(f86(a1),x90182),x90182)),a104)))
% 157.60/157.51 [9020]P107(f866(f866(f243(a1),x90201),x90202))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),x90201),x90201)),f866(f866(f23(a1),f866(f866(f86(a1),x90202),x90202)),a104)))
% 157.60/157.51 [9314]~P107(f866(f866(f243(a1),x93141),x93142))+P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93141),x93141)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x93142),x93142)),a104)))
% 157.60/157.51 [9316]~P107(f866(f866(f244(a1),x93161),x93162))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x93161),x93161)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x93162),x93162)),a104)))
% 157.60/157.51 [9583]P107(f866(f866(f243(a1),x95831),x95832))+~P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),x95831),x95831)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x95832),x95832)),a104)))
% 157.60/157.51 [9585]P107(f866(f866(f244(a1),x95851),x95852))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),x95851),x95851)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),x95852),x95852)),a104)))
% 157.60/157.51 [9618]~P107(f866(f66(x96181),x96182))+P107(f866(f66(f937(x96181,a925)),f866(f270(f937(x96181,a925)),f866(f866(f7(f937(x96181,a925),f937(x96181,a925),a925),f243(f937(x96181,a925))),x96182))))
% 157.60/157.51 [9667]~E(f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),x96671),f195(f937(f936(a930,a930),a925)))),f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),x96672),f195(f937(f936(a930,a930),a925)))))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x96671),x96672)),a115))
% 157.60/157.51 [9753]E(f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),x97531),f195(f937(f936(a930,a930),a925)))),f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),x97532),f195(f937(f936(a930,a930),a925)))))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x97531),x97532)),a115))
% 157.60/157.51 [9789]P107(f866(f866(f243(a1),f2(a1)),f646(x97891,x97892)))+E(f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97891)),f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97892)))
% 157.60/157.51 [10283]~P5(x102831)+E(f43(x102831,f866(f270(x102831),f866(f866(f8(f937(x102831,a925),a925,x102831),f94(x102831)),f866(f866(f8(f937(x102831,a925),f937(x102831,a925),x102831),f866(f18(x102831,a925,a925),f866(f866(f8(a925,f937(a925,a925),x102831),a337),f866(f866(f7(x102831,f937(x102831,a925),a925),f336(x102831)),x102832)))),f866(f7(x102831,x102831,a925),f243(x102831)))))),f42(x102831,x102832))
% 157.60/157.51 [10307]P107(f866(f866(f336(a930),f2(a930)),x103071))+E(f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),a930),f336(a930)),a119)),x103071))),f866(f866(f7(a930,a930,a925),f244(a930)),x103072)))),f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,f937(a930,a925),a925),f336(a930)),x103071))),f866(f866(f7(a930,a930,a925),f244(a930)),f866(a119,x103072))))))
% 157.60/157.51 [7825]~P96(x78251)+E(f866(f866(f87(x78251),x78252),f866(f110(x78251),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),x78252)
% 157.60/157.51 [8083]~P96(x80831)+E(f866(f866(f86(x80831),f866(f110(x80831),x80832)),f84(x80831)),f866(f110(x80831),f866(f866(f86(a1),x80832),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))
% 157.60/157.51 [8227]P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x82272)))+E(f866(f866(f252(a1),x82271),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x82272),x82272)),a104))),f84(a1))
% 157.60/157.51 [9643]~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x96432)))+E(f866(f866(f252(a1),x96431),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x96432),x96432)),a104))),f866(f866(f92(a1,a1),f866(f866(f252(a1),x96431),f866(f110(a930),x96432))),f866(f866(f18(a1,a1,a1),f866(f866(f8(a1,f937(a1,a1),a1),f87(a1)),f866(f87(a1),x96431))),f5(a1))))
% 157.60/157.51 [10013]~P107(f866(f866(f243(a930),f658(x100132,x100131)),f866(x100131,f658(x100132,x100131))))+P107(f866(f66(a930),f866(f270(a930),f866(f866(f7(a930,a930,a925),f866(f866(f8(a930,f937(a930,a925),a930),f243(a930)),x100131)),x100132))))
% 157.60/157.51 [10149]~P107(f866(f866(f243(a930),f866(f110(a930),x101491)),f866(a119,x101492)))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x101491),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),f243(a930)),a111)),x101492))))
% 157.60/157.51 [10150]~P107(f866(f866(f244(a930),f866(f110(a930),x101501)),f866(a119,x101502)))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x101501),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),f244(a930)),a111)),x101502))))
% 157.60/157.51 [10200]P107(f866(f866(f243(a930),f866(f110(a930),x102001)),f866(a119,x102002)))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102001),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),f243(a930)),a111)),x102002))))
% 157.60/157.51 [10201]P107(f866(f866(f244(a930),f866(f110(a930),x102011)),f866(a119,x102012)))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102011),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),f244(a930)),a111)),x102012))))
% 157.60/157.51 [10231]~P107(f866(f866(f243(a930),f866(a119,x102312)),f866(f110(a930),x102311)))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102311),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f8(a930,a925,a1),f866(f243(a930),x102312)),a111)))))
% 157.60/157.51 [10232]~P107(f866(f866(f244(a930),f866(a119,x102322)),f866(f110(a930),x102321)))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102321),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f8(a930,a925,a1),f866(f244(a930),x102322)),a111)))))
% 157.60/157.51 [10273]P107(f866(f866(f243(a930),f866(a119,x102731)),f866(f110(a930),x102732)))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102732),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f8(a930,a925,a1),f866(f243(a930),x102731)),a111)))))
% 157.60/157.51 [10274]P107(f866(f866(f244(a930),f866(a119,x102741)),f866(f110(a930),x102742)))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102742),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f8(a930,a925,a1),f866(f244(a930),x102741)),a111)))))
% 157.60/157.51 [10355]~P107(f866(f866(f336(a930),f2(a930)),x103551))+E(f866(a119,f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,f937(a930,a925),a925),f866(f866(f8(a930,f937(f937(a930,a925),a925),a930),f336(a930)),a119)),x103551))),f866(f866(f7(a930,a930,a925),f244(a930)),x103552))))),f866(f40(a930),f866(f270(a930),f866(f866(f18(a930,a925,a925),f866(f866(f8(a925,f937(a925,a925),a930),a333),f866(f866(f7(a930,f937(a930,a925),a925),f336(a930)),x103551))),f866(f866(f7(a930,a930,a925),f244(a930)),f866(a119,x103552))))))
% 157.60/157.51 [8760]~P96(x87601)+E(f866(f866(f87(x87601),f866(f110(x87601),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),x87602),x87602)
% 157.60/157.51 [8821]~P96(x88211)+E(f866(f866(f86(x88211),f84(x88211)),f866(f110(x88211),x88212)),f866(f110(x88211),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),x88212)))
% 157.60/157.51 [8883]~P96(x88831)+E(f866(f866(f23(x88831),f866(f110(x88831),x88832)),f84(x88831)),f866(f110(x88831),f866(f866(f86(a1),x88832),f866(f85(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.51 [9037]~P107(f866(f866(f244(a930),f866(f110(a930),a89)),x90372))+E(f866(f866(f23(a930),x90371),f866(f866(f23(a930),x90372),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f23(a930),f866(a119,x90371)),x90372))
% 157.60/157.51 [9685]~P114(x96851)+E(f866(f866(f87(x96851),x96852),x96852),f866(f866(f252(x96851),x96852),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.51 [9686]~P81(x96861)+E(f866(f866(f252(x96861),x96862),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f87(x96861),x96862),x96862))
% 157.60/157.51 [9688]~P96(x96881)+E(f866(f866(f87(x96881),x96882),f866(f110(x96881),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f86(x96881),x96882),x96882))
% 157.60/157.51 [9929]~P128(x99291)+E(f866(f866(f252(x99291),f866(f81(x99291),x99292)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f252(x99291),x99292),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.51 [9930]~P142(x99301)+E(f866(f866(f252(x99301),f866(f85(x99301),x99302)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f252(x99301),x99302),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.51 [9926]~P96(x99261)+E(f866(f866(f87(x99261),f866(f110(x99261),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x99262),f866(f866(f86(x99261),x99262),x99262))
% 157.60/157.51 [10046]~P128(x100461)+E(f866(f81(x100461),f866(f866(f252(x100461),x100462),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x100461),x100462),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.51 [10110]~P128(x101101)+P107(f866(f866(f243(x101101),f2(x101101)),f866(f866(f252(x101101),x101102),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.60/157.51 [10264]~E(f866(a119,x102642),f866(f110(a930),x102641))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102641),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),a332),a111)),x102642)))))
% 157.60/157.51 [10265]~E(f866(f110(a930),x102651),f866(a119,x102652))+P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x102651),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),a332),a111)),x102652)))))
% 157.60/157.51 [10310]E(f866(a119,x103101),f866(f110(a930),x103102))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x103102),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),a332),a111)),x103101)))))
% 157.60/157.51 [10311]E(f866(f110(a930),x103111),f866(a119,x103112))+~P107(f866(f866(f92(a1,a925),f866(f110(a1),f866(f866(f86(a1),x103111),a104))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a337),f866(f866(f8(a925,a925,a1),a329),a200))),f866(f866(f7(a1,a930,a925),f866(f866(f8(a930,f937(a930,a925),a1),a332),a111)),x103112)))))
% 157.60/157.51 [10356]~P15(x103561,x103562)+P107(f866(f866(f336(f937(x103561,a925)),f822(x103562,x103561)),f866(f866(f8(f937(x103561,a925),a925,f937(x103561,a925)),f93(x103561)),f866(f866(f8(f937(x103561,a925),f937(x103561,a925),f937(x103561,a925)),f866(f18(x103561,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103561),a333),f866(f866(f18(x103561,x103561,a925),x103562),f5(x103561))))),f866(f866(f7(f937(x103561,a925),f937(x103561,f937(x103561,a925)),f937(x103561,a925)),f866(f866(f8(f937(f937(x103561,a925),a925),f937(f937(x103561,f937(x103561,a925)),f937(x103561,a925)),f937(x103561,a925)),f8(f937(x103561,a925),a925,x103561)),a332)),x103562)))))
% 157.60/157.51 [10108]~P96(x101081)+E(f866(f866(f252(x101081),f866(f110(x101081),a104)),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101082)),f84(x101081))
% 157.60/157.51 [10109]~P142(x101091)+E(f866(f866(f252(x101091),f866(f85(x101091),f84(x101091))),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101092)),f84(x101091))
% 157.60/157.51 [10112]~P81(x101121)+E(f866(f866(f252(x101121),x101122),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),a104))),f866(f866(f87(x101121),f866(f866(f87(x101121),x101122),x101122)),x101122))
% 157.60/157.51 [10290]~P107(f866(f866(f243(a1),f2(a1)),x102902))+E(f50(a1,f866(f866(f86(a1),f84(a1)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x102901)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x102902)),f866(f866(f86(a1),f84(a1)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a1,x102901,x102902))))
% 157.60/157.51 [10313]~P107(f866(f866(f243(a1),f2(a1)),x103132))+E(f866(f866(f41(a1),f866(f866(f86(a1),f84(a1)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103131))),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103132)),f866(f866(f41(a1),x103131),x103132))
% 157.60/157.51 [10315]~P107(f866(f866(f243(a1),x103152),f2(a1)))+E(f866(f866(f41(a1),f866(f866(f86(a1),f84(a1)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103151))),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103152)),f866(f866(f41(a1),f866(f866(f86(a1),x103151),f84(a1))),x103152))
% 157.60/157.51 [10316]~P107(f866(f866(f243(a1),x103162),f2(a1)))+E(f50(a1,f866(f866(f86(a1),f84(a1)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103161)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103162)),f866(f866(f23(a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f50(a1,f866(f866(f86(a1),x103161),f84(a1)),x103162))),f84(a1)))
% 157.60/157.51 [10191]~P96(x101911)+E(f866(f866(f252(x101911),f866(f110(x101911),a104)),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101912))),f866(f110(x101911),a104))
% 157.60/157.51 [10193]~P142(x101931)+E(f866(f866(f252(x101931),f866(f85(x101931),f84(x101931))),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101932))),f866(f85(x101931),f84(x101931)))
% 157.60/157.51 [5187]P38(x51871,x51872)+~P8(x51871,x51873,x51872)
% 157.60/157.51 [5189]P52(x51891,x51892)+~P8(x51891,x51893,x51892)
% 157.60/157.51 [5358]~P8(x53581,x53582,x53583)+P53(x53581,x53582,x53583)
% 157.60/157.51 [8293]~E(x82932,x82933)+P34(x82931,x82931,a332,x82932,x82933)
% 157.60/157.51 [8834]E(x88341,x88342)+~P34(x88343,x88343,a332,x88341,x88342)
% 157.60/157.51 [4994]E(f176(x49941,x49942,x49943),f120(x49941))+~E(x49942,f2(a930))
% 157.60/157.51 [5163]~E(f176(x51632,x51631,x51633),f120(x51632))+E(x51631,f2(a930))
% 157.60/157.51 [5363]~P37(x53631,x53633)+P37(x53631,f328(x53631,x53632,x53633))
% 157.60/157.51 [5475]~P29(x54751,x54752,x54753)+P31(a1,x54751,f185(x54752,x54753))
% 157.60/157.51 [5547]P29(x55471,x55472,x55473)+~P31(a1,x55471,f185(x55472,x55473))
% 157.60/157.51 [5617]~P8(x56171,x56172,x56173)+P8(f931(x56171),f168(x56171,x56172),f165(x56171,x56173))
% 157.60/157.51 [5618]~P53(x56181,x56182,x56183)+P53(f931(x56181),f168(x56181,x56182),f165(x56181,x56183))
% 157.60/157.51 [5729]P56(x57291,x57292,x57293)+~E(f569(x57293,x57292,x57291),f570(x57293,x57292,x57291))
% 157.60/157.51 [5730]P55(x57301,x57302,x57303)+~E(f584(x57303,x57302,x57301),f585(x57303,x57302,x57301))
% 157.60/157.51 [8299]~E(x82992,x82993)+P26(x82991,x82991,f32(x82991),x82992,x82993)
% 157.60/157.51 [8842]E(x88421,x88422)+~P26(x88423,x88423,f32(x88423),x88421,x88422)
% 157.60/157.51 [4949]~E(f866(f175(x49492),x49491),x49493)+E(x49491,f866(f175(x49492),x49493))
% 157.60/157.51 [4950]~E(x49502,f866(f175(x49501),x49503))+E(f866(f175(x49501),x49502),x49503)
% 157.60/157.51 [5000]E(x50001,x50002)+~E(f866(f175(x50003),x50001),f866(f175(x50003),x50002))
% 157.60/157.51 [5213]~P7(x52133,x52131)+P107(f866(f866(x52131,x52132),x52132))
% 157.60/157.51 [5214]~P48(x52143,x52141)+P107(f866(f866(x52141,x52142),x52142))
% 157.60/157.51 [5216]~P61(x52161,x52162)+P107(f866(f322(x52161,x52162),x52163))
% 157.60/157.51 [5280]~P37(x52801,x52802)+P37(f931(x52801),f866(f150(x52801,x52802),x52803))
% 157.60/157.51 [5285]~P107(f866(x52852,x52853))+~E(f866(f270(x52851),x52852),f195(f937(x52851,a925)))
% 157.60/157.51 [5286]~P107(f866(x52862,x52863))+~E(f195(f937(x52861,a925)),f866(f270(x52861),x52862))
% 157.60/157.51 [5298]E(x52981,f2(a930))+E(f151(x52982,f176(x52982,x52981,x52983)),x52983)
% 157.60/157.51 [5316]~P107(f866(x53161,x53163))+P107(f866(x53161,f96(x53162,x53161)))
% 157.60/157.51 [5317]~P107(f866(x53171,x53173))+P107(f866(x53171,f745(x53171,x53172)))
% 157.60/157.51 [5329]E(x53291,f2(a930))+E(f866(f148(x53292),f176(x53292,x53291,x53293)),x53293)
% 157.60/157.51 [5435]~E(x54352,x54353)+P107(f866(f866(f336(x54351),x54352),f866(a332,x54353)))
% 157.60/157.51 [5451]~E(x54512,f2(a930))+E(f866(f179(x54511),f176(x54511,x54512,x54513)),f195(f937(x54511,a925)))
% 157.60/157.51 [5497]E(f866(f175(x54971),x54972),f866(f866(f158(x54971),x54973),f120(x54971)))+~E(x54972,f866(f866(f158(x54971),x54973),f120(x54971)))
% 157.60/157.51 [5498]~E(x54983,f866(f866(f158(x54981),x54982),f120(x54981)))+E(f866(f866(f158(x54981),x54982),f120(x54981)),f866(f175(x54981),x54983))
% 157.60/157.51 [5543]~P33(x55431,x55432,x55433)+P33(x55431,x55432,f866(f175(x55431),x55433))
% 157.60/157.51 [5544]~P31(x55441,x55442,x55443)+P31(x55441,x55442,f866(f175(x55441),x55443))
% 157.60/157.51 [5548]E(f866(f40(x55481),f867(x55482,x55483,x55481)),x55482)+~E(f866(f40(x55481),x55483),f866(a119,x55482))
% 157.60/157.51 [5555]~P37(x55551,x55553)+P107(f866(f866(f336(x55551),x55552),f323(x55551,x55553)))
% 157.60/157.51 [5559]~E(f866(f175(x55592),x55591),f866(f866(f158(x55592),x55593),f120(x55592)))+E(x55591,f866(f866(f158(x55592),x55593),f120(x55592)))
% 157.60/157.51 [5560]~E(f866(f866(f158(x55602),x55603),f120(x55602)),f866(f175(x55602),x55601))+E(x55601,f866(f866(f158(x55602),x55603),f120(x55602)))
% 157.60/157.51 [5583]E(f91(f936(a930,a930),f53(x55831,x55832)),x55833)+~P107(f866(f53(x55831,x55832),x55833))
% 157.60/157.51 [5621]P33(x56211,x56212,x56213)+~P33(x56211,x56212,f866(f175(x56211),x56213))
% 157.60/157.51 [5622]P31(x56221,x56222,x56223)+~P31(x56221,x56222,f866(f175(x56221),x56223))
% 157.60/157.51 [5660]P107(f866(f866(x56601,x56602),x56602))+~P107(f866(f278(x56603,x56601),x56602))
% 157.60/157.51 [5661]~P107(f866(f866(x56612,x56613),x56613))+P107(f866(f278(x56611,x56612),x56613))
% 157.60/157.51 [5683]~E(x56832,f120(x56831))+P107(f866(f866(f336(f931(x56831)),x56832),f168(x56831,x56833)))
% 157.60/157.51 [5692]~P53(x56921,x56922,x56923)+P53(x56921,x56922,f866(f294(x56921,x56921),x56923))
% 157.60/157.51 [5693]~P56(x56931,x56932,x56933)+P56(x56931,x56932,f866(f294(x56931,x56931),x56933))
% 157.60/157.51 [5710]~P62(x57101)+E(f50(x57101,f50(x57101,x57102,x57103),x57103),f50(x57101,x57102,x57103))
% 157.60/157.51 [5815]E(x58151,x58152)+~P107(f866(f866(f336(x58153),x58151),f866(a332,x58152)))
% 157.60/157.51 [5864]~P148(x58641)+E(f197(x58641,x58642,f2(a930),x58643),x58643)
% 157.60/157.51 [5886]P53(x58861,x58862,x58863)+~P53(x58861,x58862,f866(f294(x58861,x58861),x58863))
% 157.60/157.51 [5887]P56(x58871,x58872,x58873)+~P56(x58871,x58872,f866(f294(x58871,x58871),x58873))
% 157.60/157.51 [5891]~P110(x58912)+E(f157(x58911,x58912,x58913,f120(x58911)),f120(x58911))
% 157.60/157.51 [5903]E(f177(x59031,x59032,f159(x59031,x59033)),f159(x59031,f177(x59031,x59032,x59033)))+~P107(f866(f144(x59031),x59033))
% 157.60/157.51 [6004]~P107(f866(f866(x60043,x60042),x60042))+P107(f866(f866(f336(x60041),x60042),f278(x60041,x60043)))
% 157.60/157.51 [6006]E(f866(f143(x60061,x60062),x60063),f120(x60061))+P107(f866(x60062,f680(x60063,x60062,x60061)))
% 157.60/157.51 [6065]E(f73(x60651,x60652,x60653),x60652)+P107(f866(x60653,f746(x60652,x60651,x60653)))
% 157.60/157.51 [6160]~P107(f866(f144(x61601),x61602))+P107(f866(f144(x61601),f183(x61601,x61602,x61603)))
% 157.60/157.51 [6161]~P107(f866(f144(x61611),x61613))+P107(f866(f144(x61611),f177(x61611,x61612,x61613)))
% 157.60/157.51 [6162]~P107(f866(f144(x61621),x61623))+P107(f866(f144(x61621),f184(x61621,x61622,x61623)))
% 157.60/157.51 [6163]~P107(f866(f144(x61631),x61633))+P107(f866(f144(x61631),f147(x61631,x61632,x61633)))
% 157.60/157.51 [6164]~P149(x61641,x61642,x61643)+P107(f866(x61641,f50(a1,x61642,x61643)))
% 157.60/157.51 [6180]~P33(x61803,x61801,x61802)+P107(f866(x61801,f764(x61802,x61801,x61803)))
% 157.60/157.51 [6181]~P35(x61813,x61811,x61812)+P107(f866(x61811,f774(x61812,x61811,x61813)))
% 157.60/157.51 [6182]~P35(x61823,x61821,x61822)+P107(f866(x61821,f777(x61822,x61821,x61823)))
% 157.60/157.51 [6183]~P33(x61833,x61831,x61832)+P107(f866(x61831,f806(x61831,x61832,x61833)))
% 157.60/157.51 [6184]~P33(x61843,x61841,x61842)+P107(f866(x61841,f807(x61842,x61841,x61843)))
% 157.60/157.51 [6188]P107(f866(f866(x61881,x61882),x61882))+~P107(f866(f866(f336(x61883),x61882),f278(x61883,x61881)))
% 157.60/157.51 [6203]E(f866(f143(x62031,x62032),x62033),f184(x62031,x62032,x62033))+P107(f866(x62032,f730(x62033,x62032,x62031)))
% 157.60/157.51 [6243]~P107(f866(f144(x62431),x62433))+P107(f866(f144(f931(x62431)),f60(x62431,x62432,x62433)))
% 157.60/157.51 [6279]~P111(x62791)+E(f866(f866(f108(f937(x62791,a925)),f866(f290(x62791),x62792)),f310(x62791,x62792,x62793)),f195(f937(x62791,a925)))
% 157.60/157.51 [6280]~P111(x62801)+E(f866(f866(f108(f937(x62801,a925)),f866(f308(x62801),x62802)),f313(x62801,x62802,x62803)),f195(f937(x62801,a925)))
% 157.60/157.51 [6281]~P111(x62811)+E(f866(f866(f108(f937(x62811,a925)),f866(f308(x62811),x62812)),f312(x62811,x62812,x62813)),f195(f937(x62811,a925)))
% 157.60/157.51 [6507]E(f866(f143(x65071,x65072),x65073),x65073)+~P107(f866(x65072,f681(x65073,x65072,x65071)))
% 157.60/157.51 [6509]E(f866(f866(f316(x65091),f904(x65092,x65093,x65091)),f867(x65092,x65093,x65091)),x65093)+~E(f866(f40(x65091),x65093),f866(a119,x65092))
% 157.60/157.51 [6524]P149(x65241,x65242,x65243)+~P107(f866(x65241,f50(a1,x65242,x65243)))
% 157.60/157.51 [6573]P31(x65731,x65732,x65733)+~P107(f866(x65732,f766(x65733,x65732,x65731)))
% 157.60/157.51 [6574]P31(x65741,x65742,x65743)+~P107(f866(x65742,f775(x65742,x65743,x65741)))
% 157.60/157.51 [6575]P31(x65751,x65752,x65753)+~P107(f866(x65752,f776(x65753,x65752,x65751)))
% 157.60/157.51 [6576]P29(x65761,x65762,x65763)+~P107(f866(x65761,f790(x65763,x65762,x65761)))
% 157.60/157.51 [6577]P30(x65771,x65772,x65773)+~P107(f866(x65771,f835(x65773,x65772,x65771)))
% 157.60/157.51 [6580]E(f184(x65801,x65802,x65803),x65803)+~P107(f866(x65802,f725(x65803,x65802,x65801)))
% 157.60/157.51 [6661]~P107(f866(x66612,f556(x66613,x66612,x66611)))+P107(f866(f256(x66611,x66612),x66613))
% 157.60/157.51 [6662]~P107(f866(x66622,f682(x66623,x66622,x66621)))+P107(f866(f167(x66621,x66622),x66623))
% 157.60/157.51 [6912]~P107(f866(f322(x69121,x69122),f486(x69123,x69122,x69121)))+P107(f866(f322(x69121,x69122),x69123))
% 157.60/157.51 [6913]~P107(f866(f322(x69131,x69132),f500(x69133,x69132,x69131)))+P107(f866(f322(x69131,x69132),x69133))
% 157.60/157.51 [7524]~P62(x75241)+E(f866(f866(f86(x75241),f866(f866(f87(x75241),x75242),f866(f866(f41(x75241),x75243),x75242))),f50(x75241,x75243,x75242)),x75243)
% 157.60/157.51 [7553]P29(x75531,x75532,x75533)+P107(f866(f866(f336(a1),f790(x75533,x75532,x75531)),f310(a1,x75532,x75533)))
% 157.60/157.51 [7976]E(f866(f866(f260(x79761,x79761),f517(x79762,x79763,x79761)),f517(x79762,x79763,x79761)),x79763)+~P107(f866(f866(f336(f936(x79761,x79761)),x79763),f271(x79761,x79762)))
% 157.60/157.51 [8091]~P107(f866(f866(f336(x80911),f519(x80913,x80912,x80911)),f323(x80911,x80913)))+P107(f866(f866(f336(x80911),x80912),f323(x80911,x80913)))
% 157.60/157.51 [8092]~P107(f866(f866(f336(x80921),f571(x80923,x80922,x80921)),f323(x80921,x80923)))+P107(f866(f866(f336(x80921),x80922),f323(x80921,x80923)))
% 157.60/157.51 [8093]~P107(f866(f866(f336(x80931),f572(x80933,x80932,x80931)),f323(x80931,x80933)))+P107(f866(f866(f336(x80931),x80932),f323(x80931,x80933)))
% 157.60/157.51 [8185]P33(a1,x81851,f185(x81852,x81853))+P29(f866(f78(a925,a925,a1,a329),x81851),x81852,x81853)
% 157.60/157.51 [8274]~P62(x82741)+E(f866(f866(f86(x82741),f866(f866(f87(x82741),f866(f866(f41(x82741),x82742),x82743)),x82743)),f50(x82741,x82742,x82743)),x82742)
% 157.60/157.51 [8320]~E(f866(f40(x83201),x83202),f866(a119,x83203))+~P107(f866(f866(f336(x83201),f904(x83203,x83202,x83201)),f867(x83203,x83202,x83201)))
% 157.60/157.51 [8752]~P33(a1,x87521,f185(x87522,x87523))+~P29(f866(f78(a925,a925,a1,a329),x87521),x87522,x87523)
% 157.60/157.51 [8939]P107(f866(f866(f243(f937(f936(x89391,x89391),a925)),f314(x89391,x89392)),f314(x89391,x89393)))+~P107(f866(f866(f243(f937(f936(x89391,x89391),a925)),x89392),f314(x89391,x89393)))
% 157.60/157.51 [9225]E(x92251,f120(x92252))+~P107(f866(f866(f336(f936(f931(x92252),f931(x92252))),f866(f866(f260(f931(x92252),f931(x92252)),x92251),f120(x92252))),f165(x92252,x92253)))
% 157.60/157.51 [9249]E(x92491,f120(x92492))+~P107(f866(f866(f336(f936(f931(x92492),f931(x92492))),f866(f866(f260(f931(x92492),f931(x92492)),f120(x92492)),x92491)),f165(x92492,x92493)))
% 157.60/157.51 [9375]E(f866(f866(f158(x93751),f699(x93752,x93753,x93751)),f700(x93752,x93753,x93751)),x93753)+~P107(f866(f866(f336(f936(f931(x93751),f931(x93751))),f866(f866(f260(f931(x93751),f931(x93751)),f120(x93751)),x93753)),f154(x93751,x93752)))
% 157.60/157.51 [9611]~P121(x96111)+~P107(f866(f866(f244(x96111),f866(f866(f86(x96111),f866(f866(f87(x96111),x96112),x96112)),f866(f866(f87(x96111),x96113),x96113))),f2(x96111)))
% 157.60/157.51 [9660]P107(f866(f66(x96601),x96602))+~P107(f866(f866(f336(f936(f937(x96601,a925),f937(x96601,a925))),f866(f866(f260(f937(x96601,a925),f937(x96601,a925)),x96603),x96602)),f321(x96601)))
% 157.60/157.51 [9955]~P46(x99551,x99552,x99553)+P107(f866(f866(f243(a1),f866(f866(f78(f936(a1,a1),a1,x99551,f259(a1,a1)),f221(x99551)),f239(x99551,x99552,f236(x99551,x99553)))),f2(a1)))
% 157.60/157.51 [9956]~P47(x99561,x99562,x99563)+P107(f866(f866(f244(a1),f866(f866(f78(f936(a1,a1),a1,x99561,f259(a1,a1)),f221(x99561)),f239(x99561,x99562,f236(x99561,x99563)))),f2(a1)))
% 157.60/157.51 [10076]P47(x100761,x100762,x100763)+~P107(f866(f866(f244(a1),f866(f866(f78(f936(a1,a1),a1,x100761,f259(a1,a1)),f221(x100761)),f239(x100761,x100762,f236(x100761,x100763)))),f2(a1)))
% 157.60/157.51 [10077]P46(x100771,x100772,x100773)+~P107(f866(f866(f243(a1),f866(f866(f78(f936(a1,a1),a1,x100771,f259(a1,a1)),f221(x100771)),f239(x100771,x100772,f236(x100771,x100773)))),f2(a1)))
% 157.60/157.51 [10416]~P128(x104161)+~P107(f866(f866(f244(x104161),f866(f866(f86(x104161),f866(f866(f252(x104161),x104162),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x104161),x104163),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f2(x104161)))
% 157.60/157.51 [4979]~E(x49793,f120(x49791))+E(f866(f866(f141(x49791),x49792),x49793),x49792)
% 157.60/157.51 [4980]~E(x49802,f120(x49801))+E(f866(f866(f141(x49801),x49802),x49803),x49803)
% 157.60/157.51 [4986]~E(x49862,f2(a930))+E(f866(f866(f182(x49861),x49862),x49863),f120(x49861))
% 157.60/157.51 [4995]~E(x49953,f120(x49951))+E(f866(f866(f182(x49951),x49952),x49953),f120(x49951))
% 157.60/157.51 [5035]~E(x50351,x50353)+E(x50351,f866(f866(f141(x50352),f120(x50352)),x50353))
% 157.60/157.51 [5126]~P1(x51262)+E(f866(f195(f937(x51261,x51262)),x51263),f195(x51262))
% 157.60/157.51 [5127]~P112(x51272)+E(f866(f250(f937(x51271,x51272)),x51273),f250(x51272))
% 157.60/157.51 [5145]E(x51451,f120(x51452))+~E(f866(f866(f141(x51452),x51453),x51451),x51453)
% 157.60/157.51 [5146]E(x51461,f120(x51462))+~E(f866(f866(f141(x51462),x51461),x51463),x51463)
% 157.60/157.51 [5154]E(x51541,f120(x51542))+~E(f866(f866(f141(x51542),x51543),x51541),f120(x51542))
% 157.60/157.51 [5155]E(x51551,f120(x51552))+~E(f866(f866(f141(x51552),x51551),x51553),f120(x51552))
% 157.60/157.51 [5180]~E(x51802,f2(a930))+E(f866(f866(f87(a930),x51801),x51802),f866(f866(f87(a930),x51803),x51802))
% 157.60/157.51 [5182]~E(x51821,f2(a930))+E(f866(f866(f87(a930),x51821),x51822),f866(f866(f87(a930),x51821),x51823))
% 157.60/157.51 [5239]~P114(x52391)+E(f866(f866(f87(x52391),x52392),x52393),f866(f866(f87(x52391),x52393),x52392))
% 157.60/157.51 [5240]~P83(x52401)+E(f866(f866(f117(x52401),x52402),x52403),f866(f866(f117(x52401),x52403),x52402))
% 157.60/157.51 [5242]~P102(x52421)+E(f866(f866(f117(x52421),x52422),x52423),f866(f866(f117(x52421),x52423),x52422))
% 157.60/157.51 [5243]~P114(x52431)+E(f866(f866(f86(x52431),x52432),x52433),f866(f866(f86(x52431),x52433),x52432))
% 157.60/157.51 [5244]~P83(x52441)+E(f866(f866(f108(x52441),x52442),x52443),f866(f866(f108(x52441),x52443),x52442))
% 157.60/157.51 [5246]~P103(x52461)+E(f866(f866(f108(x52461),x52462),x52463),f866(f866(f108(x52461),x52463),x52462))
% 157.60/157.51 [5248]~P110(x52481)+E(f866(f866(f241(x52481),x52482),x52483),f866(f866(f241(x52481),x52483),x52482))
% 157.60/157.51 [5250]~P110(x52501)+E(f866(f866(f242(x52501),x52502),x52503),f866(f866(f242(x52501),x52503),x52502))
% 157.60/157.51 [5311]E(f50(a930,x53111,x53112),f2(a930))+~E(x53111,f866(f866(f87(a930),x53112),x53113))
% 157.60/157.51 [5312]E(f50(a1,x53121,x53122),f2(a1))+~E(x53121,f866(f866(f87(a1),x53122),x53123))
% 157.60/157.51 [5376]E(x53761,x53762)+~E(f866(f866(f86(a930),x53763),x53761),f866(f866(f86(a930),x53763),x53762))
% 157.60/157.51 [5377]E(x53771,x53772)+~E(f866(f866(f86(a930),x53771),x53773),f866(f866(f86(a930),x53772),x53773))
% 157.60/157.51 [5387]~P3(x53871)+E(f866(f866(f86(x53871),x53872),f866(f85(x53871),x53873)),f866(f866(f23(x53871),x53872),x53873))
% 157.60/157.51 [5388]~P77(x53881)+E(f866(f866(f86(x53881),x53882),f866(f85(x53881),x53883)),f866(f866(f23(x53881),x53882),x53883))
% 157.60/157.51 [5389]~P118(x53891)+E(f866(f866(f86(x53891),x53892),f866(f85(x53891),x53893)),f866(f866(f23(x53891),x53892),x53893))
% 157.60/157.51 [5390]~P98(x53901)+E(f866(f866(f108(x53901),x53902),f866(f85(x53901),x53903)),f866(f866(f23(x53901),x53902),x53903))
% 157.60/157.51 [5391]~P77(x53911)+E(f866(f866(f23(x53911),x53912),f866(f85(x53911),x53913)),f866(f866(f86(x53911),x53912),x53913))
% 157.60/157.51 [5429]~P107(f866(x54293,x54292))+P107(f866(f866(f336(x54291),x54292),x54293))
% 157.60/157.51 [5431]~P71(x54312)+E(f866(f866(f9(x54311,x54312),x54313),f195(f937(x54311,a925))),f84(x54312))
% 157.60/157.51 [5433]~P72(x54332)+E(f866(f866(f6(x54331,x54332),x54333),f195(f937(x54331,a925))),f2(x54332))
% 157.60/157.51 [5469]~P114(x54691)+P57(x54691,x54692,f866(f866(f87(x54691),x54693),x54692))
% 157.60/157.51 [5470]~P114(x54701)+P57(x54701,x54702,f866(f866(f87(x54701),x54702),x54703))
% 157.60/157.51 [5487]~E(x54872,f866(f866(f86(a930),x54871),x54873))+P107(f866(f866(f243(a930),x54871),x54872))
% 157.60/157.51 [5490]~E(x54902,f195(f937(x54901,a925)))+E(f866(f866(f65(x54901),x54902),x54903),f195(f937(f937(x54901,a925),a925)))
% 157.60/157.51 [5491]~E(x54912,f195(f937(x54911,a925)))+E(f195(f937(f937(x54911,a925),a925)),f866(f866(f65(x54911),x54912),x54913))
% 157.60/157.51 [5563]~E(f866(f292(x55632,x55633),x55631),f195(f937(x55633,a925)))+E(x55631,f195(f937(f936(x55632,x55633),a925)))
% 157.60/157.51 [5564]~E(f866(f272(x55642,x55643),x55641),f195(f937(x55642,a925)))+E(x55641,f195(f937(f936(x55642,x55643),a925)))
% 157.60/157.51 [5596]E(f866(f292(x55961,x55962),x55963),f195(f937(x55962,a925)))+~E(x55963,f195(f937(f936(x55961,x55962),a925)))
% 157.60/157.51 [5597]E(f866(f272(x55971,x55972),x55973),f195(f937(x55971,a925)))+~E(x55973,f195(f937(f936(x55971,x55972),a925)))
% 157.60/157.51 [5600]E(f282(x56001,x56002,x56003),f866(f866(f23(a106),x56002),x56003))+P107(f866(f866(f244(a106),x56002),x56003))
% 157.60/157.51 [5615]P107(f866(x56151,x56152))+~P107(f866(f866(f336(x56153),x56152),x56151))
% 157.60/157.51 [5653]E(x56531,x56532)+~E(f866(f85(f937(x56533,a925)),x56531),f866(f85(f937(x56533,a925)),x56532))
% 157.60/157.51 [5664]~E(x56641,f195(f937(x56642,a925)))+~P107(f866(f866(f336(x56642),x56643),x56641))
% 157.60/157.51 [5694]~E(x56942,f866(f866(f86(a1),x56941),f866(f107(a1),x56943)))+P107(f866(f866(f243(a1),x56941),x56942))
% 157.60/157.51 [5708]E(f866(f866(f316(x57081),x57082),x57083),x57083)+~P107(f866(f866(f336(x57081),x57082),x57083))
% 157.60/157.51 [5719]E(x57191,f195(f937(x57192,a925)))+~E(f866(f866(f65(x57192),x57191),x57193),f195(f937(f937(x57192,a925),a925)))
% 157.60/157.51 [5720]E(x57201,f195(f937(x57202,a925)))+~E(f195(f937(f937(x57202,a925),a925)),f866(f866(f65(x57202),x57201),x57203))
% 157.60/157.51 [5727]~P136(x57271)+E(f866(f866(f87(x57271),f866(f85(x57271),x57272)),f866(f85(x57271),x57273)),f866(f866(f87(x57271),x57272),x57273))
% 157.60/157.51 [5728]~P65(x57281)+E(f866(f866(f297(x57281),f866(f85(x57281),x57282)),f866(f85(x57281),x57283)),f866(f866(f297(x57281),x57282),x57283))
% 157.60/157.51 [5760]~P107(f866(x57603,x57602))+P107(f866(f866(f336(x57601),x57602),f866(f270(x57601),x57603)))
% 157.60/157.51 [5785]E(x57851,f2(a930))+E(f866(f179(x57852),f176(x57852,x57851,x57853)),f866(f866(f316(x57852),x57853),f195(f937(x57852,a925))))
% 157.60/157.51 [5807]E(f177(x58071,x58072,x58073),x58073)+P107(f866(f866(f336(x58071),x58072),f866(f179(x58071),x58073)))
% 157.60/157.51 [5812]~E(x58121,f2(a930))+P57(a930,f866(f866(f87(a930),x58121),x58122),f866(f866(f87(a930),x58121),x58123))
% 157.60/157.51 [5895]~P107(f866(f144(x58951),x58953))+P107(f866(f144(x58951),f866(f143(x58951,x58952),x58953)))
% 157.60/157.51 [5940]~P62(x59401)+E(f866(f866(f41(x59401),f50(x59401,x59402,x59403)),x59403),f2(x59401))
% 157.60/157.51 [5959]E(f183(x59591,f866(f866(f158(x59591),x59592),f120(x59591)),x59593),f120(x59591))+P107(f866(f866(f336(a930),f2(a930)),x59593))
% 157.60/157.51 [5965]E(x59651,f2(a930))+E(f866(f178(x59652),f176(x59652,x59651,x59653)),f176(x59652,f866(f866(f23(a930),x59651),f84(a930)),x59653))
% 157.60/157.51 [6016]E(f866(f866(f158(x60161),x60162),x60163),f147(x60161,x60162,x60163))+P107(f866(f866(f336(x60161),x60162),f866(f179(x60161),x60163)))
% 157.60/157.51 [6025]E(x60251,x60252)+~E(f866(f866(f87(a930),f866(a119,x60253)),x60251),f866(f866(f87(a930),f866(a119,x60253)),x60252))
% 157.60/157.51 [6026]~E(x60262,f866(f866(f86(a1),x60261),f866(f107(a1),f866(a119,x60263))))+P107(f866(f866(f244(a1),x60261),x60262))
% 157.60/157.51 [6087]~P30(x60871,x60872,x60873)+P31(a930,x60871,f146(a930,f866(f309(a930,x60872),x60873)))
% 157.60/157.51 [6135]~P57(a930,x61352,x61353)+P57(a930,f866(f866(f87(a930),x61351),x61352),f866(f866(f87(a930),x61351),x61353))
% 157.60/157.51 [6141]~E(x61413,f120(x61411))+E(f866(f866(f866(f190(f931(x61411),f931(x61411)),x61412),f174(x61411)),x61413),f120(x61411))
% 157.60/157.51 [6145]P107(f866(x61451,x61452))+~P107(f866(f866(f336(x61453),x61452),f866(f270(x61453),x61451)))
% 157.60/157.51 [6175]E(x61751,x61752)+~E(f866(f866(f316(x61753),x61751),f195(f937(x61753,a925))),f866(f866(f316(x61753),x61752),f195(f937(x61753,a925))))
% 157.60/157.51 [6190]~P111(x61901)+E(f866(f866(f108(f937(x61901,a925)),f866(f290(x61901),x61902)),f866(f309(x61901,x61902),x61903)),f195(f937(x61901,a925)))
% 157.60/157.51 [6229]E(f147(x62291,x62292,x62293),x62293)+~P107(f866(f866(f336(x62291),x62292),f866(f179(x62291),x62293)))
% 157.60/157.51 [6250]~P79(x62501)+E(f866(f317(x62501,x62501,f85(x62501)),f866(f309(x62501,x62502),x62503)),f312(x62501,f866(f85(x62501),x62503),f866(f85(x62501),x62502)))
% 157.60/157.51 [6264]E(f866(f196(f931(x62641)),f177(x62641,x62642,x62643)),f866(f196(f931(x62641)),x62643))+P107(f866(f866(f336(x62641),x62642),f866(f179(x62641),x62643)))
% 157.60/157.51 [6315]~P111(x63151)+E(f866(f866(f108(f937(x63151,a925)),f866(f309(x63151,x63152),x63153)),f866(f291(x63151),x63153)),f195(f937(x63151,a925)))
% 157.60/157.51 [6335]~P79(x63351)+E(f866(f317(x63351,x63351,f85(x63351)),f313(x63351,x63352,x63353)),f313(x63351,f866(f85(x63351),x63353),f866(f85(x63351),x63352)))
% 157.60/157.51 [6336]~P79(x63361)+E(f866(f317(x63361,x63361,f85(x63361)),f310(x63361,x63362,x63363)),f310(x63361,f866(f85(x63361),x63363),f866(f85(x63361),x63362)))
% 157.60/157.51 [6399]E(f183(x63991,f866(f866(f158(x63991),x63992),f120(x63991)),x63993),f866(f866(f158(x63991),x63992),f120(x63991)))+~P107(f866(f866(f336(a930),f2(a930)),x63993))
% 157.60/157.51 [6404]P30(x64041,x64042,x64043)+~P31(a930,x64041,f146(a930,f866(f309(a930,x64042),x64043)))
% 157.60/157.51 [6407]~P79(x64071)+E(f866(f317(x64071,x64071,f85(x64071)),f312(x64071,x64072,x64073)),f866(f309(x64071,f866(f85(x64071),x64073)),f866(f85(x64071),x64072)))
% 157.60/157.51 [6427]~P63(x64271)+E(f50(x64271,f866(f85(x64271),f50(x64271,x64272,x64273)),x64273),f50(x64271,f866(f85(x64271),x64272),x64273))
% 157.60/157.51 [6522]~P107(f866(f66(f936(x65222,x65221)),x65223))+P107(f866(f66(x65221),f866(f292(x65222,x65221),x65223)))
% 157.60/157.51 [6523]~P107(f866(f66(f936(x65231,x65232)),x65233))+P107(f866(f66(x65231),f866(f272(x65231,x65232),x65233)))
% 157.60/157.51 [6528]~P111(x65281)+E(f866(f866(f108(f937(x65281,a925)),f313(x65281,x65282,x65283)),f866(f291(x65281),x65283)),f195(f937(x65281,a925)))
% 157.60/157.51 [6529]~P111(x65291)+E(f866(f866(f108(f937(x65291,a925)),f310(x65291,x65292,x65293)),f866(f311(x65291),x65293)),f195(f937(x65291,a925)))
% 157.60/157.51 [6530]~P111(x65301)+E(f866(f866(f108(f937(x65301,a925)),f312(x65301,x65302,x65303)),f866(f311(x65301),x65303)),f195(f937(x65301,a925)))
% 157.60/157.51 [6601]E(f866(f866(f171(x66011),x66012),f642(x66012,x66013,x66011)),x66013)+~P107(f866(f866(f336(x66011),x66013),f866(f179(x66011),x66012)))
% 157.60/157.51 [6746]E(x67461,f120(x67462))+~E(f866(f866(f866(f190(f931(x67462),f931(x67462)),x67463),f174(x67462)),x67461),f120(x67462))
% 157.60/157.51 [6852]~P107(f866(f66(f936(x68522,x68521)),x68523))+P107(f866(f66(f936(x68521,x68522)),f866(f294(x68522,x68521),x68523)))
% 157.60/157.51 [7001]P56(x70011,x70012,x70013)+P107(f866(f866(f336(x70011),f570(x70013,x70012,x70011)),x70012))
% 157.60/157.51 [7002]P56(x70021,x70022,x70023)+P107(f866(f866(f336(x70021),f569(x70023,x70022,x70021)),x70022))
% 157.60/157.51 [7012]P107(f866(f322(x70121,x70122),x70123))+P107(f866(f866(x70122,f486(x70123,x70122,x70121)),x70123))
% 157.60/157.51 [7013]P107(f866(f322(x70131,x70132),x70133))+P107(f866(f866(x70132,f500(x70133,x70132,x70131)),x70133))
% 157.60/157.51 [7044]E(f866(f196(f931(x70441)),f177(x70441,x70442,x70443)),f866(f866(f23(a930),f866(f196(f931(x70441)),x70443)),f84(a930)))+~P107(f866(f866(f336(x70441),x70442),f866(f179(x70441),x70443)))
% 157.60/157.51 [7084]P107(f866(f256(x70841,x70842),x70843))+P107(f866(f866(f336(x70841),f556(x70843,x70842,x70841)),x70843))
% 157.60/157.51 [7093]~P107(f866(f66(f936(x70932,x70931)),f866(f294(x70931,x70932),x70933)))+P107(f866(f66(f936(x70931,x70932)),x70933))
% 157.60/157.51 [7150]~P107(f866(f866(f336(x71501),x71502),f866(f179(x71501),f121(x71501,x71503))))+P107(f866(f866(f336(x71501),x71502),f866(f179(x71501),x71503)))
% 157.60/157.51 [7183]E(f866(f143(x71831,x71832),x71833),x71833)+P107(f866(f866(f336(x71831),f681(x71833,x71832,x71831)),f866(f179(x71831),x71833)))
% 157.60/157.51 [7197]E(f866(f143(x71971,x71972),x71973),f120(x71971))+P107(f866(f866(f336(x71971),f680(x71973,x71972,x71971)),f866(f179(x71971),x71973)))
% 157.60/157.51 [7221]P31(x72211,x72212,x72213)+P107(f866(f866(f336(x72211),f766(x72213,x72212,x72211)),f866(f179(x72211),x72213)))
% 157.60/157.51 [7222]P31(x72221,x72222,x72223)+P107(f866(f866(f336(x72221),f776(x72223,x72222,x72221)),f866(f179(x72221),x72223)))
% 157.60/157.51 [7223]P31(x72231,x72232,x72233)+P107(f866(f866(f336(x72231),f775(x72232,x72233,x72231)),f866(f179(x72231),x72233)))
% 157.60/157.51 [7226]E(f184(x72261,x72262,x72263),x72263)+P107(f866(f866(f336(x72261),f725(x72263,x72262,x72261)),f866(f179(x72261),x72263)))
% 157.60/157.51 [7301]P107(f866(f167(x73011,x73012),x73013))+P107(f866(f866(f336(x73011),f682(x73013,x73012,x73011)),f866(f179(x73011),x73013)))
% 157.60/157.51 [7310]~P33(x73101,x73103,x73102)+P107(f866(f866(f336(x73101),f764(x73102,x73103,x73101)),f866(f179(x73101),x73102)))
% 157.60/157.51 [7311]~P35(x73111,x73113,x73112)+P107(f866(f866(f336(x73111),f774(x73112,x73113,x73111)),f866(f179(x73111),x73112)))
% 157.60/157.51 [7312]~P35(x73121,x73123,x73122)+P107(f866(f866(f336(x73121),f777(x73122,x73123,x73121)),f866(f179(x73121),x73122)))
% 157.60/157.51 [7313]~P33(x73131,x73132,x73133)+P107(f866(f866(f336(x73131),f806(x73132,x73133,x73131)),f866(f179(x73131),x73133)))
% 157.60/157.51 [7314]~P33(x73141,x73143,x73142)+P107(f866(f866(f336(x73141),f807(x73142,x73143,x73141)),f866(f179(x73141),x73142)))
% 157.60/157.51 [7348]P107(f866(f866(f336(x73481),x73482),f644(x73483,x73482,x73481)))+~P107(f866(f866(f336(x73481),x73482),f42(f937(x73481,a925),x73483)))
% 157.60/157.51 [7349]~P72(x73491)+E(f866(f866(f86(x73491),f866(f866(f6(a930,x73491),x73492),f866(f290(a930),x73493))),f866(x73492,x73493)),f866(f866(f6(a930,x73491),x73492),f866(f290(a930),f866(a119,x73493))))
% 157.60/157.51 [7361]P30(x73611,x73612,x73613)+P107(f866(f866(f336(a930),f835(x73613,x73612,x73611)),f866(f309(a930,x73612),x73613)))
% 157.60/157.51 [7439]~P33(x74392,x74391,x74393)+P107(f866(x74391,f866(f866(f171(x74392),x74393),f762(x74393,x74391,x74392))))
% 157.60/157.51 [7451]~P107(f866(f866(f336(x74511),x74512),f632(x74512,x74513,x74511)))+P107(f866(f866(f336(x74511),x74512),f43(f937(x74511,a925),x74513)))
% 157.60/157.51 [7484]~P72(x74841)+E(f866(f866(f86(x74841),f866(f866(f6(a930,x74841),x74842),f866(f308(a930),x74843))),f866(x74842,f866(a119,x74843))),f866(f866(f6(a930,x74841),x74842),f866(f308(a930),f866(a119,x74843))))
% 157.60/157.51 [7623]P107(f866(f866(f336(f931(x76231)),x76232),f168(x76231,x76233)))+P107(f866(f866(f336(x76231),f666(x76233,x76232,x76231)),f866(f179(x76231),x76232)))
% 157.60/157.51 [7638]~P107(f866(f866(f336(f931(x76381)),x76382),f168(x76381,f323(x76381,x76383))))+P107(f866(f866(f336(f931(x76381)),x76382),f323(f931(x76381),f164(x76381,x76383))))
% 157.60/157.51 [7663]~P107(f866(f866(f336(f931(x76631)),x76632),f323(f931(x76631),f164(x76631,x76633))))+P107(f866(f866(f336(f931(x76631)),x76632),f168(x76631,f323(x76631,x76633))))
% 157.60/157.51 [7696]E(f866(f866(f866(f190(f931(x76961),f931(x76961)),x76962),f174(x76961)),x76963),x76963)+~P107(f866(f866(f243(a930),f866(f196(f931(x76961)),x76963)),f84(a930)))
% 157.60/157.51 [7729]E(f866(f866(f141(x77291),f763(x77292,x77293,x77291)),f866(f866(f158(x77291),x77293),f765(x77292,x77293,x77291))),x77292)+~P107(f866(f866(f336(x77291),x77293),f866(f179(x77291),x77292)))
% 157.60/157.51 [7730]E(f866(f866(f141(x77301),f769(x77302,x77303,x77301)),f866(f866(f158(x77301),x77303),f770(x77302,x77303,x77301))),x77302)+~P107(f866(f866(f336(x77301),x77303),f866(f179(x77301),x77302)))
% 157.60/157.51 [7731]E(f866(f866(f141(x77311),f771(x77312,x77313,x77311)),f866(f866(f158(x77311),x77313),f772(x77312,x77313,x77311))),x77312)+~P107(f866(f866(f336(x77311),x77313),f866(f179(x77311),x77312)))
% 157.60/157.51 [7752]~P25(x77521,x77522,x77523,f250(f937(x77521,a925)))+P25(f931(x77521),f931(x77522),f866(f161(x77521,x77522),x77523),f250(f937(f931(x77521),a925)))
% 157.60/157.51 [7899]E(x78991,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x78992)),x78993)),f866(f264(a930,a930),x78992)))+~P107(f866(f53(x78991,x78993),x78992))
% 157.60/157.51 [7907]P25(x79071,x79072,x79073,f250(f937(x79071,a925)))+~P25(f931(x79071),f931(x79072),f866(f161(x79071,x79072),x79073),f250(f937(f931(x79071),a925)))
% 157.60/157.51 [7950]P107(f866(f866(f336(f937(x79501,a925)),f632(x79502,x79503,x79501)),x79503))+P107(f866(f866(f336(x79501),x79502),f43(f937(x79501,a925),x79503)))
% 157.60/157.51 [8041]P107(f866(f866(f336(f931(x80411)),x80412),f168(x80411,x80413)))+~P107(f866(f866(f336(x80411),f666(x80413,x80412,x80411)),x80413))
% 157.60/157.51 [8140]P31(x81401,x81402,x81403)+~P107(f866(x81402,f866(f866(f171(x81401),x81403),f768(x81403,x81402,x81401))))
% 157.60/157.51 [8164]E(x81641,x81642)+~E(f866(f866(f7(x81643,f937(x81643,a925),a925),f336(x81643)),x81641),f866(f866(f7(x81643,f937(x81643,a925),a925),f336(x81643)),x81642))
% 157.60/157.51 [8172]~P107(f866(f866(f336(f936(x81721,x81721)),x81723),f271(x81721,x81722)))+P107(f866(f866(f336(x81721),f517(x81722,x81723,x81721)),x81722))
% 157.60/157.51 [8174]~P107(f866(f866(f336(x81741),x81743),f42(f937(x81741,a925),x81742)))+P107(f866(f866(f336(f937(x81741,a925)),f644(x81742,x81743,x81741)),x81742))
% 157.60/157.51 [8294]P25(x82941,x82942,f97(x82942,x82941,f250(f937(x82942,a925)),x82943),f250(f937(x82941,a925)))+~E(f866(f317(x82942,x82941,x82943),f250(f937(x82942,a925))),f250(f937(x82941,a925)))
% 157.60/157.51 [8347]~P107(f866(f866(f336(x83471),x83472),f866(f179(x83471),f769(x83473,x83472,x83471))))+~P107(f866(f866(f336(x83471),x83472),f866(f179(x83471),x83473)))
% 157.60/157.51 [8348]~P107(f866(f866(f336(x83481),x83482),f866(f179(x83481),f772(x83483,x83482,x83481))))+~P107(f866(f866(f336(x83481),x83482),f866(f179(x83481),x83483)))
% 157.60/157.51 [8371]P30(f866(f78(a925,a925,a930,a329),x83711),x83712,x83713)+P33(a930,x83711,f146(a930,f866(f309(a930,x83712),x83713)))
% 157.60/157.51 [8532]E(x85321,f120(x85322))+P107(f866(f866(f336(x85322),f866(f259(x85322,f936(a106,a106)),f866(f283(x85322,x85321),x85323))),f866(f179(x85322),x85321)))
% 157.60/157.51 [8630]~P70(x86301)+E(f866(f149(x86301,x86301,f866(f7(x86301,x86301,x86301),f86(x86301)),x86302),f866(f175(x86301),x86303)),f866(f149(x86301,x86301,f86(x86301),x86302),x86303))
% 157.60/157.51 [8822]~P25(x88222,x88221,x88223,f250(f937(x88222,a925)))+E(f866(f317(x88221,x88222,f97(x88222,x88221,f250(f937(x88222,a925)),x88223)),f250(f937(x88221,a925))),f250(f937(x88222,a925)))
% 157.60/157.51 [8892]~P30(f866(f78(a925,a925,a930,a329),x88921),x88922,x88923)+~P33(a930,x88921,f146(a930,f866(f309(a930,x88922),x88923)))
% 157.60/157.51 [9141]~P110(x91411)+E(f866(f179(x91411),f156(x91411,x91411,f5(x91411),x91412,x91413)),f866(f866(f316(x91411),x91412),f866(f179(x91411),x91413)))
% 157.60/157.51 [9152]~E(f866(x91523,f866(f97(x91521,x91522,f250(f937(x91521,a925)),x91523),f651(x91523,x91522,x91521))),f651(x91523,x91522,x91521))+E(f866(f317(x91521,x91522,x91523),f250(f937(x91521,a925))),f250(f937(x91522,a925)))
% 157.60/157.51 [9154]P107(f866(f866(f244(a930),f2(a930)),f597(x91541,x91542,x91543)))+~P107(f866(f866(f336(f936(x91543,x91543)),x91542),f866(f866(f296(x91543,x91543,x91543),x91541),f314(x91543,x91541))))
% 157.60/157.51 [9432]~P59(x94321,x94322)+~P107(f866(f866(f336(f936(x94321,x94321)),f866(f866(f260(x94321,x94321),x94323),x94323)),f866(f866(f296(x94321,x94321,x94321),x94322),f314(x94321,x94322))))
% 157.60/157.51 [9566]~E(f866(f866(f108(f937(f936(x95661,x95661),a925)),f866(f294(x95661,x95661),x95662)),f314(x95661,x95662)),f195(f937(f936(x95661,x95661),a925)))+~P107(f866(f866(f336(f936(x95661,x95661)),f866(f866(f260(x95661,x95661),x95663),x95663)),f866(f866(f296(x95661,x95661,x95661),x95662),f314(x95661,x95662))))
% 157.60/157.51 [9746]~P107(f866(f66(x97461),x97462))+P107(f866(f866(f243(a930),f866(f40(x97461),f866(f866(f23(f937(x97461,a925)),x97462),f866(f866(f316(x97461),x97463),f195(f937(x97461,a925)))))),f866(f40(x97461),x97462)))
% 157.60/157.51 [5300]~E(x53003,f120(x53001))+E(f151(x53001,f866(f866(f158(x53001),x53002),x53003)),x53002)
% 157.60/157.51 [5308]~E(x53083,f120(x53081))+E(f121(x53081,f866(f866(f158(x53081),x53082),x53083)),f120(x53081))
% 157.60/157.51 [5338]E(x53381,f120(x53382))+E(f151(x53382,f866(f866(f158(x53382),x53383),x53381)),f151(x53382,x53381))
% 157.60/157.51 [5340]E(x53401,f120(x53402))+E(f151(x53402,f866(f866(f141(x53402),x53403),x53401)),f151(x53402,x53401))
% 157.60/157.51 [5345]~E(x53453,f120(x53451))+E(f121(x53451,f866(f866(f141(x53451),x53452),x53453)),f121(x53451,x53452))
% 157.60/157.51 [5347]~E(x53473,f120(x53471))+E(f151(x53471,f866(f866(f141(x53471),x53472),x53473)),f151(x53471,x53472))
% 157.60/157.51 [5381]E(x53811,f120(x53812))+E(f866(f148(x53812),f866(f866(f141(x53812),x53811),x53813)),f866(f148(x53812),x53811))
% 157.60/157.51 [5409]~E(x54092,f120(x54091))+E(f866(f148(x54091),f866(f866(f141(x54091),x54092),x54093)),f866(f148(x54091),x54093))
% 157.60/157.51 [5461]~P83(x54611)+E(f866(f866(f117(x54611),x54612),f866(f866(f108(x54611),x54612),x54613)),x54612)
% 157.60/157.51 [5462]~P83(x54621)+E(f866(f866(f108(x54621),x54622),f866(f866(f117(x54621),x54622),x54623)),x54622)
% 157.60/157.51 [5463]~P110(x54631)+E(f866(f866(f241(x54631),x54632),f866(f866(f242(x54631),x54632),x54633)),x54632)
% 157.60/157.51 [5464]~P110(x54641)+E(f866(f866(f242(x54641),x54642),f866(f866(f241(x54641),x54642),x54643)),x54642)
% 157.60/157.51 [5485]~P62(x54851)+E(f50(x54851,f866(f866(f87(x54851),x54852),x54853),x54853),f2(x54851))
% 157.60/157.51 [5486]~P62(x54861)+E(f50(x54861,f866(f866(f87(x54861),x54862),x54863),x54862),f2(x54861))
% 157.60/157.51 [5558]~P3(x55581)+E(f866(f85(x55581),f866(f866(f23(x55581),x55582),x55583)),f866(f866(f23(x55581),x55583),x55582))
% 157.60/157.51 [5619]E(x56191,f120(x56192))+E(f121(x56192,f866(f866(f158(x56192),x56193),x56191)),f866(f866(f158(x56192),x56193),f121(x56192,x56191)))
% 157.60/157.51 [5620]E(x56201,f120(x56202))+E(f121(x56202,f866(f866(f141(x56202),x56203),x56201)),f866(f866(f141(x56202),x56203),f121(x56202,x56201)))
% 157.60/157.51 [5623]~P5(x56231)+E(f43(x56231,f866(f866(f316(x56231),x56232),x56233)),f866(f866(f108(x56231),x56232),f43(x56231,x56233)))
% 157.60/157.51 [5624]~P5(x56241)+E(f42(x56241,f866(f866(f316(x56241),x56242),x56243)),f866(f866(f117(x56241),x56242),f42(x56241,x56243)))
% 157.60/157.51 [5669]~P99(x56691)+E(f866(f866(f87(x56691),x56692),f866(f866(f87(x56691),x56692),x56693)),f866(f866(f87(x56691),x56692),x56693))
% 157.60/157.51 [5670]~P83(x56701)+E(f866(f866(f117(x56701),x56702),f866(f866(f117(x56701),x56702),x56703)),f866(f866(f117(x56701),x56702),x56703))
% 157.60/157.51 [5672]~P102(x56721)+E(f866(f866(f117(x56721),x56722),f866(f866(f117(x56721),x56722),x56723)),f866(f866(f117(x56721),x56722),x56723))
% 157.60/157.51 [5673]~P83(x56731)+E(f866(f866(f108(x56731),x56732),f866(f866(f108(x56731),x56732),x56733)),f866(f866(f108(x56731),x56732),x56733))
% 157.60/157.51 [5675]~P103(x56751)+E(f866(f866(f108(x56751),x56752),f866(f866(f108(x56751),x56752),x56753)),f866(f866(f108(x56751),x56752),x56753))
% 157.60/157.51 [5677]~P110(x56771)+E(f866(f866(f241(x56771),x56772),f866(f866(f241(x56771),x56772),x56773)),f866(f866(f241(x56771),x56772),x56773))
% 157.60/157.51 [5679]~P110(x56791)+E(f866(f866(f242(x56791),x56792),f866(f866(f242(x56791),x56792),x56793)),f866(f866(f242(x56791),x56792),x56793))
% 157.60/157.51 [5686]~P62(x56861)+E(f50(x56861,f866(f866(f86(x56861),x56862),x56863),x56863),f50(x56861,x56862,x56863))
% 157.60/157.51 [5687]~P62(x56871)+E(f50(x56871,f866(f866(f86(x56871),x56872),x56873),x56872),f50(x56871,x56873,x56872))
% 157.60/157.51 [5695]~P136(x56951)+E(f866(f866(f87(x56951),x56952),f866(f85(x56951),x56953)),f866(f85(x56951),f866(f866(f87(x56951),x56952),x56953)))
% 157.60/157.51 [5696]~P65(x56961)+E(f866(f866(f297(x56961),x56962),f866(f85(x56961),x56963)),f866(f85(x56961),f866(f866(f297(x56961),x56962),x56963)))
% 157.60/157.51 [5697]~P82(x56971)+E(f866(f866(f86(x56971),x56972),f866(f172(x56971),x56973)),f866(f172(x56971),f866(f866(f158(x56971),x56972),x56973)))
% 157.60/157.51 [5725]~P136(x57251)+E(f866(f866(f87(x57251),f866(f85(x57251),x57252)),x57253),f866(f866(f87(x57251),x57252),f866(f85(x57251),x57253)))
% 157.60/157.51 [5731]~P8(x57311,x57312,x57313)+E(f42(f937(x57311,a925),f866(f866(f65(x57311),x57312),x57313)),x57312)
% 157.60/157.51 [5799]~P116(x57991)+E(f866(f866(f87(x57991),x57992),f866(f866(f252(x57991),x57992),x57993)),f866(f866(f252(x57991),x57992),f866(a119,x57993)))
% 157.60/157.51 [5800]~P114(x58001)+E(f866(f866(f87(x58001),x58002),f866(f866(f252(x58001),x58002),x58003)),f866(f866(f252(x58001),x58002),f866(a119,x58003)))
% 157.60/157.51 [5810]~P77(x58101)+E(f866(f866(f86(x58101),f866(f85(x58101),x58102)),f866(f866(f86(x58101),x58102),x58103)),x58103)
% 157.60/157.51 [5834]~P148(x58341)+E(f866(f866(f252(x58341),f866(f107(x58341),x58342)),x58343),f866(f107(x58341),f866(f866(f252(a930),x58342),x58343)))
% 157.60/157.51 [5835]~P142(x58351)+E(f866(f866(f252(x58351),f866(f109(x58351),x58352)),x58353),f866(f109(x58351),f866(f866(f252(a1),x58352),x58353)))
% 157.60/157.51 [5844]~P89(x58441)+E(f866(f81(x58441),f866(f866(f23(x58441),x58442),x58443)),f866(f81(x58441),f866(f866(f23(x58441),x58443),x58442)))
% 157.60/157.51 [5846]~P128(x58461)+E(f866(f866(f87(x58461),f88(x58461,x58462)),f88(x58461,x58463)),f88(x58461,f866(f866(f87(x58461),x58462),x58463)))
% 157.60/157.51 [5850]E(x58501,f120(x58502))+E(f866(f866(f141(x58502),f866(f178(x58502),x58501)),x58503),f866(f178(x58502),f866(f866(f141(x58502),x58501),x58503)))
% 157.60/157.51 [5855]~E(x58552,f866(a119,f866(f866(f86(a930),x58551),x58553)))+P107(f866(f866(f244(a930),x58551),x58552))
% 157.60/157.51 [5856]~P128(x58561)+E(f866(f866(f252(x58561),f866(f81(x58561),x58562)),x58563),f866(f81(x58561),f866(f866(f252(x58561),x58562),x58563)))
% 157.60/157.51 [5857]~P136(x58571)+E(f866(f866(f87(x58571),f866(f85(x58571),x58572)),x58573),f866(f85(x58571),f866(f866(f87(x58571),x58572),x58573)))
% 157.60/157.51 [5858]~P125(x58581)+E(f866(f866(f297(x58581),f866(f85(x58581),x58582)),x58583),f866(f85(x58581),f866(f866(f297(x58581),x58582),x58583)))
% 157.60/157.51 [5958]E(f905(x59581,x59582,x59583),f911(x59581,x59582,x59583))+E(f866(f866(f108(f937(x59583,a925)),x59582),x59581),f195(f937(x59583,a925)))
% 157.60/157.51 [5973]~P71(x59732)+E(f866(f866(f9(x59731,x59732),f866(f16(x59732,x59731),f84(x59732))),x59733),f84(x59732))
% 157.60/157.51 [5974]~P72(x59742)+E(f866(f866(f6(x59741,x59742),f866(f16(x59742,x59741),f2(x59742))),x59743),f2(x59742))
% 157.60/157.51 [5976]~P148(x59761)+E(f866(f866(f87(x59761),f866(f107(x59761),x59762)),f866(f107(x59761),x59763)),f866(f107(x59761),f866(f866(f87(a930),x59762),x59763)))
% 157.60/157.51 [5977]~P148(x59771)+E(f866(f866(f86(x59771),f866(f107(x59771),x59772)),f866(f107(x59771),x59773)),f866(f107(x59771),f866(f866(f86(a930),x59772),x59773)))
% 157.60/157.51 [5978]~P142(x59781)+E(f866(f866(f23(x59781),f866(f109(x59781),x59782)),f866(f109(x59781),x59783)),f866(f109(x59781),f866(f866(f23(a1),x59782),x59783)))
% 157.60/157.51 [5979]~P142(x59791)+E(f866(f866(f87(x59791),f866(f109(x59791),x59792)),f866(f109(x59791),x59793)),f866(f109(x59791),f866(f866(f87(a1),x59792),x59793)))
% 157.60/157.51 [5980]~P142(x59801)+E(f866(f866(f86(x59801),f866(f109(x59801),x59802)),f866(f109(x59801),x59803)),f866(f109(x59801),f866(f866(f86(a1),x59802),x59803)))
% 157.60/157.51 [5981]~P96(x59811)+E(f866(f866(f23(x59811),f866(f110(x59811),x59812)),f866(f110(x59811),x59813)),f866(f110(x59811),f866(f866(f23(a1),x59812),x59813)))
% 157.60/157.51 [5984]~P96(x59841)+E(f866(f866(f87(x59841),f866(f110(x59841),x59842)),f866(f110(x59841),x59843)),f866(f110(x59841),f866(f866(f87(a1),x59842),x59843)))
% 157.60/157.51 [5985]~P96(x59851)+E(f866(f866(f86(x59851),f866(f110(x59851),x59852)),f866(f110(x59851),x59853)),f866(f110(x59851),f866(f866(f86(a1),x59852),x59853)))
% 157.60/157.51 [6033]~E(x60333,x60332)+P107(f866(f866(f243(f937(x60331,a925)),x60332),x60333))
% 157.60/157.51 [6039]~E(x60392,x60393)+P107(f866(f866(f243(f937(x60391,a925)),x60392),x60393))
% 157.60/157.51 [6044]~P128(x60441)+E(f866(f866(f87(x60441),f866(f81(x60441),x60442)),f866(f81(x60441),x60443)),f866(f81(x60441),f866(f866(f87(x60441),x60442),x60443)))
% 157.60/157.51 [6045]~P67(x60451)+E(f866(f866(f297(x60451),f866(f81(x60451),x60452)),f866(f81(x60451),x60453)),f866(f81(x60451),f866(f866(f297(x60451),x60452),x60453)))
% 157.60/157.51 [6046]~P98(x60461)+E(f866(f866(f108(x60461),f866(f85(x60461),x60462)),f866(f85(x60461),x60463)),f866(f85(x60461),f866(f866(f117(x60461),x60462),x60463)))
% 157.60/157.51 [6047]~P77(x60471)+E(f866(f866(f86(x60471),f866(f85(x60471),x60472)),f866(f85(x60471),x60473)),f866(f85(x60471),f866(f866(f86(x60471),x60473),x60472)))
% 157.60/157.51 [6048]~P3(x60481)+E(f866(f866(f86(x60481),f866(f85(x60481),x60482)),f866(f85(x60481),x60483)),f866(f85(x60481),f866(f866(f86(x60481),x60482),x60483)))
% 157.60/157.51 [6049]~P98(x60491)+E(f866(f866(f117(x60491),f866(f85(x60491),x60492)),f866(f85(x60491),x60493)),f866(f85(x60491),f866(f866(f108(x60491),x60492),x60493)))
% 157.60/157.51 [6050]~P76(x60501)+E(f866(f866(f242(x60501),f866(f85(x60501),x60502)),f866(f85(x60501),x60503)),f866(f85(x60501),f866(f866(f241(x60501),x60502),x60503)))
% 157.60/157.51 [6051]~P76(x60511)+E(f866(f866(f241(x60511),f866(f85(x60511),x60512)),f866(f85(x60511),x60513)),f866(f85(x60511),f866(f866(f242(x60511),x60512),x60513)))
% 157.60/157.51 [6052]~P82(x60521)+E(f866(f866(f86(x60521),f866(f172(x60521),x60522)),f866(f172(x60521),x60523)),f866(f172(x60521),f866(f866(f141(x60521),x60522),x60523)))
% 157.60/157.51 [6053]E(x60531,f195(f937(x60532,a925)))+~E(f866(f866(f117(f937(x60532,a925)),x60533),x60531),f195(f937(x60532,a925)))
% 157.60/157.51 [6054]E(x60541,f195(f937(x60542,a925)))+~E(f866(f866(f117(f937(x60542,a925)),x60541),x60543),f195(f937(x60542,a925)))
% 157.60/157.51 [6055]~P150(x60551,x60552,x60553)+P107(f866(x60551,f866(f866(f41(a1),x60552),x60553)))
% 157.60/157.51 [6113]~P107(f866(f66(x61131),x61133))+P107(f866(f66(x61131),f866(f866(f316(x61131),x61132),x61133)))
% 157.60/157.51 [6114]~P107(f866(f144(x61141),x61143))+P107(f866(f144(x61141),f866(f866(f182(x61141),x61142),x61143)))
% 157.60/157.51 [6115]~P107(f866(f144(x61151),x61153))+P107(f866(f144(x61151),f866(f866(f145(x61151),x61152),x61153)))
% 157.60/157.51 [6146]~P83(x61461)+P107(f866(f866(f243(x61461),x61462),f866(f866(f117(x61461),x61463),x61462)))
% 157.60/157.51 [6147]~P102(x61471)+P107(f866(f866(f243(x61471),x61472),f866(f866(f117(x61471),x61473),x61472)))
% 157.60/157.51 [6148]~P83(x61481)+P107(f866(f866(f243(x61481),x61482),f866(f866(f117(x61481),x61482),x61483)))
% 157.60/157.51 [6149]~P102(x61491)+P107(f866(f866(f243(x61491),x61492),f866(f866(f117(x61491),x61492),x61493)))
% 157.60/157.51 [6150]~P110(x61501)+P107(f866(f866(f243(x61501),x61502),f866(f866(f242(x61501),x61503),x61502)))
% 157.60/157.51 [6151]~P110(x61511)+P107(f866(f866(f243(x61511),x61512),f866(f866(f242(x61511),x61512),x61513)))
% 157.60/157.51 [6165]~E(x61651,f2(a930))+E(f866(f866(f41(a930),f866(f866(f87(a930),x61651),x61652)),f866(f866(f87(a930),x61651),x61653)),f2(a930))
% 157.60/157.51 [6245]~P96(x62451)+E(f866(f866(f23(x62451),f866(f110(x62451),x62452)),f866(f110(x62451),x62453)),f866(f110(x62451),f866(f866(f86(a1),x62452),f866(f85(a1),x62453))))
% 157.60/157.51 [6305]E(x63051,f2(a930))+E(f866(f866(f41(a930),f866(f866(f87(a930),x63051),x63052)),f866(f866(f87(a930),x63051),x63053)),f866(f866(f41(a930),x63052),x63053))
% 157.60/157.51 [6333]E(f159(x63331,f866(f866(f158(x63331),x63332),x63333)),f866(f866(f158(x63331),x63332),f159(x63331,x63333)))+P107(f866(f866(f336(x63331),x63332),f866(f179(x63331),x63333)))
% 157.60/157.51 [6369]P150(x63691,x63692,x63693)+~P107(f866(x63691,f866(f866(f41(a1),x63692),x63693)))
% 157.60/157.51 [6440]E(x64401,f120(x64402))+E(f866(f866(f158(x64402),f866(f148(x64402),x64401)),f866(f866(f182(x64402),x64403),f866(f178(x64402),x64401))),f866(f866(f182(x64402),f866(a119,x64403)),x64401))
% 157.60/157.51 [6447]E(f866(f866(f23(f937(x64471,a925)),x64472),x64473),x64472)+~E(f866(f866(f108(f937(x64471,a925)),x64472),x64473),f195(f937(x64471,a925)))
% 157.60/157.51 [6461]E(f159(x64611,f866(f866(f158(x64611),x64612),x64613)),f159(x64611,x64613))+~P107(f866(f866(f336(x64611),x64612),f866(f179(x64611),x64613)))
% 157.60/157.51 [6491]~P107(f866(f866(f243(a930),x64911),x64913))+P107(f866(f866(f243(a930),x64911),f866(f866(f86(a930),x64912),x64913)))
% 157.60/157.51 [6493]~P107(f866(f866(f243(a930),x64931),x64932))+P107(f866(f866(f243(a930),x64931),f866(f866(f86(a930),x64932),x64933)))
% 157.60/157.51 [6495]~P107(f866(f866(f244(a930),x64951),x64953))+P107(f866(f866(f244(a930),x64951),f866(f866(f86(a930),x64952),x64953)))
% 157.60/157.51 [6497]~P107(f866(f866(f244(a930),x64971),x64972))+P107(f866(f866(f244(a930),x64971),f866(f866(f86(a930),x64972),x64973)))
% 157.60/157.51 [6536]P107(f866(f66(x65361),x65362))+~P107(f866(f66(x65361),f866(f866(f316(x65361),x65363),x65362)))
% 157.60/157.51 [6537]P107(f866(f144(x65371),x65372))+~P107(f866(f144(x65371),f866(f866(f158(x65371),x65373),x65372)))
% 157.60/157.51 [6538]P107(f866(f144(x65381),x65382))+~P107(f866(f144(x65381),f866(f866(f141(x65381),x65383),x65382)))
% 157.60/157.51 [6539]P107(f866(f144(x65391),x65392))+~P107(f866(f144(x65391),f866(f866(f141(x65391),x65392),x65393)))
% 157.60/157.51 [6591]~P114(x65911)+E(f866(f866(f86(x65911),x65912),f866(f866(f87(x65911),x65913),x65912)),f866(f866(f87(x65911),f866(f866(f86(x65911),x65913),f84(x65911))),x65912))
% 157.60/157.51 [6637]~E(x66371,x66372)+~P107(f866(f866(f244(f937(x66373,a925)),x66371),x66372))
% 157.60/157.51 [6684]P107(f866(f866(f336(x66841),x66842),x66843))+P107(f866(f866(f336(x66841),x66842),f866(f85(f937(x66841,a925)),x66843)))
% 157.60/157.51 [6692]E(f151(x66921,f866(f866(f145(x66921),x66922),x66923)),f151(x66921,x66923))+~P107(f866(f866(f244(a930),x66922),f866(f196(f931(x66921)),x66923)))
% 157.60/157.51 [6693]E(f866(f866(f182(x66931),x66932),f121(x66931,x66933)),f866(f866(f182(x66931),x66932),x66933))+~P107(f866(f866(f244(a930),x66932),f866(f196(f931(x66931)),x66933)))
% 157.60/157.51 [6748]E(f866(f866(f866(f190(f931(x67481),f931(x67481)),x67482),f174(x67481)),x67483),x67483)+~E(f50(a930,x67482,f866(f196(f931(x67481)),x67483)),f2(a930))
% 157.60/157.51 [6755]~P8(x67551,x67553,x67552)+E(f866(f866(f296(x67551,x67551,x67551),f866(f294(x67551,x67551),x67552)),x67552),x67552)
% 157.60/157.51 [6800]~E(f866(f866(f117(f937(x68001,a925)),x68002),x68003),x68003)+P107(f866(f866(f243(f937(x68001,a925)),x68002),x68003))
% 157.60/157.51 [6805]~P55(x68051,x68051,x68053)+P55(x68051,x68051,f866(f866(f190(f936(x68051,x68051),a925),x68052),x68053))
% 157.60/157.51 [6809]~P107(f866(f866(f336(x68091),x68093),f866(f179(x68091),x68092)))+P107(f866(f866(f244(a930),f2(a930)),f866(f196(f931(x68091)),x68092)))
% 157.60/157.51 [6835]~P89(x68351)+E(f866(f81(x68351),f866(f866(f86(x68351),f866(f81(x68351),x68352)),f866(f81(x68351),x68353))),f866(f866(f86(x68351),f866(f81(x68351),x68352)),f866(f81(x68351),x68353)))
% 157.60/157.51 [6845]E(f866(f866(f41(a930),f866(f866(f87(a930),x68451),x68452)),f866(f866(f87(a930),x68451),x68453)),f866(f866(f41(a930),x68452),x68453))+~P107(f866(f866(f244(a930),f2(a930)),x68451))
% 157.60/157.51 [6982]~P107(f866(f66(x69821),x69823))+E(f866(f866(f69(x69821,f937(x69821,a925),f316(x69821)),x69822),x69823),f866(f866(f117(f937(x69821,a925)),x69823),x69822))
% 157.60/157.51 [7037]E(f866(f866(f117(f937(x70371,a925)),x70372),x70373),x70372)+~P107(f866(f866(f243(f937(x70371,a925)),x70373),x70372))
% 157.60/157.51 [7039]E(f866(f866(f117(f937(x70391,a925)),x70392),x70393),x70393)+~P107(f866(f866(f243(f937(x70391,a925)),x70392),x70393))
% 157.60/157.51 [7040]E(f866(f866(f108(f937(x70401,a925)),x70402),x70403),x70403)+~P107(f866(f866(f243(f937(x70401,a925)),x70403),x70402))
% 157.60/157.51 [7041]E(f866(f866(f108(f937(x70411,a925)),x70412),x70413),x70412)+~P107(f866(f866(f243(f937(x70411,a925)),x70412),x70413))
% 157.60/157.51 [7091]~P107(f866(f144(x70911),x70912))+E(f866(f866(f23(f937(x70911,a925)),f866(f179(x70911),x70912)),f866(f866(f316(x70911),x70913),f195(f937(x70911,a925)))),f866(f179(x70911),f177(x70911,x70913,x70912)))
% 157.60/157.51 [7145]P37(x71451,x71452)+~P37(x71451,f866(f866(f190(f936(x71451,x71451),a925),x71453),x71452))
% 157.60/157.51 [7209]P107(f866(f54(x72091,x72092),f866(a56,x72093)))+~P107(f866(f54(f866(f85(a1),x72091),f866(f85(a1),x72092)),x72093))
% 157.60/157.51 [7214]E(f866(f866(f23(f937(x72141,a925)),f866(f866(f316(x72141),x72142),x72143)),f866(f866(f316(x72141),x72142),f195(f937(x72141,a925)))),x72143)+P107(f866(f866(f336(x72141),x72142),x72143))
% 157.60/157.51 [7235]E(f866(f866(f108(f937(x72351,a925)),f866(f179(x72351),x72352)),f866(f179(x72351),x72353)),f195(f937(x72351,a925)))+~P107(f866(f144(x72351),f866(f866(f141(x72351),x72352),x72353)))
% 157.60/157.51 [7250]~P107(f866(f866(f336(x72501),x72502),f866(f179(x72501),x72503)))+~P107(f866(f144(x72501),f866(f866(f158(x72501),x72502),x72503)))
% 157.60/157.51 [7320]P31(x73201,x73202,x73203)+P107(f866(f866(f244(a930),f768(x73203,x73202,x73201)),f866(f196(f931(x73201)),x73203)))
% 157.60/157.51 [7330]E(f866(f866(f108(f937(x73301,a925)),x73302),x73303),f195(f937(x73301,a925)))+P107(f866(f866(f336(x73301),f905(x73303,x73302,x73301)),x73302))
% 157.60/157.51 [7331]E(f866(f866(f108(f937(x73311,a925)),x73312),x73313),f195(f937(x73311,a925)))+P107(f866(f866(f336(x73311),f911(x73313,x73312,x73311)),x73313))
% 157.60/157.51 [7334]E(f121(x73341,f866(f866(f182(x73341),x73342),x73343)),f866(f866(f182(x73341),f866(f866(f23(a930),x73342),f84(a930))),x73343))+~P107(f866(f866(f243(a930),x73342),f866(f196(f931(x73341)),x73343)))
% 157.60/157.51 [7394]~P33(x73943,x73942,x73941)+P107(f866(f866(f244(a930),f762(x73941,x73942,x73943)),f866(f196(f931(x73943)),x73941)))
% 157.60/157.51 [7412]P107(f866(f866(f244(a930),f2(a930)),x74121))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x74122),x74121)),f866(f866(f87(a930),x74123),x74121)))
% 157.60/157.51 [7413]P107(f866(f866(f244(a930),f2(a930)),x74131))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x74131),x74132)),f866(f866(f87(a930),x74131),x74133)))
% 157.60/157.51 [7416]~P107(f866(f866(f336(x74161),x74162),x74163))+~P107(f866(f866(f336(x74161),x74162),f866(f85(f937(x74161,a925)),x74163)))
% 157.60/157.51 [7422]~P107(f866(f866(f244(f937(x74221,a925)),x74222),x74223))+P107(f866(f866(f243(f937(x74221,a925)),x74222),x74223))
% 157.60/157.51 [7532]~P107(f866(f866(f243(a930),x75323),x75322))+P107(f866(f866(f243(a930),f866(f866(f23(a930),x75321),x75322)),f866(f866(f23(a930),x75321),x75323)))
% 157.60/157.51 [7533]~P107(f866(f866(f243(a930),x75331),x75333))+P107(f866(f866(f243(a930),f866(f866(f23(a930),x75331),x75332)),f866(f866(f23(a930),x75333),x75332)))
% 157.60/157.51 [7535]~P107(f866(f866(f243(a930),x75352),x75353))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x75351),x75352)),f866(f866(f87(a930),x75351),x75353)))
% 157.60/157.51 [7537]~P107(f866(f866(f243(a930),x75371),x75373))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x75371),x75372)),f866(f866(f87(a930),x75373),x75372)))
% 157.60/157.51 [7538]~P107(f866(f866(f243(a930),x75382),x75383))+P107(f866(f866(f243(a930),f866(f866(f86(a930),x75381),x75382)),f866(f866(f86(a930),x75381),x75383)))
% 157.60/157.51 [7539]~P107(f866(f866(f243(a930),x75391),x75393))+P107(f866(f866(f243(a930),f866(f866(f86(a930),x75391),x75392)),f866(f866(f86(a930),x75393),x75392)))
% 157.60/157.51 [7540]~P107(f866(f866(f243(a930),x75401),x75403))+P107(f866(f866(f243(a930),f866(f866(f41(a930),x75401),x75402)),f866(f866(f41(a930),x75403),x75402)))
% 157.60/157.51 [7541]~P107(f866(f866(f243(a1),x75412),x75413))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x75411),x75412)),f866(f866(f86(a1),x75411),x75413)))
% 157.60/157.51 [7544]~P107(f866(f866(f244(a930),x75442),x75443))+P107(f866(f866(f244(a930),f866(f866(f86(a930),x75441),x75442)),f866(f866(f86(a930),x75441),x75443)))
% 157.60/157.51 [7545]~P107(f866(f866(f244(a930),x75451),x75453))+P107(f866(f866(f244(a930),f866(f866(f86(a930),x75451),x75452)),f866(f866(f86(a930),x75453),x75452)))
% 157.60/157.51 [7546]~P107(f866(f866(f244(a1),x75461),x75463))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x75461),x75462)),f866(f866(f86(a1),x75463),x75462)))
% 157.60/157.51 [7622]E(x76221,x76222)+~P107(f866(f866(f336(x76223),x76221),f866(f866(f316(x76223),x76222),f195(f937(x76223,a925)))))
% 157.60/157.51 [7624]~E(f866(f866(f108(f937(x76241,a925)),x76242),x76243),f195(f937(x76241,a925)))+P107(f866(f866(f243(f937(x76241,a925)),x76242),f866(f85(f937(x76241,a925)),x76243)))
% 157.60/157.51 [7629]P107(f866(f866(f336(f937(x76291,a925)),x76292),f866(f315(x76291),x76293)))+~P107(f866(f866(f243(f937(x76291,a925)),x76292),x76293))
% 157.60/157.51 [7634]P107(f866(f866(f336(x76341),f431(x76342,x76343,x76341)),x76343))+P107(f866(f866(f243(f937(x76341,a925)),x76343),x76342))
% 157.60/157.51 [7680]E(f866(f866(f158(x76801),f866(f866(f171(x76801),x76802),x76803)),f866(f866(f145(x76801),f866(a119,x76803)),x76802)),f866(f866(f145(x76801),x76803),x76802))+~P107(f866(f866(f244(a930),x76803),f866(f196(f931(x76801)),x76802)))
% 157.60/157.51 [7706]P107(f866(f866(f336(f936(x77061,x77061)),x77062),f314(x77061,x77063)))+~P107(f866(f866(f336(f936(x77061,x77061)),x77062),x77063))
% 157.60/157.51 [7715]~P107(f866(f866(f336(f937(x77151,a925)),x77152),f866(f315(x77151),x77153)))+P107(f866(f866(f243(f937(x77151,a925)),x77152),x77153))
% 157.60/157.51 [7758]P107(f866(f866(f243(f937(x77581,a925)),x77582),f42(f937(x77581,a925),x77583)))+~P107(f866(f866(f336(f937(x77581,a925)),x77582),x77583))
% 157.60/157.51 [7780]~P142(x77801)+E(f866(f866(f87(x77801),f866(f866(f252(x77801),f866(f85(x77801),f84(x77801))),x77802)),f866(f866(f252(x77801),x77803),x77802)),f866(f866(f252(x77801),f866(f85(x77801),x77803)),x77802))
% 157.60/157.51 [7803]E(f866(f866(f171(x78031),x78032),f866(f866(f23(a930),f866(f196(f931(x78031)),x78032)),f866(a119,x78033))),f866(f866(f171(x78031),f866(f175(x78031),x78032)),x78033))+~P107(f866(f866(f244(a930),x78033),f866(f196(f931(x78031)),x78032)))
% 157.60/157.51 [7820]~E(f866(f866(f108(f937(x78201,a925)),f623(x78203,x78202,x78201)),x78203),f195(f937(x78201,a925)))+E(f866(f866(f108(f937(x78201,a925)),f42(f937(x78201,a925),x78202)),x78203),f195(f937(x78201,a925)))
% 157.60/157.51 [7882]~P107(f866(f866(f336(x78823),x78822),f866(f179(x78823),x78821)))+P107(f866(f866(f244(a930),f642(x78821,x78822,x78823)),f866(f196(f931(x78823)),x78821)))
% 157.60/157.51 [7890]P107(f866(f866(f336(x78901),f866(f866(f171(x78901),x78902),x78903)),f866(f179(x78901),x78902)))+~P107(f866(f866(f244(a930),x78903),f866(f196(f931(x78901)),x78902)))
% 157.60/157.51 [7988]~P107(f866(x79882,f726(x79883,x79882,x79881)))+E(f866(f866(f145(x79881),f866(f196(f931(x79881)),f184(x79881,x79882,x79883))),x79883),f120(x79881))
% 157.60/157.51 [8001]P107(f866(f866(f243(f937(f931(x80011),a925)),f168(x80011,x80012)),f168(x80011,x80013)))+~P107(f866(f866(f243(f937(x80011,a925)),x80012),x80013))
% 157.60/157.51 [8002]P107(f866(f866(f243(f937(f931(x80021),a925)),f167(x80021,x80022)),f167(x80021,x80023)))+~P107(f866(f866(f243(f937(x80021,a925)),x80022),x80023))
% 157.60/157.51 [8028]E(f866(f866(f108(f937(x80281,a925)),f42(f937(x80281,a925),x80282)),x80283),f195(f937(x80281,a925)))+P107(f866(f866(f336(f937(x80281,a925)),f623(x80283,x80282,x80281)),x80282))
% 157.60/157.51 [8030]~P107(f866(f866(f336(f937(x80301,a925)),x80303),x80302))+P107(f866(f866(f243(f937(x80301,a925)),f43(f937(x80301,a925),x80302)),x80303))
% 157.60/157.51 [8032]E(f866(f866(f108(f937(x80321,a925)),x80322),x80323),f195(f937(x80321,a925)))+~P107(f866(f866(f243(f937(x80321,a925)),x80322),f866(f85(f937(x80321,a925)),x80323)))
% 157.60/157.51 [8078]E(f866(f866(f23(a930),f866(f866(f86(a930),f866(f172(a930),x80781)),x80782)),f866(f866(f171(a930),x80781),x80783)),f866(f172(a930),f866(f866(f166(a930,x80781),x80783),x80782)))+~P107(f866(f866(f244(a930),x80783),f866(f196(f931(a930)),x80781)))
% 157.60/157.51 [8129]P107(f866(f866(f243(a930),x81291),x81292))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x81293),x81291)),f866(f866(f86(a930),x81293),x81292)))
% 157.60/157.51 [8132]P107(f866(f866(f244(a930),x81321),x81322))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),x81323),x81321)),f866(f866(f86(a930),x81323),x81322)))
% 157.60/157.51 [8133]P107(f866(f866(f244(a930),x81331),x81332))+~P107(f866(f866(f244(a930),f866(f866(f87(a930),x81333),x81331)),f866(f866(f87(a930),x81333),x81332)))
% 157.60/157.51 [8134]P107(f866(f866(f244(a930),x81341),x81342))+~P107(f866(f866(f244(a930),f866(f866(f87(a930),x81341),x81343)),f866(f866(f87(a930),x81342),x81343)))
% 157.60/157.51 [8162]P107(f866(f866(f244(a930),f2(a930)),x81621))+~P107(f866(f866(f244(a930),f866(f866(f87(a930),x81622),x81621)),f866(f866(f87(a930),x81623),x81621)))
% 157.60/157.51 [8163]P107(f866(f866(f244(a930),f2(a930)),x81631))+~P107(f866(f866(f244(a930),f866(f866(f87(a930),x81631),x81632)),f866(f866(f87(a930),x81631),x81633)))
% 157.60/157.51 [8201]~P107(f866(f866(f336(x82011),f431(x82013,x82012,x82011)),x82013))+P107(f866(f866(f243(f937(x82011,a925)),x82012),x82013))
% 157.60/157.51 [8237]E(f255(x82371,x82372,x82373),x82372)+~P107(f866(f866(f243(f937(x82371,a925)),x82373),f866(f866(f316(x82371),x82372),f195(f937(x82371,a925)))))
% 157.60/157.51 [8287]~P107(f866(f144(x82871),x82873))+E(f866(f143(x82871,f866(f866(f8(a925,a925,x82871),a329),f866(a332,x82872))),x82873),f177(x82871,x82872,x82873))
% 157.60/157.51 [8312]E(f866(f866(f145(x83121),f866(f196(f931(x83121)),f184(x83121,x83122,x83123))),x83123),f120(x83121))+P107(f866(f866(f336(x83121),f726(x83123,x83122,x83121)),f866(f179(x83121),x83123)))
% 157.60/157.51 [8316]E(f866(f866(f141(x83161),f866(f866(f182(x83161),x83162),x83163)),f866(f866(f158(x83161),f866(f866(f171(x83161),x83163),x83162)),f120(x83161))),f866(f866(f182(x83161),f866(a119,x83162)),x83163))+~P107(f866(f866(f244(a930),x83162),f866(f196(f931(x83161)),x83163)))
% 157.60/157.51 [8376]E(f866(f143(x83761,f866(f866(f8(a925,a925,x83761),a329),f866(a332,x83762))),x83763),x83763)+P107(f866(f866(f336(x83761),x83762),f866(f179(x83761),x83763)))
% 157.60/157.51 [8382]P107(f866(f866(f243(f937(f937(x83821,a925),a925)),f256(x83821,x83822)),f256(x83821,x83823)))+~P107(f866(f866(f243(f937(x83821,a925)),x83822),x83823))
% 157.60/157.51 [8421]~P107(f866(f144(x84211),x84213))+P107(f866(f144(x84211),f866(f866(f866(f190(f931(x84211),f931(x84211)),x84212),f174(x84211)),x84213)))
% 157.60/157.51 [8427]~P107(f866(f866(f244(a930),x84272),x84273))+P107(f866(f866(f244(a930),f866(f866(f87(a930),f866(a119,x84271)),x84272)),f866(f866(f87(a930),f866(a119,x84271)),x84273)))
% 157.60/157.51 [8447]P107(f866(f866(f243(f937(f937(x84471,a925),a925)),f866(f315(x84471),x84472)),f866(f315(x84471),x84473)))+~P107(f866(f866(f243(f937(x84471,a925)),x84472),x84473))
% 157.60/157.51 [8516]~E(f866(f317(x85161,x85162,x85163),f250(f937(x85161,a925))),f250(f937(x85162,a925)))+E(f866(f78(x85161,x85162,x85162,x85163),f97(x85161,x85162,f250(f937(x85161,a925)),x85163)),f32(x85162))
% 157.60/157.51 [8610]~P107(f866(f866(f243(f937(x86101,a925)),x86103),x86102))+P107(f866(f866(f243(f937(x86101,a925)),f866(f85(f937(x86101,a925)),x86102)),f866(f85(f937(x86101,a925)),x86103)))
% 157.60/157.51 [8643]E(f866(f317(a930,a930,f866(f866(f7(a930,a930,a930),f23(a930)),x86431)),f866(f309(a930,x86432),x86433)),f866(f309(a930,f866(f866(f23(a930),x86432),x86431)),f866(f866(f23(a930),x86433),x86431)))+~P107(f866(f866(f244(a930),x86431),x86433))
% 157.60/157.51 [8669]~P82(x86691)+E(f866(f866(f86(x86691),x86692),f866(f149(x86691,x86691,f86(x86691),f2(x86691)),x86693)),f866(f149(x86691,x86691,f86(x86691),x86692),x86693))
% 157.60/157.51 [8746]~P89(x87461)+P107(f866(f866(f243(x87461),f866(f81(x87461),f866(f866(f23(x87461),x87462),x87463))),f866(f866(f86(x87461),f866(f81(x87461),x87462)),f866(f81(x87461),x87463))))
% 157.60/157.51 [8747]~P89(x87471)+P107(f866(f866(f243(x87471),f866(f81(x87471),f866(f866(f86(x87471),x87472),x87473))),f866(f866(f86(x87471),f866(f81(x87471),x87472)),f866(f81(x87471),x87473))))
% 157.60/157.51 [8758]E(f866(f866(f86(a1),f866(f866(f87(a1),x87581),f50(a1,f866(f866(f41(a1),x87582),x87581),x87583))),f50(a1,x87582,x87581)),f50(a1,x87582,f866(f866(f87(a1),x87581),x87583)))+~P107(f866(f866(f244(a1),f2(a1)),x87583))
% 157.60/157.51 [8764]E(f866(f866(f141(x87641),f866(f866(f182(x87641),x87642),x87643)),f866(f866(f158(x87641),f866(f148(x87641),f866(f866(f145(x87641),x87642),x87643))),f120(x87641))),f866(f866(f182(x87641),f866(a119,x87642)),x87643))+~P107(f866(f866(f244(a930),x87642),f866(f196(f931(x87641)),x87643)))
% 157.60/157.51 [8784]E(f866(f276(x87841,f866(f866(f161(x87841,f936(a106,x87841)),f866(f260(a106,x87841),f84(a106))),x87842)),f866(a3,x87843)),f866(f866(f171(x87841),x87842),x87843))+~P107(f866(f866(f244(a930),x87843),f866(f196(f931(x87841)),x87842)))
% 157.60/157.51 [8852]P107(f866(f866(f336(f936(x88521,x88521)),x88522),f866(f866(f296(x88521,x88521,x88521),x88523),f314(x88521,x88523))))+~P107(f866(f866(f336(f936(x88521,x88521)),x88522),x88523))
% 157.60/157.51 [8863]E(f866(f317(x88631,x88632,x88633),f250(f937(x88631,a925))),f250(f937(x88632,a925)))+~E(f866(f78(x88631,x88632,x88632,x88633),f97(x88631,x88632,f250(f937(x88631,a925)),x88633)),f32(x88632))
% 157.60/157.51 [8872]P107(f866(f866(f243(a930),x88721),x88722))+~P107(f866(f866(f243(a930),f866(f866(f87(a930),f866(a119,x88723)),x88721)),f866(f866(f87(a930),f866(a119,x88723)),x88722)))
% 157.60/157.51 [8888]P107(f866(f866(f243(f937(x88881,a925)),x88882),x88883))+~P107(f866(f866(f243(f937(x88881,a925)),f866(f85(f937(x88881,a925)),x88883)),f866(f85(f937(x88881,a925)),x88882)))
% 157.60/157.51 [8911]P107(f866(f144(x89111),x89112))+~P107(f866(f144(x89111),f866(f866(f866(f190(f931(x89111),f931(x89111)),x89113),f174(x89111)),x89112)))
% 157.60/157.51 [8984]E(f866(f293(x89841,x89841,f314(x89841,x89842)),x89843),x89843)+~P107(f866(f866(f243(f937(x89841,a925)),f866(f293(x89841,x89841,x89842),x89843)),x89843))
% 157.60/157.51 [9032]~P110(x90321)+P13(x90321,f866(f143(x90321,f866(f866(f7(x90321,x90321,a925),a332),f866(x90322,x90323))),x90323))
% 157.60/157.51 [9039]~P107(f866(f866(f243(a930),x90391),x90392))+P107(f866(f866(f243(a930),x90391),f866(f149(a930,a930,f86(a930),x90392),x90393)))
% 157.60/157.51 [9127]~P107(f866(f866(f336(f936(x91271,x91271)),x91272),f314(x91271,x91273)))+P107(f866(f866(f336(f936(x91271,x91271)),x91272),f866(f866(f190(f936(x91271,x91271),a925),f586(x91273,x91272,x91271)),x91273)))
% 157.60/157.51 [9212]~P82(x92121)+E(f866(f866(f86(x92121),x92122),f866(f149(x92121,x92121,f866(f7(x92121,x92121,x92121),f86(x92121)),f2(x92121)),f866(f175(x92121),x92123))),f866(f149(x92121,x92121,f86(x92121),x92122),x92123))
% 157.60/157.51 [9329]~P26(x93292,x93291,x93293,f250(f937(x93292,a925)),f250(f937(x93291,a925)))+E(f97(x93291,x93292,f250(f937(x93291,a925)),f97(x93292,x93291,f250(f937(x93292,a925)),x93293)),x93293)
% 157.60/157.51 [9480]P55(x94801,x94802,x94803)+P107(f866(f866(f336(f936(x94801,x94802)),f866(f866(f260(x94801,x94802),f588(x94803,x94802,x94801)),f585(x94803,x94802,x94801))),x94803))
% 157.60/157.51 [9481]P55(x94811,x94812,x94813)+P107(f866(f866(f336(f936(x94811,x94812)),f866(f866(f260(x94811,x94812),f588(x94813,x94812,x94811)),f584(x94813,x94812,x94811))),x94813))
% 157.60/157.51 [9551]~P107(f866(f866(f336(f936(x95511,x95511)),x95512),f866(f866(f296(x95511,x95511,x95511),x95513),f314(x95511,x95513))))+P107(f866(f866(f336(f936(x95511,x95511)),x95512),f866(f866(f190(f936(x95511,x95511),a925),f597(x95513,x95512,x95511)),x95513)))
% 157.60/157.51 [9552]~P107(f866(x95521,f866(f866(f171(x95522),x95523),f866(f196(f931(x95522)),f184(x95522,x95521,x95523)))))+~P107(f866(f866(f244(a930),f866(f196(f931(x95522)),f184(x95522,x95521,x95523))),f866(f196(f931(x95522)),x95523)))
% 157.60/157.51 [9641]~P107(f866(f866(f243(f937(x96411,a925)),x96412),x96413))+P107(f866(f866(f243(f937(x96411,a925)),f866(f866(f7(x96411,f937(x96411,a925),a925),f336(x96411)),x96412)),f866(f866(f7(x96411,f937(x96411,a925),a925),f336(x96411)),x96413)))
% 157.60/157.51 [9698]~P107(f866(f866(f336(f936(f937(x96981,a925),f937(x96981,a925))),f866(f866(f260(f937(x96981,a925),f937(x96981,a925)),x96982),x96983)),f321(x96981)))+P107(f866(f866(f244(f937(x96981,a925)),x96982),x96983))
% 157.60/157.51 [9722]P56(x97221,x97222,x97223)+~P107(f866(f866(f336(f936(x97221,x97221)),f866(f866(f260(x97221,x97221),f570(x97223,x97222,x97221)),f569(x97223,x97222,x97221))),x97223))
% 157.60/157.51 [9723]P56(x97231,x97232,x97233)+~P107(f866(f866(f336(f936(x97231,x97231)),f866(f866(f260(x97231,x97231),f569(x97233,x97232,x97231)),f570(x97233,x97232,x97231))),x97233))
% 157.60/157.51 [9760]~P107(f866(f866(f336(f936(f931(x97601),f931(x97601))),f866(f866(f260(f931(x97601),f931(x97601)),x97602),x97602)),f154(x97601,x97603)))+P107(f866(f866(f336(f936(x97601,x97601)),f866(f866(f260(x97601,x97601),f657(x97602,x97603,x97601)),f657(x97602,x97603,x97601))),x97603))
% 157.60/157.51 [9810]P107(f866(f866(f243(f937(x98101,a925)),x98102),x98103))+~P107(f866(f866(f243(f937(x98101,a925)),f866(f866(f7(x98101,f937(x98101,a925),a925),f336(x98101)),x98102)),f866(f866(f7(x98101,f937(x98101,a925),a925),f336(x98101)),x98103)))
% 157.60/157.51 [9891]E(f866(f866(f23(a930),f866(f866(f6(a930,a930),x98911),f866(f290(a930),x98912))),f866(f866(f6(a930,a930),x98913),f866(f290(a930),x98912))),f866(f866(f6(a930,a930),f866(f866(f18(a930,a930,a930),f866(f866(f8(a930,f937(a930,a930),a930),f23(a930)),x98911)),x98913)),f866(f290(a930),x98912)))+~P107(f866(f866(f243(a930),f866(x98913,f420(x98912,x98911,x98913))),f866(x98911,f420(x98912,x98911,x98913))))
% 157.60/157.51 [5892]~P77(x58921)+E(f866(f866(f23(x58921),f866(f866(f86(x58921),x58922),x58923)),x58923),x58922)
% 157.60/157.51 [5893]~P77(x58931)+E(f866(f866(f86(x58931),f866(f866(f23(x58931),x58932),x58933)),x58933),x58932)
% 157.60/157.51 [6122]~P77(x61221)+E(f866(f866(f86(x61221),x61222),f866(f866(f86(x61221),f866(f85(x61221),x61222)),x61223)),x61223)
% 157.60/157.51 [6206]~P81(x62061)+E(f866(f866(f87(x62061),f866(f866(f252(x62061),x62062),x62063)),x62062),f866(f866(f252(x62061),x62062),f866(a119,x62063)))
% 157.60/157.51 [6207]~P114(x62071)+E(f866(f866(f87(x62071),f866(f866(f252(x62071),x62072),x62073)),x62072),f866(f866(f252(x62071),x62072),f866(a119,x62073)))
% 157.60/157.51 [6424]~P128(x64241)+E(f866(f81(x64241),f866(f866(f252(x64241),f866(f85(x64241),x64242)),x64243)),f866(f81(x64241),f866(f866(f252(x64241),x64242),x64243)))
% 157.60/157.51 [6467]~P81(x64671)+E(f866(f866(f87(x64671),f866(f866(f252(x64671),x64672),x64673)),x64672),f866(f866(f87(x64671),x64672),f866(f866(f252(x64671),x64672),x64673)))
% 157.60/157.51 [6527]E(f866(f866(f23(a106),f866(f866(f86(a106),x65271),x65272)),x65273),f282(x65271,x65272,x65273))+~P107(f866(f866(f244(a106),x65272),x65273))
% 157.60/157.51 [6550]~E(f866(f866(f145(x65501),x65503),x65502),f120(x65501))+P107(f866(f866(f243(a930),f866(f196(f931(x65501)),x65502)),x65503))
% 157.60/157.51 [6689]E(f866(f866(f87(a930),f866(f110(a930),x66891)),f866(f866(f87(a930),f866(f110(a930),x66892)),x66893)),f2(a930))+~P107(f866(f866(f244(a1),x66891),a89))
% 157.60/157.51 [6707]~P65(x67071)+E(f866(f866(f252(x67071),f866(f866(f297(x67071),f84(x67071)),x67072)),x67073),f866(f866(f297(x67071),f84(x67071)),f866(f866(f252(x67071),x67072),x67073)))
% 157.60/157.51 [6785]E(f866(f866(f23(a930),f866(f866(f86(a930),x67851),x67852)),x67853),f866(f866(f23(a930),x67851),f866(f866(f23(a930),x67853),x67852)))+~P107(f866(f866(f243(a930),x67852),x67853))
% 157.60/157.51 [6787]E(f866(f866(f23(a930),f866(f866(f86(a930),x67871),x67872)),x67873),f866(f866(f86(a930),x67871),f866(f866(f23(a930),x67872),x67873)))+~P107(f866(f866(f243(a930),x67873),x67872))
% 157.60/157.51 [6826]~P83(x68261)+P107(f866(f866(f243(x68261),f866(f866(f108(x68261),x68262),x68263)),x68263))
% 157.60/157.51 [6827]~P103(x68271)+P107(f866(f866(f243(x68271),f866(f866(f108(x68271),x68272),x68273)),x68273))
% 157.60/157.51 [6828]~P83(x68281)+P107(f866(f866(f243(x68281),f866(f866(f108(x68281),x68282),x68283)),x68282))
% 157.60/157.51 [6829]~P103(x68291)+P107(f866(f866(f243(x68291),f866(f866(f108(x68291),x68292),x68293)),x68292))
% 157.60/157.51 [6830]~P110(x68301)+P107(f866(f866(f243(x68301),f866(f866(f241(x68301),x68302),x68303)),x68303))
% 157.60/157.51 [6831]~P110(x68311)+P107(f866(f866(f243(x68311),f866(f866(f241(x68311),x68312),x68313)),x68312))
% 157.60/157.51 [6844]E(f866(f866(f41(a1),f866(f866(f41(a1),x68441),x68442)),x68443),f866(f866(f41(a1),x68441),f866(f866(f87(a1),x68442),x68443)))+~P107(f866(f866(f244(a1),f2(a1)),x68443))
% 157.60/157.51 [6894]~P114(x68941)+E(f866(f866(f86(x68941),f866(f866(f87(x68941),x68942),x68943)),x68943),f866(f866(f87(x68941),f866(f866(f86(x68941),x68942),f84(x68941))),x68943))
% 157.60/157.51 [6895]~P96(x68951)+E(f866(f866(f87(x68951),f866(f85(x68951),f866(f110(x68951),x68952))),x68953),f866(f866(f87(x68951),f866(f110(x68951),f866(f85(a1),x68952))),x68953))
% 157.60/157.51 [6968]~P82(x69681)+E(f866(f172(x69681),f866(f866(f161(x69682,x69681),f866(f16(x69681,x69682),f2(x69681))),x69683)),f2(x69681))
% 157.60/157.51 [6983]E(f866(f866(f86(a930),f866(f110(a930),x69831)),f866(f866(f86(a930),f866(f110(a930),x69832)),x69833)),f866(f866(f86(a930),f866(f110(a930),x69832)),x69833))+~P107(f866(a200,f866(f110(a1),x69831)))
% 157.60/157.51 [6997]~P5(x69971)+E(f43(x69971,f866(f866(f316(x69971),x69972),f866(f866(f316(x69971),x69973),f195(f937(x69971,a925))))),f866(f866(f108(x69971),x69972),x69973))
% 157.60/157.51 [6998]~P5(x69981)+E(f42(x69981,f866(f866(f316(x69981),x69982),f866(f866(f316(x69981),x69983),f195(f937(x69981,a925))))),f866(f866(f117(x69981),x69982),x69983))
% 157.60/157.51 [7020]E(f866(f866(f182(x70201),x70202),x70203),x70203)+~P107(f866(f866(f243(a930),f866(f196(f931(x70201)),x70203)),x70202))
% 157.60/157.51 [7032]E(f866(f866(f145(x70321),x70322),x70323),f120(x70321))+~P107(f866(f866(f243(a930),f866(f196(f931(x70321)),x70323)),x70322))
% 157.60/157.51 [7043]E(f866(f866(f86(a930),f866(f866(f23(a930),x70431),x70432)),x70433),f866(f866(f23(a930),f866(f866(f86(a930),x70431),x70433)),x70432))+~P107(f866(f866(f243(a930),x70432),x70431))
% 157.60/157.51 [7057]~P107(f866(f866(f244(a930),x70571),x70573))+P107(f866(f866(f244(a930),f866(f866(f23(a930),x70571),x70572)),x70573))
% 157.60/157.51 [7085]~P110(x70851)+E(f177(x70851,x70852,f866(f866(f155(x70851,x70851,f5(x70851)),x70852),x70853)),x70853)
% 157.60/157.51 [7173]E(f866(f866(f23(a930),f866(f866(f86(a930),x71731),x71732)),f866(a119,x71733)),f866(f866(f23(a930),x71731),f866(a119,f866(f866(f23(a930),x71733),x71732))))+~P107(f866(f866(f243(a930),x71732),x71733))
% 157.60/157.51 [7174]~P128(x71741)+P107(f866(f866(f243(x71741),f2(x71741)),f866(f866(f252(x71741),f866(f81(x71741),x71742)),x71743)))
% 157.60/157.51 [7219]P24(x72191,x72192,x72193)+~P107(f866(f866(f243(f937(f929(x72191),a925)),x72193),x72192))
% 157.60/157.51 [7261]~P107(f866(f66(x72611),x72612))+P107(f866(f66(x72611),f866(f866(f23(f937(x72611,a925)),x72612),x72613)))
% 157.60/157.51 [7262]~P107(f866(f66(x72621),x72623))+P107(f866(f66(x72621),f866(f866(f108(f937(x72621,a925)),x72622),x72623)))
% 157.60/157.51 [7263]~P107(f866(f66(x72631),x72632))+P107(f866(f66(x72631),f866(f866(f108(f937(x72631,a925)),x72632),x72633)))
% 157.60/157.51 [7402]~P37(x74021,x74023)+P37(x74021,f866(f866(f108(f937(f936(x74021,x74021),a925)),x74022),x74023))
% 157.60/157.51 [7403]~P37(x74031,x74032)+P37(x74031,f866(f866(f108(f937(f936(x74031,x74031),a925)),x74032),x74033))
% 157.60/157.51 [7528]~P83(x75281)+E(f13(x75281,f866(f179(x75281),f866(f866(f158(x75281),x75282),x75283))),f866(f149(x75281,x75281,f117(x75281),x75282),x75283))
% 157.60/157.51 [7529]~P83(x75291)+E(f10(x75291,f866(f179(x75291),f866(f866(f158(x75291),x75292),x75293))),f866(f149(x75291,x75291,f108(x75291),x75292),x75293))
% 157.60/157.51 [7530]~P110(x75301)+E(f14(x75301,f866(f179(x75301),f866(f866(f158(x75301),x75302),x75303))),f866(f149(x75301,x75301,f242(x75301),x75302),x75303))
% 157.60/157.51 [7531]~P110(x75311)+E(f15(x75311,f866(f179(x75311),f866(f866(f158(x75311),x75312),x75313))),f866(f149(x75311,x75311,f241(x75311),x75312),x75313))
% 157.60/157.51 [7591]~P107(f866(f66(x75911),x75912))+P107(f866(f866(f243(a930),f866(f40(x75911),x75912)),f866(f40(x75911),f866(f866(f316(x75911),x75913),x75912))))
% 157.60/157.51 [7598]E(f866(f866(f117(f937(a930,a925)),f866(f309(a930,x75981),x75982)),f866(f309(a930,x75982),f866(f866(f86(a930),x75982),x75983))),f866(f309(a930,x75981),f866(f866(f86(a930),x75982),x75983)))+~P107(f866(f866(f243(a930),x75981),x75982))
% 157.60/157.51 [7607]P107(f866(f866(f243(a930),x76071),x76072))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x76073),x76071)),x76072))
% 157.60/157.51 [7608]P107(f866(f866(f243(a930),x76081),x76082))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x76081),x76083)),x76082))
% 157.60/157.51 [7609]P107(f866(f866(f244(a930),x76091),x76092))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),x76091),x76093)),x76092))
% 157.60/157.51 [7647]~P110(x76471)+E(f11(x76471,f241(x76471),f866(f179(x76471),f866(f866(f158(x76471),x76472),x76473))),f866(f149(x76471,x76471,f241(x76471),x76472),x76473))
% 157.60/157.51 [7648]~P110(x76481)+E(f12(x76481,f242(x76481),f866(f179(x76481),f866(f866(f158(x76481),x76482),x76483))),f866(f149(x76481,x76481,f242(x76481),x76482),x76483))
% 157.60/157.51 [7652]~E(x76522,f195(f937(f936(x76521,x76521),a925)))+P107(f866(f866(f243(f937(f936(x76521,x76521),a925)),x76522),x76523))
% 157.60/157.51 [7753]E(f866(f866(f117(f937(x77531,a925)),x77532),f866(f866(f23(f937(x77531,a925)),x77533),x77532)),x77533)+~P107(f866(f866(f243(f937(x77531,a925)),x77532),x77533))
% 157.60/157.51 [7754]~P107(f866(f866(f243(a930),x77541),f866(f866(f86(a930),x77543),x77542)))+P107(f866(f866(f243(a930),f866(f866(f23(a930),x77541),x77542)),x77543))
% 157.60/157.51 [7755]~P107(f866(f866(f244(a930),x77551),f866(f866(f23(a930),x77553),x77552)))+P107(f866(f866(f244(a930),f866(f866(f86(a930),x77551),x77552)),x77553))
% 157.60/157.51 [7810]E(x78101,f120(x78102))+E(f866(f148(x78102),f866(f866(f866(f190(f931(x78102),f931(x78102)),x78103),f174(x78102)),x78101)),f866(f866(f171(x78102),x78101),f50(a930,x78103,f866(f196(f931(x78102)),x78101))))
% 157.60/157.51 [7819]E(f866(f866(f316(x78191),x78192),f866(f866(f23(f937(x78191,a925)),x78193),f866(f866(f316(x78191),x78192),f195(f937(x78191,a925))))),x78193)+~P107(f866(f866(f336(x78191),x78192),x78193))
% 157.60/157.51 [7978]P107(f866(f866(f243(a930),x79781),f866(f866(f86(a930),x79782),x79783)))+~P107(f866(f866(f243(a930),f866(f866(f23(a930),x79781),x79783)),x79782))
% 157.60/157.51 [7979]P107(f866(f866(f244(a930),x79791),f866(f866(f23(a930),x79792),x79793)))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),x79791),x79793)),x79792))
% 157.60/157.51 [8005]P107(f866(f66(x80051),x80052))+~P107(f866(f66(x80051),f866(f866(f117(f937(x80051,a925)),x80053),x80052)))
% 157.60/157.51 [8006]P107(f866(f66(x80061),x80062))+~P107(f866(f66(x80061),f866(f866(f117(f937(x80061,a925)),x80062),x80063)))
% 157.60/157.51 [8077]~P45(x80771,x80773)+P107(f866(f866(f336(f936(x80771,x80771)),f866(f866(f260(x80771,x80771),x80772),x80772)),x80773))
% 157.60/157.51 [8210]E(f866(f866(f171(a930),f146(a930,f866(f309(a930,x82101),x82102))),x82103),f866(f866(f86(a930),x82101),x82103))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),x82101),x82103)),x82102))
% 157.60/157.51 [8276]E(f866(f866(f182(a930),x82761),f146(a930,f866(f309(a930,x82762),x82763))),f146(a930,f866(f309(a930,x82762),f866(f866(f86(a930),x82762),x82761))))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x82762),x82761)),x82763))
% 157.60/157.51 [8332]~P96(x83321)+E(f866(f866(f252(x83321),x83322),f866(f110(a930),f866(f866(f86(a1),x83323),x83323))),f866(f866(f92(x83321,x83321),f866(f866(f252(x83321),x83322),f866(f110(a930),x83323))),f866(f866(f18(x83321,x83321,x83321),f87(x83321)),f5(x83321))))
% 157.60/157.51 [8591]E(f866(f866(f141(x85911),f866(f866(f182(x85911),x85912),x85913)),f866(f866(f158(x85911),f866(f866(f171(x85911),x85913),x85912)),f866(f866(f145(x85911),f866(a119,x85912)),x85913))),x85913)+~P107(f866(f866(f244(a930),x85912),f866(f196(f931(x85911)),x85913)))
% 157.60/157.51 [8598]P107(f866(f866(f243(f937(x85981,a925)),f322(x85981,x85982)),f322(x85981,x85983)))+~P107(f866(f866(f243(f937(x85981,f937(x85981,a925))),x85983),x85982))
% 157.60/157.51 [8599]~P56(x85991,x85992,x85993)+P56(x85991,x85992,f866(f866(f23(f937(f936(x85991,x85991),a925)),x85993),f314(x85991,f195(f937(f936(x85991,x85991),a925)))))
% 157.60/157.51 [8618]P107(f866(f866(f243(f937(x86181,a925)),f323(x86181,x86182)),f323(x86181,x86183)))+~P107(f866(f866(f243(f937(f936(x86181,x86181),a925)),x86183),x86182))
% 157.60/157.51 [8624]~P107(f866(f866(f244(f937(x86241,a925)),x86243),x86242))+P107(f866(f866(f336(x86241),f518(x86242,x86243,x86241)),f866(f866(f23(f937(x86241,a925)),x86242),x86243)))
% 157.60/157.51 [8626]~P121(x86261)+P107(f866(f866(f243(x86261),f2(x86261)),f866(f866(f86(x86261),f866(f866(f87(x86261),x86262),x86262)),f866(f866(f87(x86261),x86263),x86263))))
% 157.60/157.51 [8658]P107(f866(f866(f243(f937(x86581,a925)),f866(f289(x86581),x86582)),f866(f289(x86581),x86583)))+~P107(f866(f866(f243(f937(f936(x86581,x86581),a925)),x86582),x86583))
% 157.60/157.51 [8687]~P54(x86871,x86872)+~P107(f866(f866(f336(f936(x86871,x86871)),f866(f866(f260(x86871,x86871),x86873),x86873)),x86872))
% 157.60/157.51 [8689]~P37(x86891,x86892)+~P107(f866(f866(f336(f936(x86891,x86891)),f866(f866(f260(x86891,x86891),x86893),x86893)),x86892))
% 157.60/157.51 [8748]P107(f866(f866(f243(f937(x87481,a925)),f43(f937(x87481,a925),x87482)),f43(f937(x87481,a925),x87483)))+~P107(f866(f866(f243(f937(f937(x87481,a925),a925)),x87483),x87482))
% 157.60/157.51 [8749]P107(f866(f866(f243(f937(x87491,a925)),f42(f937(x87491,a925),x87492)),f42(f937(x87491,a925),x87493)))+~P107(f866(f866(f243(f937(f937(x87491,a925),a925)),x87492),x87493))
% 157.60/157.51 [8803]~P8(x88031,x88033,x88032)+P107(f866(f866(f243(f937(f936(x88031,x88031),a925)),x88032),f866(f866(f262(x88031,x88031),x88033),f866(f16(f937(x88031,a925),x88031),x88033))))
% 157.60/157.51 [8804]~P53(x88041,x88043,x88042)+P107(f866(f866(f243(f937(f936(x88041,x88041),a925)),x88042),f866(f866(f262(x88041,x88041),x88043),f866(f16(f937(x88041,a925),x88041),x88043))))
% 157.60/157.51 [8853]~P89(x88531)+P107(f866(f866(f243(x88531),f866(f866(f23(x88531),f866(f81(x88531),x88532)),f866(f81(x88531),x88533))),f866(f81(x88531),f866(f866(f23(x88531),x88533),x88532))))
% 157.60/157.51 [8854]~P89(x88541)+P107(f866(f866(f243(x88541),f866(f866(f23(x88541),f866(f81(x88541),x88542)),f866(f81(x88541),x88543))),f866(f81(x88541),f866(f866(f23(x88541),x88542),x88543))))
% 157.60/157.51 [8886]P107(f866(f866(f243(f937(f936(x88861,x88861),a925)),f314(x88861,x88862)),f314(x88861,x88863)))+~P107(f866(f866(f243(f937(f936(x88861,x88861),a925)),x88862),x88863))
% 157.60/157.51 [8997]~P25(x89972,x89971,x89973,f250(f937(x89972,a925)))+E(f866(f78(x89971,x89972,x89972,f97(x89972,x89971,f250(f937(x89972,a925)),x89973)),x89973),f32(x89972))
% 157.60/157.51 [9057]P56(x90571,x90572,x90573)+~P56(x90571,x90572,f866(f866(f23(f937(f936(x90571,x90571),a925)),x90573),f314(x90571,f195(f937(f936(x90571,x90571),a925)))))
% 157.60/157.51 [9077]P107(f866(f866(f243(f937(f936(f931(x90771),f931(x90771)),a925)),f164(x90771,x90772)),f164(x90771,x90773)))+~P107(f866(f866(f243(f937(f936(x90771,x90771),a925)),x90772),x90773))
% 157.60/157.51 [9078]P107(f866(f866(f243(f937(f936(f931(x90781),f931(x90781)),a925)),f165(x90781,x90782)),f165(x90781,x90783)))+~P107(f866(f866(f243(f937(f936(x90781,x90781),a925)),x90782),x90783))
% 157.60/157.51 [9099]~P53(x90991,x90993,x90992)+P107(f866(f866(f243(f937(f936(x90991,x90991),a925)),x90992),f866(f866(f296(x90991,x90991,x90991),f866(f294(x90991,x90991),x90992)),x90992)))
% 157.60/157.51 [9155]~P107(f866(f144(x91551),x91552))+E(f866(f143(x91551,f866(f866(f7(x91551,f937(x91551,a925),a925),f336(x91551)),f866(f179(x91551),f183(x91551,x91552,x91553)))),x91552),f183(x91551,x91552,x91553))
% 157.60/157.51 [9210]E(x92101,x92102)+~P107(f866(f866(f336(f936(x92103,x92103)),f866(f866(f260(x92103,x92103),x92101),x92102)),f314(x92103,f195(f937(f936(x92103,x92103),a925)))))
% 157.60/157.51 [9292]P107(f866(f866(f336(x92921),x92922),f323(x92921,x92923)))+P107(f866(f866(f336(f936(x92921,x92921)),f866(f866(f260(x92921,x92921),f519(x92923,x92922,x92921)),x92922)),x92923))
% 157.60/157.51 [9293]P107(f866(f866(f336(x92931),x92932),f323(x92931,x92933)))+P107(f866(f866(f336(f936(x92931,x92931)),f866(f866(f260(x92931,x92931),f571(x92933,x92932,x92931)),x92932)),x92933))
% 157.60/157.51 [9294]P107(f866(f866(f336(x92941),x92942),f323(x92941,x92943)))+P107(f866(f866(f336(f936(x92941,x92941)),f866(f866(f260(x92941,x92941),f572(x92943,x92942,x92941)),x92942)),x92943))
% 157.60/157.51 [9330]P25(x93301,x93302,x93303,f250(f937(x93301,a925)))+~E(f866(f78(x93302,x93301,x93301,f97(x93301,x93302,f250(f937(x93301,a925)),x93303)),x93303),f32(x93301))
% 157.60/157.51 [9384]~P107(f866(f866(f336(f931(x93841)),x93843),f168(x93841,x93842)))+P107(f866(f167(x93841,f866(f866(f7(x93841,f937(x93841,a925),a925),f336(x93841)),x93842)),x93843))
% 157.60/157.51 [9407]P107(f866(x94073,x94072))+E(f866(f270(x94071),f866(f866(f18(x94071,a925,a925),f866(f866(f8(a925,f937(a925,a925),x94071),a333),f866(a332,x94072))),x94073)),f195(f937(x94071,a925)))
% 157.60/157.51 [9423]~P89(x94231)+P107(f866(f866(f243(x94231),f866(f81(x94231),f866(f866(f23(x94231),f866(f81(x94231),x94232)),f866(f81(x94231),x94233)))),f866(f81(x94231),f866(f866(f23(x94231),x94232),x94233))))
% 157.60/157.51 [9437]~P107(f866(x94373,x94372))+E(f866(f270(x94371),f866(f866(f18(x94371,a925,a925),f866(f866(f8(a925,f937(a925,a925),x94371),a333),f866(a332,x94372))),x94373)),f866(f866(f316(x94371),x94372),f195(f937(x94371,a925))))
% 157.60/157.51 [9444]~P107(f866(f866(f336(f937(x94441,a925)),x94443),f866(f315(x94441),x94442)))+P107(f866(f256(x94441,f866(f866(f7(x94441,f937(x94441,a925),a925),f336(x94441)),x94442)),x94443))
% 157.60/157.51 [9479]P37(x94791,x94792)+P107(f866(f866(f336(f936(x94791,x94791)),f866(f866(f260(x94791,x94791),f866(f525(x94792,x94791),f866(a119,x94793))),f866(f525(x94792,x94791),x94793))),x94792))
% 157.60/157.51 [9620]P107(f866(f866(f336(f931(x96201)),x96202),f168(x96201,x96203)))+~P107(f866(f167(x96201,f866(f866(f7(x96201,f937(x96201,a925),a925),f336(x96201)),x96203)),x96202))
% 157.60/157.51 [9633]P107(f866(f866(f336(f937(x96331,a925)),x96332),f866(f315(x96331),x96333)))+~P107(f866(f256(x96331,f866(f866(f7(x96331,f937(x96331,a925),a925),f336(x96331)),x96333)),x96332))
% 157.60/157.51 [9693]P107(f866(f866(f336(x96931),f866(f276(x96931,x96932),x96933)),f866(f179(x96931),f866(f866(f161(f936(a106,x96931),x96931),f264(a106,x96931)),x96932))))+~P107(f866(f866(f244(a106),x96933),f866(f172(a106),f866(f866(f161(f936(a106,x96931),a106),f259(a106,x96931)),x96932))))
% 157.60/157.51 [9739]P107(f866(f866(f243(f937(f936(f931(x97391),f931(x97391)),a925)),f165(x97391,x97392)),f866(f866(f262(f931(x97391),f931(x97391)),f168(x97391,x97393)),f866(f16(f937(f931(x97391),a925),f931(x97391)),f168(x97391,x97393)))))+~P107(f866(f866(f243(f937(f936(x97391,x97391),a925)),x97392),f866(f866(f262(x97391,x97391),x97393),f866(f16(f937(x97391,a925),x97391),x97393))))
% 157.60/157.51 [9763]P107(f866(f866(f336(x97631),f866(f259(x97631,f936(a106,a106)),f866(f274(x97631,x97632),x97633))),f866(f179(x97631),f866(f866(f161(f936(a106,x97631),x97631),f264(a106,x97631)),x97632))))+~P107(f866(f866(f244(a106),f2(a106)),f866(f172(a106),f866(f866(f161(f936(a106,x97631),a106),f259(a106,x97631)),x97632))))
% 157.60/157.51 [9778]~P107(f866(f866(f243(f937(f936(x97781,x97781),a925)),x97782),f866(f866(f262(x97781,x97781),x97783),f866(f16(f937(x97781,a925),x97781),x97783))))+P107(f866(f866(f243(f937(f936(x97781,x97781),a925)),f866(f866(f296(x97781,x97781,x97781),x97782),f314(x97781,x97782))),f866(f866(f262(x97781,x97781),x97783),f866(f16(f937(x97781,a925),x97781),x97783))))
% 157.60/157.51 [10079]~P37(x100791,x100792)+~P107(f866(f866(f336(f936(x100791,x100791)),f866(f866(f260(x100791,x100791),f866(x100793,f866(a119,f526(x100792,x100791,x100793)))),f866(x100793,f526(x100792,x100791,x100793)))),x100792))
% 157.60/157.51 [10080]~P37(x100801,x100802)+~P107(f866(f866(f336(f936(x100801,x100801)),f866(f866(f260(x100801,x100801),f866(x100803,f866(a119,f578(x100803,x100802,x100801)))),f866(x100803,f578(x100803,x100802,x100801)))),x100802))
% 157.60/157.51 [10324]P107(f866(f866(f243(f937(f936(f937(x103241,a925),f937(x103241,a925)),a925)),f866(f866(f296(f937(x103241,a925),f937(x103241,a925),f937(x103241,a925)),f327(x103241,x103242)),f866(f866(f117(f937(f936(f937(x103241,a925),f937(x103241,a925)),a925)),f327(x103241,x103243)),f866(f866(f316(f936(f937(x103241,a925),f937(x103241,a925))),f866(f866(f260(f937(x103241,a925),f937(x103241,a925)),f195(f937(x103241,a925))),f195(f937(x103241,a925)))),f195(f937(f936(f937(x103241,a925),f937(x103241,a925)),a925)))))),f327(x103241,x103242)))+~P107(f866(f866(f243(f937(f936(x103241,x103241),a925)),f866(f866(f296(x103241,x103241,x103241),x103242),x103243)),x103242))
% 157.60/157.51 [10325]P107(f866(f866(f243(f937(f936(f937(x103251,a925),f937(x103251,a925)),a925)),f866(f866(f296(f937(x103251,a925),f937(x103251,a925),f937(x103251,a925)),f325(x103251,x103252)),f866(f866(f117(f937(f936(f937(x103251,a925),f937(x103251,a925)),a925)),f325(x103251,x103253)),f866(f866(f316(f936(f937(x103251,a925),f937(x103251,a925))),f866(f866(f260(f937(x103251,a925),f937(x103251,a925)),f195(f937(x103251,a925))),f195(f937(x103251,a925)))),f195(f937(f936(f937(x103251,a925),f937(x103251,a925)),a925)))))),f325(x103251,x103252)))+~P107(f866(f866(f243(f937(f936(x103251,x103251),a925)),f866(f866(f296(x103251,x103251,x103251),x103252),x103253)),x103252))
% 157.60/157.51 [7527]~P107(f866(f866(f243(a930),x75272),x75271))+E(f866(f866(f23(a930),f866(a119,f866(f866(f23(a930),x75271),x75272))),x75273),f866(f866(f23(a930),f866(a119,x75271)),f866(f866(f86(a930),x75272),x75273)))
% 157.60/157.51 [7566]~P62(x75661)+E(f866(f866(f86(x75661),f50(x75661,x75662,x75663)),f866(f866(f87(x75661),f866(f866(f41(x75661),x75662),x75663)),x75663)),x75662)
% 157.60/157.51 [7759]E(f866(f866(f87(a930),f866(f110(a930),x77591)),f866(f866(f87(a930),f866(f110(a930),x77592)),x77593)),f866(f866(f87(a930),f866(f110(a930),f866(f866(f87(a1),x77591),x77592))),x77593))+P107(f866(f866(f244(a1),x77591),a89))
% 157.60/157.51 [8219]~P107(f866(f866(f243(a930),x82193),x82192))+P107(f866(f866(f243(a930),x82191),f866(f866(f23(a930),f866(f866(f86(a930),x82192),x82191)),x82193)))
% 157.60/157.51 [8412]~P107(f866(f866(f243(a930),x84121),x84122))+E(f866(f866(f141(a930),f146(a930,f866(f309(a930,x84121),x84122))),f146(a930,f866(f309(a930,x84122),f866(f866(f86(a930),x84122),x84123)))),f146(a930,f866(f309(a930,x84121),f866(f866(f86(a930),x84122),x84123))))
% 157.60/157.51 [8666]~P107(f866(f66(x86661),x86662))+E(f866(a119,f866(f40(x86661),f866(f866(f23(f937(x86661,a925)),x86662),f866(f866(f316(x86661),x86663),f195(f937(x86661,a925)))))),f866(f40(x86661),f866(f866(f316(x86661),x86663),x86662)))
% 157.60/157.51 [8705]~P107(f866(f66(x87051),x87052))+E(f866(f866(f86(a930),f84(a930)),f866(f40(x87051),f866(f866(f23(f937(x87051,a925)),x87052),f866(f866(f316(x87051),x87053),f195(f937(x87051,a925)))))),f866(f40(x87051),f866(f866(f316(x87051),x87053),x87052)))
% 157.60/157.51 [8895]E(f866(f866(f23(a930),f866(f40(x88951),x88952)),f866(f40(x88951),f866(f866(f108(f937(x88951,a925)),x88952),x88953))),f866(f40(x88951),f866(f866(f23(f937(x88951,a925)),x88952),x88953)))+~P107(f866(f66(x88951),f866(f866(f108(f937(x88951,a925)),x88952),x88953)))
% 157.60/157.51 [9150]~P6(f866(x91502,f458(x91502,x91503,x91501)))+E(f866(f107(a1),f866(f866(f9(x91501,a930),f866(f866(f8(a1,a930,x91501),a111),x91502)),x91503)),f866(f866(f9(x91501,a1),x91502),x91503))
% 157.60/157.51 [9151]~P6(f866(x91512,f459(x91512,x91513,x91511)))+E(f866(f107(a1),f866(f866(f6(x91511,a930),f866(f866(f8(a1,a930,x91511),a111),x91512)),x91513)),f866(f866(f6(x91511,a1),x91512),x91513))
% 157.60/157.51 [9193]~P107(f866(f66(x91931),x91933))+P107(f866(f866(f243(a930),f866(f866(f23(a930),f866(f40(x91931),x91932)),f866(f40(x91931),x91933))),f866(f40(x91931),f866(f866(f23(f937(x91931,a925)),x91932),x91933))))
% 157.60/157.51 [9220]P107(f866(f866(f336(x92201),f458(x92202,x92203,x92201)),x92203))+E(f866(f107(a1),f866(f866(f9(x92201,a930),f866(f866(f8(a1,a930,x92201),a111),x92202)),x92203)),f866(f866(f9(x92201,a1),x92202),x92203))
% 157.60/157.51 [9221]P107(f866(f866(f336(x92211),f459(x92212,x92213,x92211)),x92213))+E(f866(f107(a1),f866(f866(f6(x92211,a930),f866(f866(f8(a1,a930,x92211),a111),x92212)),x92213)),f866(f866(f6(x92211,a1),x92212),x92213))
% 157.60/157.51 [9284]E(f91(x92841,f866(f866(f7(x92841,f937(x92841,a925),a925),f336(x92841)),f866(f866(f23(f937(x92841,a925)),x92842),f866(f866(f316(x92841),x92843),f195(f937(x92841,a925)))))),f255(x92841,x92843,x92842))+P107(f866(f866(f243(f937(x92841,a925)),x92842),f866(f866(f316(x92841),x92843),f195(f937(x92841,a925)))))
% 157.60/157.51 [9634]E(f866(f866(f161(f931(x96341),x96341),f866(f866(f7(f931(x96341),a930,x96341),f171(x96341)),x96342)),f866(f143(f931(x96341),f866(f866(f8(a930,a925,f931(x96341)),f866(f244(a930),x96342)),f196(f931(x96341)))),x96343)),f866(f866(f171(f931(x96341)),f186(x96341,x96343)),x96342))+~P107(f866(f866(f244(a930),x96342),f866(f196(f931(f931(x96341))),f186(x96341,x96343))))
% 157.60/157.51 [9713]E(f866(f143(x97131,x97132),x97133),f184(x97131,x97132,x97133))+P107(f866(f866(f336(x97131),f730(x97133,x97132,x97131)),f866(f179(x97131),f866(f866(f145(x97131),f866(f196(f931(x97131)),f184(x97131,x97132,x97133))),x97133))))
% 157.60/157.51 [9851]E(f866(f866(f145(x98511),f866(f196(f931(x98511)),f184(x98511,x98512,x98513))),x98513),f120(x98511))+~P107(f866(x98512,f866(f148(x98511),f866(f866(f145(x98511),f866(f196(f931(x98511)),f184(x98511,x98512,x98513))),x98513))))
% 157.60/157.51 [9944]~P107(f866(f866(f336(f936(x99441,x99441)),x99442),f314(x99441,x99443)))+P107(f866(f866(f336(f936(x99441,x99441)),x99442),f866(f866(f44(a930,f937(f936(x99441,x99441),a925)),f250(f937(a930,a925))),f866(f866(f7(a930,f937(f936(x99441,x99441),a925),f937(f936(x99441,x99441),a925)),f190(f936(x99441,x99441),a925)),x99443))))
% 157.60/157.51 [10006]~P107(f866(f866(f243(f937(x100061,a925)),f866(f866(f44(a930,f937(x100061,a925)),f866(f309(a930,f2(a930)),f421(x100063,x100062,x100061))),x100062)),x100063))+P107(f866(f866(f243(f937(x100061,a925)),f866(f866(f44(a930,f937(x100061,a925)),f250(f937(a930,a925))),x100062)),x100063))
% 157.60/157.51 [10052]~P107(f866(f866(f244(a1),f2(a1)),x100523))+P107(f866(f866(f244(a1),x100521),f866(f866(f86(a1),x100522),f866(f866(f87(a1),f866(f866(f86(a1),f866(f81(a1),f866(f866(f23(a1),x100522),x100521))),f84(a1))),x100523))))
% 157.60/157.51 [10066]~P37(x100661,f866(f866(f117(f937(f936(x100661,x100661),a925)),x100662),x100663))+P37(x100661,f866(f866(f117(f937(f936(x100661,x100661),a925)),f866(f866(f117(f937(f936(x100661,x100661),a925)),f866(f866(f296(x100661,x100661,x100661),x100662),x100662)),f866(f866(f296(x100661,x100661,x100661),x100663),x100662))),x100663))
% 157.60/157.51 [10142]P37(x101421,f866(f866(f117(f937(f936(x101421,x101421),a925)),x101422),x101423))+~P37(x101421,f866(f866(f117(f937(f936(x101421,x101421),a925)),f866(f866(f117(f937(f936(x101421,x101421),a925)),f866(f866(f296(x101421,x101421,x101421),x101422),x101422)),f866(f866(f296(x101421,x101421,x101421),x101423),x101422))),x101423))
% 157.60/157.51 [9716]~P142(x97161)+E(f866(f109(x97161),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x97162),x97163)),f195(f937(f936(a930,a930),a925)))))),f866(f866(f23(x97161),f866(f107(x97161),x97162)),f866(f107(x97161),x97163)))
% 157.60/157.51 [9798]P107(f866(x97983,x97982))+E(f866(f270(x97981),f866(f866(f18(x97981,a925,a925),f866(f866(f8(a925,f937(a925,a925),x97981),a333),f866(f866(f7(x97981,x97981,a925),a332),x97982))),x97983)),f195(f937(x97981,a925)))
% 157.60/157.51 [9800]~P107(f866(x98003,x98002))+E(f866(f270(x98001),f866(f866(f18(x98001,a925,a925),f866(f866(f8(a925,f937(a925,a925),x98001),a333),f866(f866(f7(x98001,x98001,a925),a332),x98002))),x98003)),f866(f866(f316(x98001),x98002),f195(f937(x98001,a925))))
% 157.60/157.51 [10032]E(x100321,x100322)+P107(f866(f866(f251(x100323,x100323,f866(f866(f8(f937(x100323,a925),f937(x100323,a925),x100323),f866(f8(a925,a925,x100323),a329)),a332)),x100321),x100322))
% 157.60/157.51 [10121]~E(x101211,x101212)+~P107(f866(f866(f251(x101213,x101213,f866(f866(f8(f937(x101213,a925),f937(x101213,a925),x101213),f866(f8(a925,a925,x101213),a329)),a332)),x101211),x101212))
% 157.60/157.51 [10134]~P107(f866(f66(x101341),x101343))+E(f866(f866(f69(x101341,f937(x101341,a925),f866(f866(f8(f937(x101341,a925),f937(f937(x101341,a925),f937(x101341,a925)),x101341),f866(f7(f937(x101341,a925),f937(x101341,a925),f937(x101341,a925)),f23(f937(x101341,a925)))),f866(f866(f7(x101341,f937(x101341,a925),f937(x101341,a925)),f316(x101341)),f195(f937(x101341,a925))))),x101342),x101343),f866(f866(f23(f937(x101341,a925)),x101342),x101343))
% 157.60/157.51 [10164]~P107(f866(f866(f244(a1),f2(a1)),x101643))+P107(f866(f866(f244(a1),f866(f866(f23(a1),x101641),f866(f866(f87(a1),f866(f866(f86(a1),f866(f81(a1),f866(f866(f23(a1),x101641),x101642))),f84(a1))),x101643))),x101642))
% 157.60/157.51 [10412]~P107(f866(f866(f336(x104121),x104123),f323(x104121,x104122)))+P107(f866(f322(x104121,f866(f866(f7(x104121,f937(f936(x104121,x104121),a925),f937(x104121,a925)),f866(f866(f8(f937(x104121,f937(f937(f936(x104121,x104121),a925),a925)),f937(f937(f936(x104121,x104121),a925),f937(x104121,a925)),x104121),f7(x104121,f937(f936(x104121,x104121),a925),a925)),f866(f866(f8(f937(x104121,f936(x104121,x104121)),f937(x104121,f937(f937(f936(x104121,x104121),a925),a925)),x104121),f866(f8(f936(x104121,x104121),f937(f937(f936(x104121,x104121),a925),a925),x104121),f336(f936(x104121,x104121)))),f260(x104121,x104121)))),x104122)),x104123))
% 157.60/157.51 [10427]P107(f866(f866(f336(x104271),x104272),f323(x104271,x104273)))+~P107(f866(f322(x104271,f866(f866(f7(x104271,f937(f936(x104271,x104271),a925),f937(x104271,a925)),f866(f866(f8(f937(x104271,f937(f937(f936(x104271,x104271),a925),a925)),f937(f937(f936(x104271,x104271),a925),f937(x104271,a925)),x104271),f7(x104271,f937(f936(x104271,x104271),a925),a925)),f866(f866(f8(f937(x104271,f936(x104271,x104271)),f937(x104271,f937(f937(f936(x104271,x104271),a925),a925)),x104271),f866(f8(f936(x104271,x104271),f937(f937(f936(x104271,x104271),a925),a925),x104271),f336(f936(x104271,x104271)))),f260(x104271,x104271)))),x104273)),x104272))
% 157.60/157.51 [10004]~P107(f866(f66(x100041),f866(f270(x100041),x100043)))+P107(f866(f66(x100041),f866(f270(x100041),f866(f866(f18(x100041,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100041),a333),x100042)),x100043))))
% 157.60/157.51 [10005]~P107(f866(f66(x100051),f866(f270(x100051),x100052)))+P107(f866(f66(x100051),f866(f270(x100051),f866(f866(f18(x100051,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100051),a333),x100052)),x100053))))
% 157.60/157.51 [10100]P107(f866(f66(x101001),f866(f270(x101001),x101002)))+~P107(f866(f66(x101001),f866(f270(x101001),f866(f866(f18(x101001,a925,a925),f866(f866(f8(a925,f937(a925,a925),x101001),a334),x101003)),x101002))))
% 157.60/157.51 [10101]P107(f866(f66(x101011),f866(f270(x101011),x101012)))+~P107(f866(f66(x101011),f866(f270(x101011),f866(f866(f18(x101011,a925,a925),f866(f866(f8(a925,f937(a925,a925),x101011),a334),x101012)),x101013))))
% 157.60/157.51 [10389]~P107(f866(f66(x103891),x103892))+P107(f866(f66(f931(x103891)),f866(f270(f931(x103891)),f866(f866(f18(f931(x103891),a925,a925),f866(f866(f8(a925,f937(a925,a925),f931(x103891)),a333),f866(f866(f7(f931(x103891),f937(x103891,a925),a925),f866(f866(f8(f937(x103891,a925),f937(f937(x103891,a925),a925),f931(x103891)),f243(f937(x103891,a925))),f179(x103891))),x103892))),f866(f866(f7(f931(x103891),a930,a925),f866(f866(f8(a930,f937(a930,a925),f931(x103891)),a332),f196(f931(x103891)))),x103893)))))
% 157.60/157.51 [10390]~P107(f866(f66(x103901),x103902))+P107(f866(f66(f931(x103901)),f866(f270(f931(x103901)),f866(f866(f18(f931(x103901),a925,a925),f866(f866(f8(a925,f937(a925,a925),f931(x103901)),a333),f866(f866(f7(f931(x103901),f937(x103901,a925),a925),f866(f866(f8(f937(x103901,a925),f937(f937(x103901,a925),a925),f931(x103901)),f243(f937(x103901,a925))),f179(x103901))),x103902))),f866(f866(f7(f931(x103901),a930,a925),f866(f866(f8(a930,f937(a930,a925),f931(x103901)),f243(a930)),f196(f931(x103901)))),x103903)))))
% 157.60/157.51 [10114]~P114(x101141)+E(f866(f866(f252(x101141),x101142),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101143)),f866(f866(f87(x101141),f866(f866(f252(x101141),x101142),x101143)),f866(f866(f252(x101141),x101142),x101143)))
% 157.60/157.51 [10145]~P81(x101451)+E(f866(f866(f252(x101451),f866(f866(f252(x101451),x101452),x101453)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f252(x101451),x101452),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101453)))
% 157.60/157.51 [10192]~P142(x101921)+E(f866(f866(f252(x101921),f866(f85(x101921),x101922)),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101923)),f866(f866(f252(x101921),x101922),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101923)))
% 157.60/157.51 [10334]~P128(x103341)+P107(f866(f866(f243(x103341),f2(x103341)),f866(f866(f86(x103341),f866(f866(f252(x103341),x103342),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103341),x103343),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))))
% 157.60/157.52 [10202]~P114(x102021)+E(f866(f866(f252(x102021),x102022),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x102023))),f866(f866(f87(x102021),x102022),f866(f866(f87(x102021),f866(f866(f252(x102021),x102022),x102023)),f866(f866(f252(x102021),x102022),x102023))))
% 157.60/157.52 [10252]~P81(x102521)+E(f866(f866(f87(x102521),x102522),f866(f866(f252(x102521),f866(f866(f252(x102521),x102522),x102523)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x102521),x102522),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x102523))))
% 157.60/157.52 [10289]~P128(x102891)+P107(f866(f866(f243(x102891),f2(x102891)),f866(f866(f252(x102891),x102892),f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x102893))))
% 157.60/157.52 [10365]~P96(x103651)+E(f866(f866(f23(x103651),f866(f866(f86(x103651),f866(f866(f252(x103651),x103652),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103651),x103653),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f866(f866(f87(x103651),f866(f866(f87(x103651),f866(f110(x103651),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103652)),x103653)),f866(f866(f252(x103651),f866(f866(f23(x103651),x103652),x103653)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.52 [10366]~P96(x103661)+E(f866(f866(f86(x103661),f866(f866(f86(x103661),f866(f866(f252(x103661),x103662),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103661),x103663),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f866(f866(f87(x103661),f866(f866(f87(x103661),f866(f110(x103661),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103662)),x103663)),f866(f866(f252(x103661),f866(f866(f86(x103661),x103662),x103663)),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.60/157.52 [4920]E(x49201,x49202)+~E(f31(x49203,x49201),f31(x49204,x49202))
% 157.60/157.52 [4921]E(x49211,x49212)+~E(f31(x49211,x49213),f31(x49212,x49214))
% 157.60/157.52 [4922]E(x49221,x49222)+~E(f26(x49223,x49221),f26(x49224,x49222))
% 157.60/157.52 [4923]E(x49231,x49232)+~E(f26(x49231,x49233),f26(x49232,x49234))
% 157.60/157.52 [4924]E(x49241,x49242)+~E(f30(x49243,x49241),f30(x49244,x49242))
% 157.60/157.52 [4925]E(x49251,x49252)+~E(f30(x49251,x49253),f30(x49252,x49254))
% 157.60/157.52 [8022]P25(x80221,x80222,x80223,x80224)+~E(f445(x80224,x80223,x80222,x80221),f453(x80224,x80223,x80222,x80221))
% 157.60/157.52 [8310]P34(x83101,x83102,x83103,x83104,f120(x83102))+~E(x83104,f120(x83101))
% 157.60/157.52 [8311]P34(x83111,x83112,x83113,f120(x83111),x83114)+~E(x83114,f120(x83112))
% 157.60/157.52 [8843]~P34(x88432,x88433,x88434,x88431,f120(x88433))+E(x88431,f120(x88432))
% 157.60/157.52 [8844]~P34(x88443,x88442,x88444,f120(x88443),x88441)+E(x88441,f120(x88442))
% 157.60/157.52 [5304]~P17(x53043,x53041,x53044)+E(f866(f866(x53041,x53042),x53042),x53042)
% 157.60/157.52 [5556]P107(f866(x55562,x55564))+E(f866(f143(x55561,x55562),f176(x55561,x55563,x55564)),f120(x55561))
% 157.60/157.52 [5593]~E(x55934,f195(f937(x55931,a925)))+E(f866(f317(x55931,x55932,x55933),x55934),f195(f937(x55932,a925)))
% 157.60/157.52 [5840]~P107(f866(x58402,x58404))+E(f866(f143(x58401,x58402),f176(x58401,x58403,x58404)),f176(x58401,x58403,x58404))
% 157.60/157.52 [5871]~E(f866(f317(x58712,x58713,x58714),x58711),f195(f937(x58713,a925)))+E(x58711,f195(f937(x58712,a925)))
% 157.60/157.52 [6060]~P7(x60601,x60603)+E(f279(x60601,x60602,f278(x60601,x60603),x60604),x60604)
% 157.60/157.52 [6166]~P110(x61662)+E(f866(f866(f155(x61661,x61662,x61663),x61664),f120(x61661)),f866(f866(f158(x61661),x61664),f120(x61661)))
% 157.60/157.52 [6521]~E(x65211,f195(f937(x65212,a925)))+~P107(f866(f67(x65212,x65213,x65211),x65214))
% 157.60/157.52 [6543]~P60(x65431,x65433,x65434,x65432)+P107(f866(f66(x65431),x65432))
% 157.60/157.52 [6545]~P60(x65451,x65453,x65452,x65454)+P107(f866(f66(x65451),x65452))
% 157.60/157.52 [6552]~P60(x65522,x65523,x65524,x65521)+~E(x65521,f195(f937(x65522,a925)))
% 157.60/157.52 [6585]~P111(x65851)+E(f866(f866(f108(f937(x65851,a925)),f866(f309(x65851,x65852),x65853)),f310(x65851,x65853,x65854)),f195(f937(x65851,a925)))
% 157.60/157.52 [6612]~P107(f866(f866(x66123,x66124),x66122))+P107(f866(f866(f336(x66121),x66122),f300(x66121,x66123,x66124)))
% 157.60/157.52 [6613]~P107(f866(f866(x66133,x66134),x66132))+P107(f866(f866(f336(x66131),x66132),f301(x66131,x66133,x66134)))
% 157.60/157.52 [6614]~P107(f866(f866(x66143,x66142),x66144))+P107(f866(f866(f336(x66141),x66142),f305(x66141,x66143,x66144)))
% 157.60/157.52 [6615]~P107(f866(f866(x66153,x66152),x66154))+P107(f866(f866(f336(x66151),x66152),f302(x66151,x66153,x66154)))
% 157.60/157.52 [6680]~P49(x66804,x66801,x66802,x66803)+P107(f866(f866(x66801,x66802),x66803))
% 157.60/157.52 [6759]~P111(x67591)+E(f866(f866(f108(f937(x67591,a925)),f313(x67591,x67592,x67593)),f310(x67591,x67593,x67594)),f195(f937(x67591,a925)))
% 157.60/157.52 [6760]~P111(x67601)+E(f866(f866(f108(f937(x67601,a925)),f310(x67601,x67602,x67603)),f313(x67601,x67603,x67604)),f195(f937(x67601,a925)))
% 157.60/157.52 [6761]~P111(x67611)+E(f866(f866(f108(f937(x67611,a925)),f310(x67611,x67612,x67613)),f312(x67611,x67613,x67614)),f195(f937(x67611,a925)))
% 157.60/157.52 [6762]~P111(x67621)+E(f866(f866(f108(f937(x67621,a925)),f312(x67621,x67622,x67623)),f313(x67621,x67623,x67624)),f195(f937(x67621,a925)))
% 157.60/157.52 [6763]~P111(x67631)+E(f866(f866(f108(f937(x67631,a925)),f312(x67631,x67632,x67633)),f312(x67631,x67633,x67634)),f195(f937(x67631,a925)))
% 157.60/157.52 [6803]P107(f866(f866(x68031,x68032),f537(x68032,x68031)))+~P107(f866(f257(x68033,x68034,x68031),x68032))
% 157.60/157.52 [6807]~P49(x68071,x68072,x68073,x68074)+~P107(f866(f866(x68072,x68074),x68073))
% 157.60/157.52 [6881]~P110(x68812)+E(f866(f179(x68811),f157(x68811,x68812,x68813,x68814)),f866(f179(x68811),x68814))
% 157.60/157.52 [6931]~P148(x69311)+E(f197(x69311,x69312,f866(a119,x69313),x69314),f197(x69311,x69312,x69313,f866(x69312,x69314)))
% 157.60/157.52 [6992]~P107(f866(f866(f336(x69924),x69923),f300(x69924,x69921,x69922)))+P107(f866(f866(x69921,x69922),x69923))
% 157.60/157.52 [6993]~P107(f866(f866(f336(x69934),x69933),f301(x69934,x69931,x69932)))+P107(f866(f866(x69931,x69932),x69933))
% 157.60/157.52 [6994]~P107(f866(f866(f336(x69944),x69942),f305(x69944,x69941,x69943)))+P107(f866(f866(x69941,x69942),x69943))
% 157.60/157.52 [6995]~P107(f866(f866(f336(x69954),x69952),f302(x69954,x69951,x69953)))+P107(f866(f866(x69951,x69952),x69953))
% 157.60/157.52 [7070]E(f866(f40(f938(x70701,x70702)),f320(x70701,x70702,x70703,x70704)),f2(a930))+P107(f866(f66(x70702),x70704))
% 157.60/157.52 [7071]E(f866(f40(f938(x70711,x70712)),f320(x70711,x70712,x70713,x70714)),f2(a930))+P107(f866(f66(x70711),x70713))
% 157.60/157.52 [7269]~P14(x72694,x72691,x72692)+E(f866(f78(x72691,x72691,x72691,f866(x72692,x72693)),f866(x72692,x72693)),f866(x72692,x72693))
% 157.60/157.52 [7509]E(f285(x75091,x75092,x75093,x75094),f866(f260(f937(a106,f937(a925,f934(f932(x75091)))),f936(a106,a106)),f46(x75091)))+~P107(f866(f866(f243(a106),x75093),f2(a106)))
% 157.60/157.52 [8141]~E(x81412,x81413)+P107(f866(f866(f336(f936(x81411,x81411)),f866(f866(f260(x81411,x81411),x81412),x81413)),f314(x81411,x81414)))
% 157.60/157.52 [8170]~P25(x81701,x81702,x81703,f250(f937(x81701,a925)))+E(f866(f83(x81701,x81702,f250(f937(x81701,a925)),x81703),f866(x81703,x81704)),x81704)
% 157.60/157.52 [8171]~P25(x81711,x81712,x81713,f250(f937(x81711,a925)))+E(f866(f97(x81711,x81712,f250(f937(x81711,a925)),x81713),f866(x81713,x81714)),x81714)
% 157.60/157.52 [8259]~P107(f866(f866(f336(f931(x82591)),f866(f866(f158(x82591),x82594),x82592)),f168(x82591,x82593)))+P107(f866(f866(f336(f931(x82591)),x82592),f168(x82591,x82593)))
% 157.60/157.52 [8260]~P107(f866(f866(f336(f931(x82601)),f866(f866(f141(x82601),x82604),x82602)),f168(x82601,x82603)))+P107(f866(f866(f336(f931(x82601)),x82602),f168(x82601,x82603)))
% 157.60/157.52 [8261]~P107(f866(f866(f336(f931(x82611)),f866(f866(f141(x82611),x82612),x82614)),f168(x82611,x82613)))+P107(f866(f866(f336(f931(x82611)),x82612),f168(x82611,x82613)))
% 157.60/157.52 [8272]~P110(x82721)+P13(x82721,f866(f866(f161(x82722,x82721),x82723),f157(x82722,x82721,x82723,x82724)))
% 157.60/157.52 [8370]P25(x83704,x83703,x83701,x83702)+E(f866(x83701,f445(x83702,x83701,x83703,x83704)),f866(x83701,f453(x83702,x83701,x83703,x83704)))
% 157.60/157.52 [8476]~P25(x84762,x84761,x84764,x84763)+P25(x84761,x84762,f83(x84762,x84761,x84763,x84764),f866(f317(x84762,x84761,x84764),x84763))
% 157.60/157.52 [8616]P37(f936(x86162,x86164),f288(x86162,x86164,x86161,x86163))+P107(f866(x86161,f524(x86162,x86163,x86164,x86161)))
% 157.60/157.52 [8730]E(x87301,x87302)+~P107(f866(f866(f336(f936(x87303,x87303)),f866(f866(f260(x87303,x87303),x87301),x87302)),f271(x87303,x87304)))
% 157.60/157.52 [8795]~P107(f866(f66(f938(x87953,x87951)),f320(x87953,x87951,x87954,x87952)))+P107(f866(f66(x87951),x87952))
% 157.60/157.52 [8796]~P107(f866(f66(f938(x87961,x87963)),f320(x87961,x87963,x87962,x87964)))+P107(f866(f66(x87961),x87962))
% 157.60/157.52 [8805]~P25(x88051,x88052,x88053,x88054)+P26(x88051,x88052,x88053,x88054,f866(f317(x88051,x88052,x88053),x88054))
% 157.60/157.52 [8806]P11(x88061,x88062,x88063,x88064)+~E(f866(x88064,f836(x88062,x88064,x88063,x88061)),f866(x88064,f837(x88062,x88064,x88063,x88061)))
% 157.60/157.52 [8896]~P26(x88962,x88963,x88964,x88961,f195(f937(x88963,a925)))+E(x88961,f195(f937(x88962,a925)))
% 157.60/157.52 [8897]~P26(x88973,x88972,x88974,f195(f937(x88973,a925)),x88971)+E(x88971,f195(f937(x88972,a925)))
% 157.60/157.52 [8989]P37(f936(x89891,x89892),f288(x89891,x89892,x89893,x89894))+~P37(x89892,f866(x89894,f524(x89891,x89894,x89892,x89893)))
% 157.60/157.52 [9556]E(f866(f866(f166(x95561,x95562),f677(x95563,x95564,x95562,x95561)),f678(x95563,x95564,x95562,x95561)),x95564)+~P107(f866(f866(f336(f936(f931(x95561),f931(x95561))),f866(f866(f260(f931(x95561),f931(x95561)),x95562),x95564)),f164(x95561,x95563)))
% 157.60/157.52 [9561]~P107(f866(f866(f336(f936(f931(x95611),f931(x95611))),f866(f866(f260(f931(x95611),f931(x95611)),x95612),x95613)),f152(x95611,x95614)))+P107(f866(f866(f336(f936(f931(x95611),f931(x95611))),f866(f866(f260(f931(x95611),f931(x95611)),x95612),x95613)),f154(x95611,x95614)))
% 157.60/157.52 [9670]P107(f866(f66(x96701),x96702))+~P107(f866(f866(f336(f936(f937(x96701,a925),f937(x96701,a925))),f866(f866(f260(f937(x96701,a925),f937(x96701,a925)),x96703),x96702)),f325(x96701,x96704)))
% 157.60/157.52 [9671]P107(f866(f66(x96711),x96712))+~P107(f866(f866(f336(f936(f937(x96711,a925),f937(x96711,a925))),f866(f866(f260(f937(x96711,a925),f937(x96711,a925)),x96712),x96713)),f325(x96711,x96714)))
% 157.60/157.52 [9674]~E(x96741,f195(f937(x96742,a925)))+~P107(f866(f866(f336(f936(f937(x96742,a925),f937(x96742,a925))),f866(f866(f260(f937(x96742,a925),f937(x96742,a925)),x96743),x96741)),f325(x96742,x96744)))
% 157.60/157.52 [10300]P11(x103001,x103002,x103003,x103004)+~P107(f866(f866(f265(x103001,x103001,a925),f866(f866(f7(x103001,f937(x103001,x103002),f937(x103001,a925)),f866(f866(f8(f937(x103002,a925),f937(f937(x103001,x103002),f937(x103001,a925)),x103001),f8(x103002,a925,x103001)),f866(f866(f8(x103002,f937(x103002,a925),x103001),a332),x103004))),x103004)),f559(x103004,x103003,x103002,x103001)))
% 157.60/157.52 [5205]~E(x52052,f120(x52051))+E(f866(f866(f166(x52051,x52052),x52053),x52054),f120(x52051))
% 157.60/157.52 [5206]~E(x52064,f120(x52061))+E(f866(f866(f161(x52061,x52062),x52063),x52064),f120(x52062))
% 157.60/157.52 [5437]E(x54371,f120(x54372))+~E(f866(f866(f161(x54372,x54373),x54374),x54371),f120(x54373))
% 157.60/157.52 [5438]E(x54381,f120(x54382))+~E(f866(f866(f166(x54382,x54381),x54383),x54384),f120(x54382))
% 157.60/157.52 [5477]E(x54771,x54772)+~E(f866(f866(f141(x54773),x54774),x54771),f866(f866(f141(x54773),x54774),x54772))
% 157.60/157.52 [5478]E(x54781,x54782)+~E(f866(f866(f141(x54783),x54781),x54784),f866(f866(f141(x54783),x54782),x54784))
% 157.60/157.52 [5629]P107(f866(x56293,x56292))+E(f177(x56291,x56292,f866(f143(x56291,x56293),x56294)),f866(f143(x56291,x56293),x56294))
% 157.60/157.52 [5631]~P107(f866(x56312,x56313))+P33(x56311,x56312,f866(f866(f158(x56311),x56313),x56314))
% 157.60/157.52 [5640]E(x56401,x56402)+~E(f146(a930,f866(f309(a930,x56401),x56403)),f866(f866(f158(a930),x56402),x56404))
% 157.60/157.52 [5688]~P27(x56882,x56883)+P27(x56881,f866(f866(f79(x56882,x56881),x56883),x56884))
% 157.60/157.52 [5689]~P37(x56892,x56893)+P37(x56891,f866(f866(f295(x56892,x56891),x56893),x56894))
% 157.60/157.52 [5690]~P38(x56902,x56903)+P38(x56901,f866(f866(f295(x56902,x56901),x56903),x56904))
% 157.60/157.52 [5691]~P52(x56912,x56913)+P52(x56911,f866(f866(f295(x56912,x56911),x56913),x56914))
% 157.60/157.52 [5823]~P33(x58231,x58232,x58234)+P33(x58231,x58232,f866(f866(f158(x58231),x58233),x58234))
% 157.60/157.52 [5824]~P33(x58241,x58242,x58244)+P33(x58241,x58242,f866(f866(f141(x58241),x58243),x58244))
% 157.60/157.52 [5825]~P33(x58251,x58252,x58253)+P33(x58251,x58252,f866(f866(f141(x58251),x58253),x58254))
% 157.60/157.52 [5914]~E(x59141,f120(x59142))+~E(f866(f866(f141(x59142),x59143),f866(f866(f158(x59142),x59144),f120(x59142))),x59141)
% 157.60/157.52 [5941]~P31(x59413,x59411,f866(f866(f158(x59413),x59412),x59414))+P107(f866(x59411,x59412))
% 157.60/157.52 [5951]E(f121(x59511,x59512),x59513)+~E(f866(f866(f141(x59511),x59513),f866(f866(f158(x59511),x59514),f120(x59511))),x59512)
% 157.60/157.52 [5952]E(f151(x59521,x59522),x59523)+~E(f866(f866(f141(x59521),x59524),f866(f866(f158(x59521),x59523),f120(x59521))),x59522)
% 157.60/157.52 [6062]~E(f146(a930,f866(f309(a930,x60621),x60622)),f866(f866(f158(a930),x60623),x60624))+P107(f866(f866(f244(a930),x60621),x60622))
% 157.60/157.52 [6071]P31(x60711,x60712,x60713)+~P31(x60711,x60712,f866(f866(f158(x60711),x60714),x60713))
% 157.60/157.52 [6072]P31(x60721,x60722,x60723)+~P31(x60721,x60722,f866(f866(f141(x60721),x60724),x60723))
% 157.60/157.52 [6073]P31(x60731,x60732,x60733)+~P31(x60731,x60732,f866(f866(f141(x60731),x60733),x60734))
% 157.60/157.52 [6271]E(x62711,f866(f866(f141(x62712),f866(f175(x62712),x62713)),f866(f866(f158(x62712),x62714),f120(x62712))))+~E(f866(f175(x62712),x62711),f866(f866(f158(x62712),x62714),x62713))
% 157.60/157.52 [6442]~P111(x64421)+E(f866(f866(f108(f937(x64421,a925)),f866(f309(x64421,x64422),x64423)),f866(f309(x64421,x64423),x64424)),f195(f937(x64421,a925)))
% 157.60/157.52 [6453]E(f866(f866(f171(x64531),f176(x64531,x64532,x64533)),x64534),x64533)+~P107(f866(f866(f244(a930),x64534),x64532))
% 157.60/157.52 [6480]~P72(x64801)+E(f866(f172(x64801),f866(f866(f161(a1,x64801),x64802),f185(x64803,x64804))),f866(f866(f6(a1,x64801),x64802),f866(f179(a1),f185(x64803,x64804))))
% 157.60/157.52 [6481]~P72(x64811)+E(f866(f866(f6(a1,x64811),x64812),f866(f179(a1),f185(x64813,x64814))),f866(f172(x64811),f866(f866(f161(a1,x64811),x64812),f185(x64813,x64814))))
% 157.60/157.52 [6625]~E(x66252,f866(f866(f141(x66251),f866(f175(x66251),x66254)),f866(f866(f158(x66251),x66253),f120(x66251))))+E(f866(f175(x66251),x66252),f866(f866(f158(x66251),x66253),x66254))
% 157.60/157.52 [6643]~P19(x66432,x66433,x66434,x66431)+E(f866(x66431,f195(f937(x66432,a925))),f32(x66433))
% 157.60/157.52 [6669]~P111(x66691)+E(f866(f866(f108(f937(x66691,a925)),f313(x66691,x66692,x66693)),f866(f309(x66691,x66693),x66694)),f195(f937(x66691,a925)))
% 157.60/157.52 [6882]E(x68821,f195(f937(x68822,a925)))+~E(f320(x68823,x68822,x68824,x68821),f195(f937(f938(x68823,x68822),a925)))
% 157.60/157.52 [6883]E(x68831,f195(f937(x68832,a925)))+~E(f320(x68832,x68833,x68831,x68834),f195(f937(f938(x68832,x68833),a925)))
% 157.60/157.52 [6953]~P110(x69532)+E(f866(f196(f931(x69531)),f157(x69531,x69532,x69533,x69534)),f866(f196(f931(x69531)),x69534))
% 157.60/157.52 [6964]~P107(f866(f258(x69643,x69644,x69641),x69642))+P107(f866(f866(x69641,f531(x69642,x69641)),x69642))
% 157.60/157.52 [7003]~P107(f866(f66(x70032),x70034))+P107(f866(f66(x70031),f866(f317(x70032,x70031,x70033),x70034)))
% 157.60/157.52 [7231]~P25(x72312,x72311,x72313,x72314)+E(f866(f40(x72311),f866(f317(x72312,x72311,x72313),x72314)),f866(f40(x72312),x72314))
% 157.60/157.52 [7249]E(f866(f317(x72491,x72492,x72493),f866(f318(x72491,x72492,x72493),x72494)),x72494)+~E(f866(f317(x72491,x72492,x72493),f250(f937(x72491,a925))),f250(f937(x72492,a925)))
% 157.60/157.52 [7661]~P25(x76611,x76612,x76613,f250(f937(x76611,a925)))+E(f866(f318(x76611,x76612,x76613),f866(f317(x76611,x76612,x76613),x76614)),x76614)
% 157.60/157.52 [7938]E(x79381,x79382)+~P107(f866(f866(f336(x79383),x79381),f866(f179(x79383),f176(x79383,x79384,x79382))))
% 157.60/157.52 [7947]~E(x79471,f2(a930))+~P107(f866(f866(f336(x79472),x79473),f866(f179(x79472),f176(x79472,x79471,x79474))))
% 157.60/157.52 [7981]P107(f866(x79811,x79812))+~P107(f866(f866(f336(x79813),x79812),f866(f179(x79813),f184(x79813,x79811,x79814))))
% 157.60/157.52 [8088]~P107(f866(f866(f336(f931(x80881)),f866(f866(f158(x80881),x80882),x80884)),f168(x80881,x80883)))+P107(f866(f866(f336(x80881),x80882),x80883))
% 157.60/157.52 [8216]~P107(f866(f866(f336(x82161),x82162),f866(f179(x82161),f183(x82161,x82163,x82164))))+P107(f866(f866(f336(x82161),x82162),f866(f179(x82161),x82163)))
% 157.60/157.52 [8217]~P107(f866(f866(f336(x82171),x82172),f866(f179(x82171),f177(x82171,x82174,x82173))))+P107(f866(f866(f336(x82171),x82172),f866(f179(x82171),x82173)))
% 157.60/157.52 [8218]~P107(f866(f866(f336(x82181),x82182),f866(f179(x82181),f184(x82181,x82184,x82183))))+P107(f866(f866(f336(x82181),x82182),f866(f179(x82181),x82183)))
% 157.60/157.52 [8228]E(f866(f196(f931(x82281)),x82282),x82283)+~P107(f866(f866(f336(f931(x82281)),x82282),f866(f179(f931(x82281)),f60(x82281,x82283,x82284))))
% 157.60/157.52 [8323]P107(f866(x83233,x83232))+E(f866(f143(x83231,f866(f866(f8(a925,a925,x83231),a329),f866(a332,x83232))),f866(f143(x83231,x83233),x83234)),f866(f143(x83231,x83233),x83234))
% 157.60/157.52 [8428]E(f866(f866(f171(x84281),f184(x84281,x84282,x84283)),x84284),f866(f866(f171(x84281),x84283),x84284))+~P107(f866(f866(f244(a930),x84284),f866(f196(f931(x84281)),f184(x84281,x84282,x84283))))
% 157.60/157.52 [8514]~P72(x85141)+E(f866(f866(f6(a930,x85141),f866(f866(f8(a930,x85141,a930),x85142),a119)),f866(f309(a930,x85143),x85144)),f866(f866(f6(a930,x85141),x85142),f866(f309(a930,f866(a119,x85143)),f866(a119,x85144))))
% 157.60/157.52 [8524]~P72(x85241)+E(f866(f866(f6(a930,x85241),f866(f866(f8(a930,x85241,a930),x85242),a119)),f310(a930,x85243,x85244)),f866(f866(f6(a930,x85241),x85242),f310(a930,f866(a119,x85243),f866(a119,x85244))))
% 157.60/157.52 [8651]~P25(x86511,x86513,x86514,f250(f937(x86511,a925)))+P25(x86511,f937(x86512,x86513),f866(f866(f8(x86513,f937(x86512,x86513),x86511),f16(x86513,x86512)),x86514),f250(f937(x86511,a925)))
% 157.60/157.52 [8737]~P25(x87372,x87371,x87374,x87373)+E(f866(f317(x87371,x87372,f83(x87372,x87371,x87373,x87374)),f866(f317(x87372,x87371,x87374),x87373)),x87373)
% 157.60/157.52 [8797]~P107(f866(f866(f336(f936(x87971,x87971)),f866(f866(f260(x87971,x87971),x87972),x87974)),f271(x87971,x87973)))+P107(f866(f866(f336(x87971),x87972),x87973))
% 157.60/157.52 [8920]~P25(x89202,x89201,x89203,f250(f937(x89202,a925)))+E(f866(f317(x89201,x89202,f97(x89202,x89201,f250(f937(x89202,a925)),x89203)),f866(f317(x89202,x89201,x89203),x89204)),x89204)
% 157.60/157.52 [8995]~P26(x89951,x89952,x89953,x89954,f250(f937(x89952,a925)))+E(f866(f317(x89951,x89952,x89953),f250(f937(x89951,a925))),f250(f937(x89952,a925)))
% 157.60/157.52 [9028]~E(f866(f866(f6(x90281,a930),x90284),x90283),f866(a119,x90282))+P107(f866(f866(f336(x90281),f481(x90282,x90283,x90284,x90281)),x90283))
% 157.60/157.52 [9049]~E(f866(f866(f6(x90494,a930),x90491),x90493),f866(a119,x90492))+P107(f866(f866(f244(a930),f2(a930)),f866(x90491,f481(x90492,x90493,x90491,x90494))))
% 157.60/157.52 [9060]~P107(f866(f66(x90602),x90604))+P107(f866(f866(f243(a930),f866(f40(x90601),f866(f317(x90602,x90601,x90603),x90604))),f866(f40(x90602),x90604)))
% 157.60/157.52 [9061]E(f866(f866(f260(x90611,x90612),f649(x90613,x90614,x90612,x90611)),f650(x90613,x90614,x90612,x90611)),x90614)+~P107(f866(f866(f336(f936(x90611,x90612)),x90614),f866(f294(x90612,x90611),x90613)))
% 157.60/157.52 [9069]P25(x90691,x90692,x90693,x90694)+P107(f866(f866(f336(x90691),f445(x90694,x90693,x90692,x90691)),x90694))
% 157.60/157.52 [9070]P25(x90701,x90702,x90703,x90704)+P107(f866(f866(f336(x90701),f453(x90704,x90703,x90702,x90701)),x90704))
% 157.60/157.52 [9140]P11(x91401,x91402,x91403,x91404)+P107(f866(f866(f336(f936(x91401,x91401)),f559(x91404,x91403,x91402,x91401)),x91403))
% 157.60/157.52 [9198]P107(f866(x91981,x91982))+~P107(f866(x91981,f866(f866(f260(x91983,x91984),f494(x91984,x91983,x91981)),f495(x91984,x91983,x91981))))
% 157.60/157.52 [9215]E(f866(f196(f931(x92151)),x92152),f866(f196(f931(x92151)),x92153))+~P107(f866(f866(f336(f936(f931(x92151),f931(x92151))),f866(f866(f260(f931(x92151),f931(x92151)),x92152),x92153)),f152(x92151,x92154)))
% 157.60/157.52 [9216]E(f866(f196(f931(x92161)),x92162),f866(f196(f931(x92161)),x92163))+~P107(f866(f866(f336(f936(f931(x92161),f931(x92161))),f866(f866(f260(f931(x92161),f931(x92161)),x92162),x92163)),f164(x92161,x92164)))
% 157.60/157.52 [9219]E(f866(f196(f931(x92191)),x92192),f866(f196(f931(x92191)),x92193))+~P107(f866(f866(f336(f936(f931(x92191),f931(x92191))),f866(f866(f260(f931(x92191),f931(x92191)),x92192),x92193)),f165(x92191,x92194)))
% 157.60/157.52 [9288]P107(f866(f866(f243(a930),f162(x92881,x92882,x92883)),f162(x92881,x92884,x92883)))+P107(f866(f866(f336(x92881),f676(x92884,x92882,x92883,x92881)),f866(f179(x92881),x92883)))
% 157.60/157.52 [9291]E(f866(f196(f931(x92911)),x92912),f866(f196(f931(x92911)),x92913))+~P107(f866(f866(f336(f936(f931(x92911),f931(x92911))),f866(f866(f260(f931(x92911),f931(x92911)),x92912),x92913)),f314(f931(x92911),f164(x92911,x92914))))
% 157.60/157.52 [9527]~P25(x95271,x95272,x95273,x95274)+~P107(f866(f866(f244(a930),f866(f40(x95272),f866(f317(x95271,x95272,x95273),x95274))),f866(f40(x95271),x95274)))
% 157.60/157.52 [9574]~P107(f866(f866(f336(f936(f931(x95741),f931(x95741))),f866(f866(f260(f931(x95741),f931(x95741)),x95742),x95743)),f164(x95741,x95744)))+P107(f866(f866(f336(f936(f931(x95741),f931(x95741))),f866(f866(f260(f931(x95741),f931(x95741)),x95742),x95743)),f165(x95741,f314(x95741,x95744))))
% 157.60/157.52 [9578]~P107(f866(f866(f336(f936(f931(x95781),f931(x95781))),f866(f866(f260(f931(x95781),f931(x95781)),x95782),x95783)),f165(x95781,x95784)))+P107(f866(f866(f336(f936(f931(x95781),f931(x95781))),f866(f866(f260(f931(x95781),f931(x95781)),x95782),x95783)),f314(f931(x95781),f164(x95781,x95784))))
% 157.60/157.52 [9594]P107(f866(f866(f336(f936(x95941,x95941)),f866(f866(f260(x95941,x95941),x95942),x95943)),f314(x95941,x95944)))+~P107(f866(f866(f336(f936(x95941,x95941)),f866(f866(f260(x95941,x95941),x95942),x95943)),f866(f866(f296(x95941,x95941,x95941),x95944),f314(x95941,x95944))))
% 157.60/157.52 [9779]E(f866(f866(f141(x97791),f693(x97792,x97793,x97794,x97791)),f866(f866(f158(x97791),f694(x97792,x97793,x97794,x97791)),f696(x97792,x97793,x97794,x97791))),x97794)+~P107(f866(f866(f336(f936(f931(x97791),f931(x97791))),f866(f866(f260(f931(x97791),f931(x97791)),x97794),x97793)),f164(x97791,x97792)))
% 157.60/157.52 [9780]E(f866(f866(f141(x97801),f693(x97802,x97803,x97804,x97801)),f866(f866(f158(x97801),f695(x97802,x97803,x97804,x97801)),f696(x97802,x97803,x97804,x97801))),x97803)+~P107(f866(f866(f336(f936(f931(x97801),f931(x97801))),f866(f866(f260(f931(x97801),f931(x97801)),x97804),x97803)),f164(x97801,x97802)))
% 157.60/157.52 [9858]P107(f866(f866(f336(f936(x98581,x98581)),f866(f866(f260(x98581,x98581),x98582),f611(x98583,x98584,x98582,x98581))),f314(x98581,x98583)))+~P107(f866(f866(f336(f936(x98581,x98581)),f866(f866(f260(x98581,x98581),x98582),x98584)),f866(f866(f296(x98581,x98581,x98581),x98583),f314(x98581,x98583))))
% 157.60/157.52 [9927]P107(f866(f866(f243(a930),f162(x99271,x99272,x99273)),f162(x99271,x99274,x99273)))+~P107(f866(f866(f244(a930),f866(x99272,f676(x99274,x99272,x99273,x99271))),f866(x99274,f676(x99274,x99272,x99273,x99271))))
% 157.60/157.52 [10000]P107(f866(f866(f336(f936(x100001,x100001)),f866(f866(f260(x100001,x100001),f603(x100002,x100003,x100004,x100001)),x100003)),f314(x100001,x100002)))+~P107(f866(f866(f336(f936(x100001,x100001)),f866(f866(f260(x100001,x100001),x100004),x100003)),f866(f866(f296(x100001,x100001,x100001),x100002),f314(x100001,x100002))))
% 157.60/157.52 [5457]~E(x54572,x54573)+E(f177(x54571,x54572,f866(f866(f158(x54571),x54573),x54574)),x54574)
% 157.60/157.52 [5586]P107(f866(x55862,x55863))+E(f184(x55861,x55862,f866(f866(f158(x55861),x55863),x55864)),f120(x55861))
% 157.60/157.52 [5652]~P92(x56522)+E(f866(f866(f85(f937(x56521,x56522)),x56523),x56524),f866(f85(x56522),f866(x56523,x56524)))
% 157.60/157.52 [5665]~E(x56652,f2(a930))+E(f866(f866(f145(x56651),x56652),f866(f866(f158(x56651),x56653),x56654)),f866(f866(f158(x56651),x56653),x56654))
% 157.60/157.52 [5666]P107(f866(x56662,x56663))+E(f866(f143(x56661,x56662),f866(f866(f158(x56661),x56663),x56664)),f866(f143(x56661,x56662),x56664))
% 157.60/157.52 [5805]~E(x58052,x58054)+P107(f866(f866(f866(f316(x58051),x58052),x58053),x58054))
% 157.60/157.52 [5814]E(x58141,f120(x58142))+E(f151(x58143,f866(f866(f161(x58142,x58143),x58144),x58141)),f866(x58144,f151(x58142,x58141)))
% 157.60/157.52 [5828]~E(x58281,f68(x58282,x58284))+E(f866(x58281,f866(f866(f316(x58282),x58283),f195(f937(x58282,a925)))),x58283)
% 157.60/157.52 [5866]E(x58661,f120(x58662))+E(f866(f148(x58663),f866(f866(f161(x58662,x58663),x58664),x58661)),f866(x58664,f866(f148(x58662),x58661)))
% 157.60/157.52 [5971]~P107(f866(x59713,x59714))+P107(f866(f866(f866(f316(x59711),x59712),x59713),x59714))
% 157.60/157.52 [6090]~P18(x60902,x60904,x60901)+E(f866(x60901,f866(f866(f316(x60902),x60903),f195(f937(x60902,a925)))),x60903)
% 157.60/157.52 [6118]~E(x61182,x61183)+P107(f866(f866(f336(x61181),x61182),f866(f866(f316(x61181),x61183),x61184)))
% 157.60/157.52 [6123]~P114(x61231)+E(f866(f866(f87(x61231),x61232),f866(f866(f87(x61231),x61233),x61234)),f866(f866(f87(x61231),x61233),f866(f866(f87(x61231),x61232),x61234)))
% 157.60/157.52 [6124]~P83(x61241)+E(f866(f866(f117(x61241),x61242),f866(f866(f117(x61241),x61243),x61244)),f866(f866(f117(x61241),x61243),f866(f866(f117(x61241),x61242),x61244)))
% 157.60/157.52 [6126]~P102(x61261)+E(f866(f866(f117(x61261),x61262),f866(f866(f117(x61261),x61263),x61264)),f866(f866(f117(x61261),x61263),f866(f866(f117(x61261),x61262),x61264)))
% 157.60/157.52 [6127]~P114(x61271)+E(f866(f866(f86(x61271),x61272),f866(f866(f86(x61271),x61273),x61274)),f866(f866(f86(x61271),x61273),f866(f866(f86(x61271),x61272),x61274)))
% 157.60/157.52 [6128]~P83(x61281)+E(f866(f866(f108(x61281),x61282),f866(f866(f108(x61281),x61283),x61284)),f866(f866(f108(x61281),x61283),f866(f866(f108(x61281),x61282),x61284)))
% 157.60/157.52 [6130]~P103(x61301)+E(f866(f866(f108(x61301),x61302),f866(f866(f108(x61301),x61303),x61304)),f866(f866(f108(x61301),x61303),f866(f866(f108(x61301),x61302),x61304)))
% 157.60/157.52 [6132]~P110(x61321)+E(f866(f866(f241(x61321),x61322),f866(f866(f241(x61321),x61323),x61324)),f866(f866(f241(x61321),x61323),f866(f866(f241(x61321),x61322),x61324)))
% 157.60/157.52 [6134]~P110(x61341)+E(f866(f866(f242(x61341),x61342),f866(f866(f242(x61341),x61343),x61344)),f866(f866(f242(x61341),x61343),f866(f866(f242(x61341),x61342),x61344)))
% 157.60/157.52 [6140]E(x61401,x61402)+E(f177(x61403,x61401,f866(f866(f158(x61403),x61402),x61404)),f866(f866(f158(x61403),x61402),f177(x61403,x61401,x61404)))
% 157.60/157.52 [6153]~P107(f866(x61532,x61533))+E(f866(f143(x61531,x61532),f866(f866(f158(x61531),x61533),x61534)),f866(f866(f158(x61531),x61533),f866(f143(x61531,x61532),x61534)))
% 157.60/157.52 [6291]~P107(f866(x62912,x62913))+E(f184(x62911,x62912,f866(f866(f158(x62911),x62913),x62914)),f866(f866(f158(x62911),x62913),f184(x62911,x62912,x62914)))
% 157.60/157.52 [6353]E(x63531,f195(f937(x63532,a925)))+E(f866(f866(f44(x63532,f937(x63533,a925)),x63531),f866(f16(f937(x63533,a925),x63532),x63534)),x63534)
% 157.60/157.52 [6354]E(x63541,f195(f937(x63542,a925)))+E(f866(f866(f45(x63542,f937(x63543,a925)),x63541),f866(f16(f937(x63543,a925),x63542),x63544)),x63544)
% 157.60/157.52 [6363]~E(x63634,f195(f937(x63632,a925)))+E(f866(f866(f262(x63631,x63632),x63633),f866(f16(f937(x63632,a925),x63631),x63634)),f195(f937(f936(x63631,x63632),a925)))
% 157.60/157.52 [6364]~E(x63643,f195(f937(x63641,a925)))+E(f866(f866(f262(x63641,x63642),x63643),f866(f16(f937(x63642,a925),x63641),x63644)),f195(f937(f936(x63641,x63642),a925)))
% 157.60/157.52 [6415]E(x64151,f2(a930))+E(f866(f866(f145(x64152),x64151),f866(f866(f158(x64152),x64153),x64154)),f866(f866(f145(x64152),f866(f866(f23(a930),x64151),f84(a930))),x64154))
% 157.60/157.52 [6436]E(x64361,f195(f937(x64362,a925)))+E(f866(f317(x64362,x64363,f866(f16(x64363,x64362),x64364)),x64361),f866(f866(f316(x64363),x64364),f195(f937(x64363,a925))))
% 157.60/157.52 [6439]E(f866(f318(x64391,x64392,f866(f16(x64392,x64391),x64393)),x64394),f195(f937(x64391,a925)))+P107(f866(f866(f336(x64392),x64393),x64394))
% 157.60/157.52 [6505]~E(x65053,f195(f937(x65051,a925)))+E(f866(f866(f44(x65051,f937(x65052,a925)),x65053),f866(f16(f937(x65052,a925),x65051),x65054)),f195(f937(x65052,a925)))
% 157.60/157.52 [6506]~E(x65063,f195(f937(x65061,a925)))+E(f866(f866(f45(x65061,f937(x65062,a925)),x65063),f866(f16(f937(x65062,a925),x65061),x65064)),f250(f937(x65062,a925)))
% 157.60/157.52 [6508]~P62(x65081)+E(f50(x65081,f866(f866(f87(x65081),x65082),x65083),f866(f866(f87(x65081),x65082),x65084)),f866(f866(f87(x65081),x65082),f50(x65081,x65083,x65084)))
% 157.60/157.52 [6679]E(f866(f318(x66791,x66792,f866(f16(x66792,x66791),x66793)),x66794),f250(f937(x66791,a925)))+~P107(f866(f866(f336(x66792),x66793),x66794))
% 157.60/157.52 [6705]~P107(f866(f866(f336(x67051),x67052),x67054))+P107(f866(f866(f336(x67051),x67052),f866(f866(f316(x67051),x67053),x67054)))
% 157.60/157.52 [6710]P107(f866(x67101,x67102))+~P107(f866(f167(x67103,x67101),f866(f866(f158(x67103),x67102),x67104)))
% 157.60/157.52 [6719]~E(x67193,f866(f866(f23(a930),f866(f196(f931(x67191)),x67192)),f84(a930)))+E(f121(x67191,f866(f866(f166(x67191,x67192),x67193),x67194)),f121(x67191,x67192))
% 157.60/157.52 [6737]~P110(x67371)+E(f866(f866(f108(f937(x67371,a925)),f866(f308(x67371),x67372)),f310(x67371,x67373,x67374)),f310(x67371,x67373,f866(f866(f241(x67371),x67372),x67374)))
% 157.60/157.52 [6738]~P110(x67381)+E(f866(f866(f108(f937(x67381,a925)),f866(f291(x67381),x67382)),f310(x67381,x67383,x67384)),f310(x67381,f866(f866(f242(x67381),x67382),x67383),x67384))
% 157.60/157.52 [6754]E(f866(f866(f108(f937(x67541,a925)),x67542),f866(f866(f316(x67541),x67543),x67544)),f866(f866(f108(f937(x67541,a925)),x67542),x67544))+P107(f866(f866(f336(x67541),x67543),x67542))
% 157.60/157.52 [6766]E(f177(x67661,x67662,f866(f866(f141(x67661),x67663),x67664)),f866(f866(f141(x67661),x67663),f177(x67661,x67662,x67664)))+P107(f866(f866(f336(x67661),x67662),f866(f179(x67661),x67663)))
% 157.60/157.52 [6772]~P81(x67721)+E(f866(f866(f87(x67721),f866(f866(f252(x67721),x67722),x67723)),f866(f866(f252(x67721),x67722),x67724)),f866(f866(f252(x67721),x67722),f866(f866(f86(a930),x67723),x67724)))
% 157.60/157.52 [6773]~P114(x67731)+E(f866(f866(f87(x67731),f866(f866(f252(x67731),x67732),x67733)),f866(f866(f252(x67731),x67732),x67734)),f866(f866(f252(x67731),x67732),f866(f866(f86(a930),x67733),x67734)))
% 157.60/157.52 [6812]~P114(x68121)+E(f866(f866(f86(x68121),f866(f866(f87(x68121),x68122),x68123)),f866(f866(f87(x68121),x68122),x68124)),f866(f866(f87(x68121),x68122),f866(f866(f86(x68121),x68123),x68124)))
% 157.60/157.52 [6813]~P101(x68131)+E(f866(f866(f108(x68131),f866(f866(f117(x68131),x68132),x68133)),f866(f866(f117(x68131),x68132),x68134)),f866(f866(f117(x68131),x68132),f866(f866(f108(x68131),x68133),x68134)))
% 157.60/157.52 [6814]~P101(x68141)+E(f866(f866(f117(x68141),f866(f866(f108(x68141),x68142),x68143)),f866(f866(f108(x68141),x68142),x68144)),f866(f866(f108(x68141),x68142),f866(f866(f117(x68141),x68143),x68144)))
% 157.60/157.52 [6815]~P110(x68151)+E(f866(f866(f242(x68151),f866(f866(f241(x68151),x68152),x68153)),f866(f866(f241(x68151),x68152),x68154)),f866(f866(f241(x68151),x68152),f866(f866(f242(x68151),x68153),x68154)))
% 157.60/157.52 [6816]~P110(x68161)+E(f866(f866(f241(x68161),f866(f866(f242(x68161),x68162),x68163)),f866(f866(f242(x68161),x68162),x68164)),f866(f866(f242(x68161),x68162),f866(f866(f241(x68161),x68163),x68164)))
% 157.60/157.52 [6847]~P62(x68471)+E(f50(x68471,f866(f866(f87(x68471),x68472),x68473),f866(f866(f87(x68471),x68474),x68473)),f866(f866(f87(x68471),f50(x68471,x68472,x68474)),x68473))
% 157.60/157.52 [6850]~E(f866(f196(f931(x68501)),x68503),f866(f196(f931(x68502)),x68504))+E(f866(f866(f161(f936(x68501,x68502),x68502),f264(x68501,x68502)),f866(f866(f188(x68501,x68502),x68503),x68504)),x68504)
% 157.60/157.52 [6851]~E(f866(f196(f931(x68511)),x68513),f866(f196(f931(x68512)),x68514))+E(f866(f866(f161(f936(x68511,x68512),x68511),f259(x68511,x68512)),f866(f866(f188(x68511,x68512),x68513),x68514)),x68513)
% 157.60/157.52 [6856]P107(f866(f167(x68561,x68562),x68563))+~P107(f866(f167(x68561,x68562),f866(f866(f158(x68561),x68564),x68563)))
% 157.60/157.52 [6857]P107(f866(f167(x68571,x68572),x68573))+~P107(f866(f167(x68571,x68572),f866(f866(f141(x68571),x68574),x68573)))
% 157.60/157.52 [6858]P107(f866(f167(x68581,x68582),x68583))+~P107(f866(f167(x68581,x68582),f866(f866(f141(x68581),x68583),x68584)))
% 157.60/157.52 [6863]~P63(x68631)+E(f50(x68631,f866(f866(f23(x68631),x68632),f50(x68631,x68633,x68634)),x68634),f50(x68631,f866(f866(f23(x68631),x68632),x68633),x68634))
% 157.60/157.52 [6864]~P62(x68641)+E(f50(x68641,f866(f866(f87(x68641),x68642),f50(x68641,x68643,x68644)),x68644),f50(x68641,f866(f866(f87(x68641),x68642),x68643),x68644))
% 157.60/157.52 [6866]~P62(x68661)+E(f50(x68661,f866(f866(f86(x68661),x68662),f50(x68661,x68663,x68664)),x68664),f50(x68661,f866(f866(f86(x68661),x68662),x68663),x68664))
% 157.60/157.52 [6945]~P110(x69451)+E(f866(f866(f108(f937(x69451,a925)),f310(x69451,x69452,x69453)),f866(f308(x69451),x69454)),f310(x69451,x69452,f866(f866(f241(x69451),x69453),x69454)))
% 157.60/157.52 [6946]~P110(x69461)+E(f866(f866(f108(f937(x69461,a925)),f310(x69461,x69462,x69463)),f866(f291(x69461),x69464)),f310(x69461,f866(f866(f242(x69461),x69462),x69464),x69463))
% 157.60/157.52 [6950]~E(f866(f196(f931(x69501)),x69503),f866(f196(f931(x69502)),x69504))+E(f866(f866(f188(x69501,x69502),f866(f175(x69501),x69503)),f866(f175(x69502),x69504)),f866(f175(f936(x69501,x69502)),f866(f866(f188(x69501,x69502),x69503),x69504)))
% 157.60/157.52 [6961]E(x69611,f866(f866(f23(a930),f866(f196(f931(x69612)),x69613)),f84(a930)))+E(f121(x69612,f866(f866(f166(x69612,x69613),x69611),x69614)),f866(f866(f166(x69612,f121(x69612,x69613)),x69611),x69614))
% 157.60/157.52 [6975]~P107(f866(f144(x69752),x69754))+P107(f866(f144(f936(x69751,x69752)),f866(f866(f188(x69751,x69752),x69753),x69754)))
% 157.60/157.52 [6976]~P107(f866(f144(x69761),x69763))+P107(f866(f144(f936(x69761,x69762)),f866(f866(f188(x69761,x69762),x69763),x69764)))
% 157.60/157.52 [7234]E(f866(f866(f41(a930),x72341),x72342),x72343)+~P107(f866(f53(x72341,x72342),f866(f866(f260(a930,a930),x72343),x72344)))
% 157.60/157.52 [7257]E(f50(a930,x72571,x72572),x72573)+~P107(f866(f53(x72571,x72572),f866(f866(f260(a930,a930),x72574),x72573)))
% 157.60/157.52 [7260]P107(f866(f144(x72601),x72602))+~P107(f866(f144(x72603),f866(f866(f161(x72601,x72603),x72604),x72602)))
% 157.60/157.52 [7343]E(f177(x73431,x73432,f866(f866(f141(x73431),x73433),x73434)),f866(f866(f141(x73431),f177(x73431,x73432,x73433)),x73434))+~P107(f866(f866(f336(x73431),x73432),f866(f179(x73431),x73433)))
% 157.60/157.52 [7434]~P63(x74341)+E(f50(x74341,f866(f866(f23(x74341),f50(x74341,x74342,x74343)),x74344),x74343),f50(x74341,f866(f866(f23(x74341),x74342),x74344),x74343))
% 157.60/157.52 [7437]~P62(x74371)+E(f50(x74371,f866(f866(f87(x74371),f50(x74371,x74372,x74373)),x74374),x74373),f50(x74371,f866(f866(f87(x74371),x74372),x74374),x74373))
% 157.60/157.52 [7438]~P62(x74381)+E(f50(x74381,f866(f866(f86(x74381),f50(x74381,x74382,x74383)),x74384),x74383),f50(x74381,f866(f866(f86(x74381),x74382),x74384),x74383))
% 157.60/157.52 [7631]~E(x76311,f866(f866(f158(x76312),x76313),x76314))+~P107(f866(f866(f243(a930),f866(f196(f931(x76312)),x76311)),f866(f196(f931(x76312)),x76314)))
% 157.60/157.52 [7832]P25(x78321,x78322,x78323,f866(f179(x78321),x78324))+~P107(f866(f144(x78322),f866(f866(f161(x78321,x78322),x78323),x78324)))
% 157.60/157.52 [7905]~P107(f866(f866(f243(f937(x79051,a925)),x79052),x79054))+P107(f866(f866(f243(f937(x79051,a925)),x79052),f866(f866(f316(x79051),x79053),x79054)))
% 157.60/157.52 [7939]~P63(x79391)+E(f50(x79391,f866(f866(f23(x79391),f50(x79391,x79392,x79393)),f50(x79391,x79394,x79393)),x79393),f50(x79391,f866(f866(f23(x79391),x79392),x79394),x79393))
% 157.60/157.52 [7940]~P62(x79401)+E(f50(x79401,f866(f866(f87(x79401),f50(x79401,x79402,x79403)),f50(x79401,x79404,x79403)),x79403),f50(x79401,f866(f866(f87(x79401),x79402),x79404),x79403))
% 157.60/157.52 [7941]~P62(x79411)+E(f50(x79411,f866(f866(f86(x79411),f50(x79411,x79412,x79413)),f50(x79411,x79414,x79413)),x79413),f50(x79411,f866(f866(f86(x79411),x79412),x79414),x79413))
% 157.60/157.52 [8045]~E(f866(x80454,f881(x80454,x80453,x80451,x80452)),f195(f937(x80452,a925)))+E(f866(f866(f44(x80451,f937(x80452,a925)),x80453),x80454),f195(f937(x80452,a925)))
% 157.60/157.52 [8046]~E(f866(x80464,f594(x80464,x80463,x80461,x80462)),f250(f937(x80462,a925)))+E(f866(f866(f45(x80461,f937(x80462,a925)),x80463),x80464),f250(f937(x80462,a925)))
% 157.60/157.52 [8047]~E(f866(x80474,f883(x80474,x80473,x80472,x80471)),f195(f937(x80472,a925)))+E(f866(f866(f44(x80471,f937(x80472,a925)),x80473),x80474),f195(f937(x80472,a925)))
% 157.60/157.52 [8048]~E(f866(x80484,f613(x80484,x80483,x80482,x80481)),f250(f937(x80482,a925)))+E(f866(f866(f45(x80481,f937(x80482,a925)),x80483),x80484),f250(f937(x80482,a925)))
% 157.60/157.52 [8429]P107(f866(x84291,x84292))+~P107(f866(f866(f336(x84293),x84292),f866(f866(f108(f937(x84293,a925)),x84294),f866(f270(x84293),x84291))))
% 157.60/157.52 [8466]~P107(f866(f866(f243(f937(x84661,a925)),x84663),x84664))+P107(f866(f866(f243(f937(x84661,a925)),f866(f866(f316(x84661),x84662),x84663)),f866(f866(f316(x84661),x84662),x84664)))
% 157.60/157.52 [8644]P107(f866(x86442,x86443))+E(f866(f866(f145(x86441),f866(f196(f931(x86441)),f184(x86441,x86442,f866(f866(f158(x86441),x86443),x86444)))),f866(f866(f158(x86441),x86443),x86444)),f866(f866(f158(x86441),x86443),x86444))
% 157.60/157.52 [8751]~P107(f866(f866(f244(a930),f866(x87514,x87512)),f866(x87514,x87513)))+P107(f866(f866(f336(f936(x87511,x87511)),f866(f866(f260(x87511,x87511),x87512),x87513)),f866(f866(f295(a930,x87511),a248),x87514)))
% 157.60/157.52 [8847]~P107(f866(x88472,f749(x88474,x88472,x88473,x88471)))+E(f184(x88471,x88472,f866(f866(f141(x88471),x88473),x88474)),f866(f866(f141(x88471),x88473),f184(x88471,x88472,x88474)))
% 157.60/157.52 [8924]P25(f931(x89241),f931(x89242),f866(f161(x89241,x89242),x89243),x89244)+~P25(x89241,x89242,x89243,f42(f937(x89241,a925),f866(f317(f931(x89241),f937(x89241,a925),f179(x89241)),x89244)))
% 157.60/157.52 [8999]~P107(f866(x89992,x89993))+E(f866(f866(f145(x89991),f866(f196(f931(x89991)),f184(x89991,x89992,f866(f866(f158(x89991),x89993),x89994)))),f866(f866(f158(x89991),x89993),x89994)),f866(f866(f145(x89991),f866(f196(f931(x89991)),f184(x89991,x89992,x89994))),x89994))
% 157.60/157.52 [9040]~E(x90402,x90403)+E(f866(f143(x90401,f866(f866(f8(a925,a925,x90401),a329),f866(a332,x90402))),f866(f866(f158(x90401),x90403),x90404)),f866(f143(x90401,f866(f866(f8(a925,a925,x90401),a329),f866(a332,x90402))),x90404))
% 157.60/157.52 [9050]E(f866(f866(f44(x90501,f937(x90502,a925)),x90503),x90504),f195(f937(x90502,a925)))+P107(f866(f866(f336(x90501),f881(x90504,x90503,x90501,x90502)),x90503))
% 157.60/157.52 [9051]E(f866(f866(f45(x90511,f937(x90512,a925)),x90513),x90514),f250(f937(x90512,a925)))+P107(f866(f866(f336(x90511),f594(x90514,x90513,x90511,x90512)),x90513))
% 157.60/157.52 [9052]E(f866(f866(f44(x90521,f937(x90522,a925)),x90523),x90524),f195(f937(x90522,a925)))+P107(f866(f866(f336(x90521),f883(x90524,x90523,x90522,x90521)),x90523))
% 157.60/157.52 [9053]E(f866(f866(f45(x90531,f937(x90532,a925)),x90533),x90534),f250(f937(x90532,a925)))+P107(f866(f866(f336(x90531),f613(x90534,x90533,x90532,x90531)),x90533))
% 157.60/157.52 [9091]P107(f866(f866(f244(a930),f866(x90911,x90912)),f866(x90911,x90913)))+~P107(f866(f866(f336(f936(x90914,x90914)),f866(f866(f260(x90914,x90914),x90912),x90913)),f866(f866(f295(a930,x90914),a248),x90911)))
% 157.60/157.52 [9119]E(f184(x91191,x91192,f866(f866(f141(x91191),x91193),x91194)),f866(f866(f141(x91191),x91193),f184(x91191,x91192,x91194)))+P107(f866(f866(f336(x91191),f749(x91194,x91192,x91193,x91191)),f866(f179(x91191),x91193)))
% 157.60/157.52 [9174]~P26(x91741,x91742,x91743,f250(f937(x91741,a925)),f250(f937(x91742,a925)))+E(f866(f317(x91741,x91742,x91743),f866(f85(f937(x91741,a925)),x91744)),f866(f85(f937(x91742,a925)),f866(f317(x91741,x91742,x91743),x91744)))
% 157.60/157.52 [9277]P107(f866(f866(f336(x92771),f690(x92772,x92773,x92774,x92771)),x92773))+~P107(f866(f866(f336(f937(x92771,a925)),x92774),f866(f866(f65(x92771),x92773),x92772)))
% 157.60/157.52 [9280]E(x92801,x92802)+~P107(f866(f866(f336(f936(x92803,x92803)),f866(f866(f260(x92803,x92803),x92801),x92802)),f866(f866(f190(f936(x92803,x92803),a925),f2(a930)),x92804)))
% 157.60/157.52 [9362]E(f866(f293(x93621,x93621,x93622),f866(f866(f316(x93621),f690(x93622,x93623,x93624,x93621)),f195(f937(x93621,a925)))),x93624)+~P107(f866(f866(f336(f937(x93621,a925)),x93624),f866(f866(f65(x93621),x93623),x93622)))
% 157.60/157.52 [9367]~P107(f866(f866(f336(f936(x93671,x93671)),f866(f866(f260(x93671,x93671),x93673),x93672)),f314(x93671,x93674)))+P107(f866(f866(f336(f936(x93671,x93671)),f866(f866(f260(x93671,x93671),x93672),x93673)),f314(x93671,f866(f294(x93671,x93671),x93674))))
% 157.60/157.52 [9380]~P62(x93801)+E(f866(f866(f86(x93801),f866(f866(f86(x93801),f866(f866(f87(x93801),x93802),f866(f866(f41(x93801),x93803),x93802))),f50(x93801,x93803,x93802))),x93804),f866(f866(f86(x93801),x93803),x93804))
% 157.60/157.52 [9391]~P107(f866(f866(f336(x93911),x93913),x93914))+P107(f866(f866(f336(f937(x93911,a925)),f866(f293(x93911,x93911,x93912),f866(f866(f316(x93911),x93913),f195(f937(x93911,a925))))),f866(f866(f65(x93911),x93914),x93912)))
% 157.60/157.52 [9403]P107(f866(f866(f336(f936(x94031,x94031)),f866(f866(f260(x94031,x94031),x94032),x94033)),f314(x94031,x94034)))+~P107(f866(f866(f336(f936(x94031,x94031)),f866(f866(f260(x94031,x94031),x94033),x94032)),f314(x94031,f866(f294(x94031,x94031),x94034))))
% 157.60/157.52 [9487]E(f866(f866(f166(x94871,f866(f175(x94871),x94872)),f866(f866(f23(a930),f866(f866(f23(a930),f866(f196(f931(x94871)),x94872)),x94873)),f84(a930))),x94874),f866(f175(x94871),f866(f866(f166(x94871,x94872),x94873),x94874)))+~P107(f866(f866(f244(a930),x94873),f866(f196(f931(x94871)),x94872)))
% 157.60/157.52 [9490]~P107(f866(x94902,f743(x94904,x94902,x94903,x94901)))+E(f866(f866(f145(x94901),f866(f196(f931(x94901)),f184(x94901,x94902,f866(f866(f141(x94901),x94903),x94904)))),f866(f866(f141(x94901),x94903),x94904)),f866(f866(f145(x94901),f866(f196(f931(x94901)),f184(x94901,x94902,x94904))),x94904))
% 157.60/157.52 [9535]~P25(x95352,x95351,x95353,f250(f937(x95352,a925)))+P107(f866(f866(f243(f937(x95351,a925)),f866(f317(x95352,x95351,x95353),f866(f85(f937(x95352,a925)),x95354))),f866(f85(f937(x95351,a925)),f866(f317(x95352,x95351,x95353),x95354))))
% 157.60/157.52 [9547]~P5(x95471)+E(f866(f149(x95471,x95472,f866(f7(x95472,x95471,x95471),f866(f866(f8(x95471,f937(x95471,x95471),x95472),f117(x95471)),x95473)),f195(x95471)),x95474),f866(f866(f44(x95472,x95471),f866(f179(x95472),x95474)),x95473))
% 157.60/157.52 [9548]~P5(x95481)+E(f866(f149(x95481,x95482,f866(f7(x95482,x95481,x95481),f866(f866(f8(x95481,f937(x95481,x95481),x95482),f108(x95481)),x95483)),f250(x95481)),x95484),f866(f866(f45(x95482,x95481),f866(f179(x95482),x95484)),x95483))
% 157.60/157.52 [9558]E(f866(f866(f145(x95581),f866(f196(f931(x95581)),f184(x95581,x95582,f866(f866(f141(x95581),x95583),x95584)))),f866(f866(f141(x95581),x95583),x95584)),f866(f866(f145(x95581),f866(f196(f931(x95581)),f184(x95581,x95582,x95584))),x95584))+P107(f866(f866(f336(x95581),f743(x95584,x95582,x95583,x95581)),f866(f179(x95581),x95583)))
% 157.60/157.52 [9628]~P107(f866(f866(f336(f936(f931(x96284),f931(x96284))),f866(f866(f260(f931(x96284),f931(x96284)),x96283),x96282)),f164(x96284,x96281)))+P107(f866(f866(f244(a930),f677(x96281,x96282,x96283,x96284)),f866(f196(f931(x96284)),x96283)))
% 157.60/157.52 [9629]~P62(x96291)+E(f866(f866(f86(x96291),f866(f866(f86(x96291),f866(f866(f87(x96291),f866(f866(f41(x96291),x96292),x96293)),x96293)),f50(x96291,x96292,x96293))),x96294),f866(f866(f86(x96291),x96292),x96294))
% 157.60/157.52 [9656]~P107(f866(f866(f336(f936(f931(x96561),f931(x96561))),f866(f866(f260(f931(x96561),f931(x96561)),x96562),x96563)),f866(f294(f931(x96561),f931(x96561)),f164(x96561,x96564))))+P107(f866(f866(f336(f936(f931(x96561),f931(x96561))),f866(f866(f260(f931(x96561),f931(x96561)),x96562),x96563)),f164(x96561,f866(f294(x96561,x96561),x96564))))
% 157.60/157.52 [9657]P107(f866(f866(f336(f936(f931(x96571),f931(x96571))),f866(f866(f260(f931(x96571),f931(x96571)),x96572),x96573)),f866(f294(f931(x96571),f931(x96571)),f164(x96571,x96574))))+~P107(f866(f866(f336(f936(f931(x96571),f931(x96571))),f866(f866(f260(f931(x96571),f931(x96571)),x96572),x96573)),f164(x96571,f866(f294(x96571,x96571),x96574))))
% 157.60/157.52 [9696]~P107(f866(f866(f336(x96961),x96963),f866(f272(x96961,x96962),x96964)))+P107(f866(f866(f336(f936(x96961,x96962)),f866(f866(f260(x96961,x96962),x96963),f538(x96964,x96962,x96963,x96961))),x96964))
% 157.60/157.52 [9697]~P107(f866(f866(f336(x96971),x96973),f866(f272(x96971,x96972),x96974)))+P107(f866(f866(f336(f936(x96971,x96972)),f866(f866(f260(x96971,x96972),x96973),f542(x96974,x96972,x96973,x96971))),x96974))
% 157.60/157.52 [9853]~P107(f866(f866(f336(f936(x98531,x98531)),f866(f866(f260(x98531,x98531),x98532),x98534)),f866(f866(f296(x98531,x98531,x98531),x98533),f314(x98531,x98533))))+P107(f866(f866(f336(f936(x98531,x98531)),f866(f866(f260(x98531,x98531),x98532),f603(x98533,x98534,x98532,x98531))),x98533))
% 157.60/157.52 [10014]P11(x100141,x100142,x100143,x100144)+P107(f866(f866(f336(f936(x100141,x100141)),f866(f866(f260(x100141,x100141),f837(x100142,x100144,x100143,x100141)),f836(x100142,x100144,x100143,x100141))),x100143))
% 157.60/157.52 [10021]~P107(f866(f866(f336(f936(x100212,x100211)),x100214),f866(f294(x100211,x100212),x100213)))+P107(f866(f866(f336(f936(x100211,x100212)),f866(f866(f260(x100211,x100212),f650(x100213,x100214,x100211,x100212)),f649(x100213,x100214,x100211,x100212))),x100213))
% 157.60/157.52 [10045]~P107(f866(f866(f336(f936(f931(x100451),f931(x100451))),f866(f866(f260(f931(x100451),f931(x100451)),x100454),x100453)),f164(x100451,x100452)))+P107(f866(f866(f336(f936(x100451,x100451)),f866(f866(f260(x100451,x100451),f694(x100452,x100453,x100454,x100451)),f695(x100452,x100453,x100454,x100451))),x100452))
% 157.60/157.52 [10136]~P107(f866(f866(f336(f936(f931(x101361),f931(x101361))),f866(f866(f260(f931(x101361),f931(x101361)),x101362),x101364)),f164(x101361,x101363)))+P107(f866(f866(f336(f936(x101361,x101361)),f866(f866(f260(x101361,x101361),f866(f866(f171(x101361),x101362),f677(x101363,x101364,x101362,x101361))),f678(x101363,x101364,x101362,x101361))),x101363))
% 157.60/157.52 [10156]~P107(f866(f66(x101562),x101564))+E(f866(f866(f866(f70(f937(x101561,a925),x101562,f117(f937(x101561,a925))),f866(f866(f7(x101562,f937(x101561,a925),f937(x101561,a925)),f866(f866(f8(x101561,f937(f937(x101561,a925),f937(x101561,a925)),x101562),f316(x101561)),x101563)),f195(f937(x101561,a925)))),f195(f937(x101561,a925))),x101564),f866(f317(x101562,x101561,x101563),x101564))
% 157.60/157.52 [10253]~P25(x102531,x102532,x102533,f250(f937(x102531,a925)))+P107(f866(f866(f243(f937(x102531,a925)),f866(f318(x102531,x102532,x102533),f866(f866(f316(x102532),x102534),f195(f937(x102532,a925))))),f866(f866(f316(x102531),f91(x102531,f866(f866(f7(x102531,x102532,a925),f866(f866(f8(x102532,f937(x102532,a925),x102531),a332),x102533)),x102534))),f195(f937(x102531,a925)))))
% 157.60/157.52 [5877]~E(f866(f866(f141(x58771),x58772),x58774),x58773)+E(f866(f866(f182(x58771),f866(f196(f931(x58771)),x58772)),x58773),x58772)
% 157.60/157.52 [5878]~E(f866(f866(f141(x58782),x58783),x58781),x58784)+E(x58781,f866(f866(f145(x58782),f866(f196(f931(x58782)),x58783)),x58784))
% 157.60/157.52 [5889]~E(x58894,f2(a930))+E(f866(f866(f171(x58891),f866(f866(f158(x58891),x58892),x58893)),x58894),x58892)
% 157.60/157.52 [6428]~P114(x64281)+E(f866(f866(f252(x64281),f866(f866(f252(x64281),x64282),x64283)),x64284),f866(f866(f252(x64281),x64282),f866(f866(f87(a930),x64283),x64284)))
% 157.60/157.52 [6429]~P81(x64291)+E(f866(f866(f252(x64291),f866(f866(f252(x64291),x64292),x64293)),x64294),f866(f866(f252(x64291),x64292),f866(f866(f87(a930),x64293),x64294)))
% 157.60/157.52 [6437]E(x64371,f2(a930))+E(f866(f866(f171(x64372),f866(f866(f158(x64372),x64373),x64374)),x64371),f866(f866(f171(x64372),x64374),f866(f866(f23(a930),x64371),f84(a930))))
% 157.60/157.52 [6463]~P125(x64631)+E(f866(f866(f297(x64631),f866(f866(f87(x64631),x64632),x64633)),x64634),f866(f866(f87(x64631),x64632),f866(f866(f297(x64631),x64633),x64634)))
% 157.60/157.52 [6465]~P69(x64651)+E(f866(f866(f87(x64651),f866(f866(f87(x64651),x64652),x64653)),x64654),f866(f866(f87(x64651),x64652),f866(f866(f87(x64651),x64653),x64654)))
% 157.60/157.52 [6466]~P114(x64661)+E(f866(f866(f87(x64661),f866(f866(f87(x64661),x64662),x64663)),x64664),f866(f866(f87(x64661),x64662),f866(f866(f87(x64661),x64663),x64664)))
% 157.60/157.52 [6468]~P83(x64681)+E(f866(f866(f117(x64681),f866(f866(f117(x64681),x64682),x64683)),x64684),f866(f866(f117(x64681),x64682),f866(f866(f117(x64681),x64683),x64684)))
% 157.60/157.52 [6470]~P102(x64701)+E(f866(f866(f117(x64701),f866(f866(f117(x64701),x64702),x64703)),x64704),f866(f866(f117(x64701),x64702),f866(f866(f117(x64701),x64703),x64704)))
% 157.60/157.52 [6471]~P114(x64711)+E(f866(f866(f86(x64711),f866(f866(f86(x64711),x64712),x64713)),x64714),f866(f866(f86(x64711),x64712),f866(f866(f86(x64711),x64713),x64714)))
% 157.60/157.52 [6472]~P70(x64721)+E(f866(f866(f86(x64721),f866(f866(f86(x64721),x64722),x64723)),x64724),f866(f866(f86(x64721),x64722),f866(f866(f86(x64721),x64723),x64724)))
% 157.60/157.52 [6473]~P83(x64731)+E(f866(f866(f108(x64731),f866(f866(f108(x64731),x64732),x64733)),x64734),f866(f866(f108(x64731),x64732),f866(f866(f108(x64731),x64733),x64734)))
% 157.60/157.52 [6475]~P103(x64751)+E(f866(f866(f108(x64751),f866(f866(f108(x64751),x64752),x64753)),x64754),f866(f866(f108(x64751),x64752),f866(f866(f108(x64751),x64753),x64754)))
% 157.60/157.52 [6477]~P110(x64771)+E(f866(f866(f241(x64771),f866(f866(f241(x64771),x64772),x64773)),x64774),f866(f866(f241(x64771),x64772),f866(f866(f241(x64771),x64773),x64774)))
% 157.60/157.52 [6479]~P110(x64791)+E(f866(f866(f242(x64791),f866(f866(f242(x64791),x64792),x64793)),x64794),f866(f866(f242(x64791),x64792),f866(f866(f242(x64791),x64793),x64794)))
% 157.60/157.52 [6488]~P62(x64881)+E(f50(x64881,f866(f866(f86(x64881),x64882),f866(f866(f87(x64881),x64883),x64884)),x64884),f50(x64881,x64882,x64884))
% 157.60/157.52 [6489]~P62(x64891)+E(f50(x64891,f866(f866(f86(x64891),x64892),f866(f866(f87(x64891),x64893),x64894)),x64893),f50(x64891,x64892,x64893))
% 157.60/157.52 [6626]E(f866(f866(f171(x66261),f866(f866(f182(x66261),x66262),x66263)),x66264),f866(f866(f171(x66261),x66263),x66264))+~P107(f866(f866(f244(a930),x66264),x66262))
% 157.60/157.52 [6808]~E(x68082,x68084)+P107(f866(f866(f179(x68081),f866(f866(f158(x68081),x68082),x68083)),x68084))
% 157.60/157.52 [6810]~P114(x68101)+E(f866(f866(f87(x68101),f866(f866(f87(x68101),x68102),x68103)),x68104),f866(f866(f87(x68101),f866(f866(f87(x68101),x68102),x68104)),x68103))
% 157.60/157.52 [6811]~P114(x68111)+E(f866(f866(f86(x68111),f866(f866(f86(x68111),x68112),x68113)),x68114),f866(f866(f86(x68111),f866(f866(f86(x68111),x68112),x68114)),x68113))
% 157.60/157.52 [6869]~P148(x68692)+E(f866(f866(f6(x68691,x68692),f866(f16(x68692,x68691),x68693)),x68694),f866(f866(f87(x68692),f866(f107(x68692),f866(f40(x68691),x68694))),x68693))
% 157.60/157.52 [7035]E(f866(f866(f108(f937(x70351,a925)),f866(f866(f316(x70351),x70352),x70353)),x70354),f866(f866(f108(f937(x70351,a925)),x70353),x70354))+P107(f866(f866(f336(x70351),x70352),x70354))
% 157.60/157.52 [7103]~P79(x71031)+E(f866(f866(f241(x71031),f866(f866(f23(x71031),x71032),x71033)),f866(f866(f23(x71031),x71034),x71033)),f866(f866(f23(x71031),f866(f866(f241(x71031),x71032),x71034)),x71033))
% 157.60/157.52 [7104]~P79(x71041)+E(f866(f866(f242(x71041),f866(f866(f23(x71041),x71042),x71043)),f866(f866(f23(x71041),x71044),x71043)),f866(f866(f23(x71041),f866(f866(f242(x71041),x71042),x71044)),x71043))
% 157.60/157.52 [7106]~P115(x71061)+E(f866(f866(f86(x71061),f866(f866(f87(x71061),x71062),x71063)),f866(f866(f87(x71061),x71064),x71063)),f866(f866(f87(x71061),f866(f866(f86(x71061),x71062),x71064)),x71063))
% 157.60/157.52 [7107]~P101(x71071)+E(f866(f866(f108(x71071),f866(f866(f117(x71071),x71072),x71073)),f866(f866(f117(x71071),x71074),x71073)),f866(f866(f117(x71071),f866(f866(f108(x71071),x71072),x71074)),x71073))
% 157.60/157.52 [7108]~P87(x71081)+E(f866(f866(f241(x71081),f866(f866(f86(x71081),x71082),x71083)),f866(f866(f86(x71081),x71084),x71083)),f866(f866(f86(x71081),f866(f866(f241(x71081),x71082),x71084)),x71083))
% 157.60/157.52 [7109]~P87(x71091)+E(f866(f866(f242(x71091),f866(f866(f86(x71091),x71092),x71093)),f866(f866(f86(x71091),x71094),x71093)),f866(f866(f86(x71091),f866(f866(f242(x71091),x71092),x71094)),x71093))
% 157.60/157.52 [7110]~P71(x71101)+E(f866(f866(f87(x71101),f866(f866(f252(x71101),x71102),x71103)),f866(f866(f252(x71101),x71104),x71103)),f866(f866(f252(x71101),f866(f866(f87(x71101),x71102),x71104)),x71103))
% 157.60/157.52 [7111]~P114(x71111)+E(f866(f866(f87(x71111),f866(f866(f252(x71111),x71112),x71113)),f866(f866(f252(x71111),x71114),x71113)),f866(f866(f252(x71111),f866(f866(f87(x71111),x71112),x71114)),x71113))
% 157.60/157.52 [7112]~P65(x71121)+E(f866(f866(f297(x71121),f866(f866(f252(x71121),x71122),x71123)),f866(f866(f252(x71121),x71124),x71123)),f866(f866(f252(x71121),f866(f866(f297(x71121),x71122),x71124)),x71123))
% 157.60/157.52 [7113]~P101(x71131)+E(f866(f866(f117(x71131),f866(f866(f108(x71131),x71132),x71133)),f866(f866(f108(x71131),x71134),x71133)),f866(f866(f108(x71131),f866(f866(f117(x71131),x71132),x71134)),x71133))
% 157.60/157.52 [7114]~P125(x71141)+E(f866(f866(f23(x71141),f866(f866(f297(x71141),x71142),x71143)),f866(f866(f297(x71141),x71144),x71143)),f866(f866(f297(x71141),f866(f866(f23(x71141),x71142),x71144)),x71143))
% 157.60/157.52 [7115]~P125(x71151)+E(f866(f866(f86(x71151),f866(f866(f297(x71151),x71152),x71153)),f866(f866(f297(x71151),x71154),x71153)),f866(f866(f297(x71151),f866(f866(f86(x71151),x71152),x71154)),x71153))
% 157.60/157.52 [7116]~P110(x71161)+E(f866(f866(f242(x71161),f866(f866(f241(x71161),x71162),x71163)),f866(f866(f241(x71161),x71164),x71163)),f866(f866(f241(x71161),f866(f866(f242(x71161),x71162),x71164)),x71163))
% 157.60/157.52 [7117]~P110(x71171)+E(f866(f866(f241(x71171),f866(f866(f242(x71171),x71172),x71173)),f866(f866(f242(x71171),x71174),x71173)),f866(f866(f242(x71171),f866(f866(f241(x71171),x71172),x71174)),x71173))
% 157.60/157.52 [7118]~P114(x71181)+E(f866(f866(f86(x71181),f866(f866(f87(x71181),x71182),x71183)),f866(f866(f87(x71181),x71184),x71183)),f866(f866(f87(x71181),f866(f866(f86(x71181),x71182),x71184)),x71183))
% 157.60/157.52 [7151]E(f866(f866(f166(x71511,x71512),x71513),x71514),x71512)+~P107(f866(f866(f243(a930),f866(f196(f931(x71511)),x71512)),x71513))
% 157.60/157.52 [7176]~P107(f866(x71763,x71764))+P107(f866(f866(f866(f117(f937(x71761,a925)),x71762),x71763),x71764))
% 157.60/157.52 [7178]~P107(f866(x71782,x71784))+P107(f866(f866(f866(f117(f937(x71781,a925)),x71782),x71783),x71784))
% 157.60/157.52 [7196]E(f866(f866(f171(x71961),f866(f866(f141(x71961),x71962),x71963)),x71964),f866(f866(f171(x71961),x71962),x71964))+~P107(f866(f866(f244(a930),x71964),f866(f196(f931(x71961)),x71962)))
% 157.60/157.52 [7207]E(f866(f866(f23(f937(x72071,a925)),f866(f866(f316(x72071),x72072),x72073)),x72074),f866(f866(f23(f937(x72071,a925)),x72073),x72074))+~P107(f866(f866(f336(x72071),x72072),x72074))
% 157.60/157.52 [7247]~E(f146(a930,f866(f309(a930,x72471),x72472)),f866(f866(f158(a930),x72474),x72473))+E(f146(a930,f866(f309(a930,f866(f866(f86(a930),x72471),f84(a930))),x72472)),x72473)
% 157.60/157.52 [7268]~P107(f866(f866(f179(x72681),x72683),x72684))+P107(f866(f866(f179(x72681),f866(f866(f158(x72681),x72682),x72683)),x72684))
% 157.60/157.52 [7318]E(x73181,f2(a930))+E(f866(f866(f158(x73182),x73183),f866(f866(f182(x73182),f866(f866(f23(a930),x73181),f84(a930))),x73184)),f866(f866(f182(x73182),x73181),f866(f866(f158(x73182),x73183),x73184)))
% 157.60/157.52 [7418]E(f866(f866(f171(x74181),x74182),f866(f866(f23(a930),x74183),f866(f196(f931(x74181)),x74184))),f866(f866(f171(x74181),f866(f866(f141(x74181),x74184),x74182)),x74183))+P107(f866(f866(f244(a930),x74183),f866(f196(f931(x74181)),x74184)))
% 157.60/157.52 [7447]E(f866(f866(f108(f937(x74471,a925)),x74472),f866(f866(f316(x74471),x74473),x74474)),f866(f866(f316(x74471),x74473),f866(f866(f108(f937(x74471,a925)),x74472),x74474)))+~P107(f866(f866(f336(x74471),x74473),x74472))
% 157.60/157.52 [7485]E(f866(f866(f171(x74851),f866(f866(f166(x74851,x74852),x74853),x74854)),x74853),x74854)+~P107(f866(f866(f244(a930),x74853),f866(f196(f931(x74851)),x74852)))
% 157.60/157.52 [7507]E(x75071,f195(f937(x75072,a925)))+E(f866(f317(f936(x75073,x75072),x75073,f259(x75073,x75072)),f866(f866(f262(x75073,x75072),x75074),f866(f16(f937(x75072,a925),x75073),x75071))),x75074)
% 157.60/157.52 [7508]E(x75081,f195(f937(x75082,a925)))+E(f866(f317(f936(x75082,x75083),x75083,f264(x75082,x75083)),f866(f866(f262(x75082,x75083),x75081),f866(f16(f937(x75083,a925),x75082),x75084))),x75084)
% 157.60/157.52 [7582]E(f866(f866(f23(f937(x75821,a925)),f866(f866(f316(x75821),x75822),x75823)),x75824),f866(f866(f316(x75821),x75822),f866(f866(f23(f937(x75821,a925)),x75823),x75824)))+P107(f866(f866(f336(x75821),x75822),x75824))
% 157.60/157.52 [7617]~E(x76174,f195(f937(x76172,a925)))+E(f866(f317(f936(x76171,x76172),x76171,f259(x76171,x76172)),f866(f866(f262(x76171,x76172),x76173),f866(f16(f937(x76172,a925),x76171),x76174))),f195(f937(x76171,a925)))
% 157.60/157.52 [7618]~E(x76183,f195(f937(x76181,a925)))+E(f866(f317(f936(x76181,x76182),x76182,f264(x76181,x76182)),f866(f866(f262(x76181,x76182),x76183),f866(f16(f937(x76182,a925),x76181),x76184))),f195(f937(x76182,a925)))
% 157.60/157.52 [7670]~P107(f866(f866(f336(x76701),x76702),x76704))+P107(f866(f866(f336(x76701),x76702),f866(f866(f117(f937(x76701,a925)),x76703),x76704)))
% 157.60/157.52 [7673]~P107(f866(f866(f336(x76731),x76732),x76733))+P107(f866(f866(f336(x76731),x76732),f866(f866(f117(f937(x76731,a925)),x76733),x76734)))
% 157.60/157.52 [7691]E(f866(f866(f108(f937(x76911,a925)),f866(f866(f316(x76911),x76912),x76913)),x76914),f866(f866(f316(x76911),x76912),f866(f866(f108(f937(x76911,a925)),x76913),x76914)))+~P107(f866(f866(f336(x76911),x76912),x76914))
% 157.60/157.52 [7961]P107(f866(x79611,x79612))+~P107(f866(f866(f866(f108(f937(x79613,a925)),x79614),x79611),x79612))
% 157.60/157.52 [7962]P107(f866(x79621,x79622))+~P107(f866(f866(f866(f108(f937(x79623,a925)),x79621),x79624),x79622))
% 157.60/157.52 [7963]E(f866(f866(f6(x79631,a930),x79632),f866(f866(f23(f937(x79631,a925)),x79633),f866(f866(f316(x79631),x79634),f195(f937(x79631,a925))))),f866(f866(f6(x79631,a930),x79632),x79633))+P107(f866(f866(f336(x79631),x79634),x79633))
% 157.60/157.52 [7968]~P72(x79681)+E(f866(f172(x79681),f866(f866(f161(a930,x79681),x79682),f146(a930,f866(f309(a930,x79683),x79684)))),f866(f866(f6(a930,x79681),x79682),f866(f179(a930),f146(a930,f866(f309(a930,x79683),x79684)))))
% 157.60/157.52 [7969]~P72(x79691)+E(f866(f866(f6(a930,x79691),x79692),f866(f179(a930),f146(a930,f866(f309(a930,x79693),x79694)))),f866(f172(x79691),f866(f866(f161(a930,x79691),x79692),f146(a930,f866(f309(a930,x79693),x79694)))))
% 157.60/157.52 [8081]~E(x80813,x80814)+P107(f866(f67(x80811,x80812,f866(f866(f316(x80811),x80813),f195(f937(x80811,a925)))),x80814))
% 157.60/157.52 [8177]P107(f866(f866(f336(x81771),x81772),f866(f179(x81771),x81773)))+~P107(f866(f866(f336(x81771),x81772),f866(f179(x81771),f866(f866(f182(x81771),x81774),x81773))))
% 157.60/157.52 [8178]P107(f866(f866(f336(x81781),x81782),f866(f179(x81781),x81783)))+~P107(f866(f866(f336(x81781),x81782),f866(f179(x81781),f866(f866(f145(x81781),x81784),x81783))))
% 157.60/157.52 [8249]P107(f866(f866(f336(x82491),x82492),x82493))+~P107(f866(f866(f336(x82491),x82492),f866(f866(f23(f937(x82491,a925)),x82493),x82494)))
% 157.60/157.52 [8251]P107(f866(f866(f336(x82511),x82512),x82513))+~P107(f866(f866(f336(x82511),x82512),f866(f866(f108(f937(x82511,a925)),x82514),x82513)))
% 157.60/157.52 [8254]P107(f866(f866(f336(x82541),x82542),x82543))+~P107(f866(f866(f336(x82541),x82542),f866(f866(f108(f937(x82541,a925)),x82543),x82544)))
% 157.60/157.52 [8269]E(f866(f866(f141(x82691),f866(f866(f182(x82691),x82692),x82693)),f866(f866(f158(x82691),x82694),f866(f866(f145(x82691),f866(a119,x82692)),x82693))),f866(f866(f166(x82691,x82693),x82692),x82694))+~P107(f866(f866(f244(a930),x82692),f866(f196(f931(x82691)),x82693)))
% 157.60/157.52 [8292]P107(f866(f866(f336(x82921),x82922),x82923))+~P107(f866(f866(f243(f937(x82921,a925)),f866(f866(f316(x82921),x82922),x82924)),x82923))
% 157.60/157.52 [8328]~P107(f866(f866(f336(x83281),x83282),x83283))+~P107(f866(f866(f336(x83281),x83282),f866(f866(f23(f937(x83281,a925)),x83284),x83283)))
% 157.60/157.52 [8358]~P107(f866(f866(f244(a930),x83584),f866(f196(f931(x83581)),x83583)))+P107(f866(f866(f336(x83581),x83582),f866(f179(x83581),f866(f866(f166(x83581,x83583),x83584),x83582))))
% 157.60/157.52 [8408]E(f866(f866(f171(x84081),f866(f866(f145(x84081),x84082),x84083)),x84084),f866(f866(f171(x84081),x84083),f866(f866(f86(a930),x84082),x84084)))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x84082),x84084)),f866(f196(f931(x84081)),x84083)))
% 157.60/157.52 [8417]~P148(x84172)+E(f866(f866(f6(x84171,x84172),f866(f866(f8(a930,x84172,x84171),f107(x84172)),x84173)),x84174),f866(f107(x84172),f866(f866(f6(x84171,a930),x84173),x84174)))
% 157.60/157.52 [8418]~P142(x84182)+E(f866(f866(f6(x84181,x84182),f866(f866(f8(a1,x84182,x84181),f109(x84182)),x84183)),x84184),f866(f109(x84182),f866(f866(f6(x84181,a1),x84183),x84184)))
% 157.60/157.52 [8468]~P68(x84682)+E(f866(f866(f9(x84681,x84682),f866(f866(f8(x84682,x84682,x84681),f81(x84682)),x84683)),x84684),f866(f81(x84682),f866(f866(f9(x84681,x84682),x84683),x84684)))
% 157.60/157.52 [8469]~P3(x84692)+E(f866(f866(f6(x84691,x84692),f866(f866(f8(x84692,x84692,x84691),f85(x84692)),x84693)),x84694),f866(f85(x84692),f866(f866(f6(x84691,x84692),x84693),x84694)))
% 157.60/157.52 [8471]E(f866(f866(f6(x84711,a930),x84712),f866(f866(f23(f937(x84711,a925)),x84713),f866(f866(f316(x84711),x84714),f195(f937(x84711,a925))))),f866(f866(f23(a930),f866(f866(f6(x84711,a930),x84712),x84713)),f866(x84712,x84714)))+~P107(f866(f866(f336(x84711),x84714),x84713))
% 157.60/157.52 [8490]P107(f866(f866(f243(f937(x84901,a925)),x84902),x84903))+~P107(f866(f866(f243(f937(x84901,a925)),f866(f866(f316(x84901),x84904),x84902)),x84903))
% 157.60/157.52 [8614]~E(f866(f317(x86142,x86143,x86141),f250(f937(x86142,a925))),f250(f937(x86143,a925)))+E(f866(x86141,f866(f97(x86142,x86143,f250(f937(x86142,a925)),x86141),x86144)),x86144)
% 157.60/157.52 [8696]P37(x86961,x86962)+~P37(x86961,f866(f866(f316(f936(x86961,x86961)),f866(f866(f260(x86961,x86961),x86963),x86964)),x86962))
% 157.60/157.52 [8697]P59(x86971,x86972)+~P59(x86971,f866(f866(f316(f936(x86971,x86971)),f866(f866(f260(x86971,x86971),x86973),x86974)),x86972))
% 157.60/157.52 [8702]~P110(x87021)+E(f866(f866(f155(x87021,x87021,f5(x87021)),x87022),f866(f866(f155(x87021,x87021,f5(x87021)),x87023),x87024)),f866(f866(f155(x87021,x87021,f5(x87021)),x87023),f866(f866(f155(x87021,x87021,f5(x87021)),x87022),x87024)))
% 157.60/157.52 [8717]E(x87171,x87172)+~P107(f866(f67(x87173,x87174,f866(f866(f316(x87173),x87171),f195(f937(x87173,a925)))),x87172))
% 157.60/157.52 [8726]E(f866(f866(f141(x87261),f866(f866(f182(x87261),x87262),x87263)),f866(f866(f182(x87261),x87264),f866(f866(f145(x87261),x87262),x87263))),f866(f866(f182(x87261),f866(f866(f86(a930),x87262),x87264)),x87263))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x87262),x87264)),f866(f196(f931(x87261)),x87263)))
% 157.60/157.52 [8767]P107(f866(f66(x87671),x87672))+~E(x87672,f866(f317(a930,x87671,x87673),f866(f270(a930),f866(f866(f7(a930,a930,a925),f244(a930)),x87674))))
% 157.60/157.52 [8787]~P94(x87871)+E(f866(f149(x87871,x87871,f86(x87871),f866(f866(f86(x87871),x87872),x87873)),x87874),f866(f866(f86(x87871),x87872),f866(f149(x87871,x87871,f86(x87871),x87873),x87874)))
% 157.60/157.52 [8823]P107(f866(f866(f243(f937(x88231,a925)),f866(f272(x88231,x88232),x88233)),f866(f272(x88231,x88232),x88234)))+~P107(f866(f866(f243(f937(f936(x88231,x88232),a925)),x88233),x88234))
% 157.60/157.52 [8835]~P107(f866(f866(f243(a930),x88352),x88354))+P107(f866(f866(f243(f937(x88351,a925)),f866(f179(x88351),f866(f866(f182(x88351),x88352),x88353))),f866(f179(x88351),f866(f866(f182(x88351),x88354),x88353))))
% 157.60/157.52 [8836]~P107(f866(f866(f243(a930),x88364),x88362))+P107(f866(f866(f243(f937(x88361,a925)),f866(f179(x88361),f866(f866(f145(x88361),x88362),x88363))),f866(f179(x88361),f866(f866(f145(x88361),x88364),x88363))))
% 157.60/157.52 [8893]~P107(f866(f66(x88931),f866(f866(f23(f937(x88931,a925)),x88932),x88934)))+P107(f866(f66(x88931),f866(f866(f23(f937(x88931,a925)),x88932),f866(f866(f316(x88931),x88933),x88934))))
% 157.60/157.52 [8935]P107(f866(f866(f336(f936(x89351,x89351)),x89352),f314(x89351,x89353)))+~P107(f866(f866(f336(f936(x89351,x89351)),x89352),f866(f866(f190(f936(x89351,x89351),a925),x89354),x89353)))
% 157.60/157.52 [9021]~P107(f866(f66(x90211),f866(f866(f23(f937(x90211,a925)),x90212),f866(f866(f316(x90211),x90214),x90213))))+P107(f866(f66(x90211),f866(f866(f23(f937(x90211,a925)),x90212),x90213)))
% 157.60/157.52 [9238]~P83(x92381)+P107(f866(f866(f243(x92381),f866(f866(f117(x92381),x92382),f866(f866(f108(x92381),x92383),x92384))),f866(f866(f108(x92381),f866(f866(f117(x92381),x92382),x92383)),f866(f866(f117(x92381),x92382),x92384))))
% 157.60/157.52 [9239]~P110(x92391)+P107(f866(f866(f243(x92391),f866(f866(f242(x92391),x92392),f866(f866(f241(x92391),x92393),x92394))),f866(f866(f241(x92391),f866(f866(f242(x92391),x92392),x92393)),f866(f866(f242(x92391),x92392),x92394))))
% 157.60/157.52 [9387]E(x93871,x93872)+~P107(f866(f866(f336(f936(x93873,x93873)),f866(f866(f260(x93873,x93873),x93871),x93872)),f866(f179(f936(x93873,x93873)),f866(f866(f188(x93873,x93873),x93874),x93874))))
% 157.60/157.52 [9417]~P107(f866(f866(f336(f936(x94171,x94171)),f866(f866(f260(x94171,x94171),x94173),x94172)),f314(x94171,x94174)))+~P37(x94171,f866(f866(f316(f936(x94171,x94171)),f866(f866(f260(x94171,x94171),x94172),x94173)),x94174))
% 157.60/157.52 [9418]~P107(f866(f866(f336(f936(x94181,x94181)),f866(f866(f260(x94181,x94181),x94183),x94182)),f314(x94181,x94184)))+~P59(x94181,f866(f866(f316(f936(x94181,x94181)),f866(f866(f260(x94181,x94181),x94182),x94183)),x94184))
% 157.60/157.52 [9422]E(x94221,x94222)+E(f866(f143(x94223,f866(f866(f8(a925,a925,x94223),a329),f866(a332,x94221))),f866(f866(f158(x94223),x94222),x94224)),f866(f866(f158(x94223),x94222),f866(f143(x94223,f866(f866(f8(a925,a925,x94223),a329),f866(a332,x94221))),x94224)))
% 157.60/157.52 [9450]~P26(x94502,x94501,x94503,f250(f937(x94502,a925)),f250(f937(x94501,a925)))+E(f866(f317(x94501,x94502,f97(x94502,x94501,f250(f937(x94502,a925)),x94503)),x94504),f866(f318(x94502,x94501,x94503),x94504))
% 157.60/157.52 [9465]~P83(x94651)+P107(f866(f866(f243(x94651),f866(f866(f117(x94651),f866(f866(f108(x94651),x94652),x94653)),f866(f866(f108(x94651),x94652),x94654))),f866(f866(f108(x94651),x94652),f866(f866(f117(x94651),x94653),x94654))))
% 157.60/157.52 [9466]~P110(x94661)+P107(f866(f866(f243(x94661),f866(f866(f242(x94661),f866(f866(f241(x94661),x94662),x94663)),f866(f866(f241(x94661),x94662),x94664))),f866(f866(f241(x94661),x94662),f866(f866(f242(x94661),x94663),x94664))))
% 157.60/157.52 [9529]~P26(x95292,x95291,x95294,f250(f937(x95292,a925)),f250(f937(x95291,a925)))+E(f866(f270(x95291),f866(f866(f8(x95292,a925,x95291),x95293),f97(x95292,x95291,f250(f937(x95292,a925)),x95294))),f866(f317(x95292,x95291,x95294),f866(f270(x95292),x95293)))
% 157.60/157.52 [9543]~E(f866(f317(x95432,x95431,x95433),f250(f937(x95432,a925))),f250(f937(x95431,a925)))+P107(f866(f866(f243(f937(x95431,a925)),f866(f85(f937(x95431,a925)),f866(f317(x95432,x95431,x95433),x95434))),f866(f317(x95432,x95431,x95433),f866(f85(f937(x95432,a925)),x95434))))
% 157.60/157.52 [9866]P107(f866(f866(f336(f936(x98661,x98661)),f866(f866(f260(x98661,x98661),x98662),x98663)),f866(f294(x98661,x98661),f866(f866(f296(x98661,x98661,x98661),x98664),f314(x98661,x98664)))))+~P107(f866(f866(f336(f936(x98661,x98661)),f866(f866(f260(x98661,x98661),x98662),x98663)),f866(f866(f296(x98661,x98661,x98661),f866(f294(x98661,x98661),x98664)),f314(x98661,f866(f294(x98661,x98661),x98664)))))
% 157.60/157.52 [9867]~P107(f866(f866(f336(f936(x98671,x98671)),f866(f866(f260(x98671,x98671),x98672),x98673)),f866(f294(x98671,x98671),f866(f866(f296(x98671,x98671,x98671),x98674),f314(x98671,x98674)))))+P107(f866(f866(f336(f936(x98671,x98671)),f866(f866(f260(x98671,x98671),x98672),x98673)),f866(f866(f296(x98671,x98671,x98671),f866(f294(x98671,x98671),x98674)),f314(x98671,f866(f294(x98671,x98671),x98674)))))
% 157.60/157.52 [9888]~P107(f866(f866(f336(x98882),x98884),f866(f292(x98881,x98882),x98883)))+P107(f866(f866(f336(f936(x98881,x98882)),f866(f866(f260(x98881,x98882),f529(x98883,x98881,x98884,x98882)),x98884)),x98883))
% 157.60/157.52 [9889]~P107(f866(f866(f336(x98892),x98894),f866(f292(x98891,x98892),x98893)))+P107(f866(f866(f336(f936(x98891,x98892)),f866(f866(f260(x98891,x98892),f540(x98893,x98891,x98894,x98892)),x98894)),x98893))
% 157.60/157.52 [9915]~P107(f866(f866(f336(x99151),x99154),f866(f866(f117(f937(x99151,a925)),x99152),x99153)))+P107(f866(f866(f866(f117(f937(x99151,a925)),f866(f866(f7(x99151,f937(x99151,a925),a925),f336(x99151)),x99152)),f866(f866(f7(x99151,f937(x99151,a925),a925),f336(x99151)),x99153)),x99154))
% 157.60/157.52 [9916]~P107(f866(f866(f336(x99161),x99164),f866(f866(f108(f937(x99161,a925)),x99162),x99163)))+P107(f866(f866(f866(f108(f937(x99161,a925)),f866(f866(f7(x99161,f937(x99161,a925),a925),f336(x99161)),x99162)),f866(f866(f7(x99161,f937(x99161,a925),a925),f336(x99161)),x99163)),x99164))
% 157.60/157.52 [9998]~P107(f866(f866(f336(f936(x99981,x99981)),f866(f866(f260(x99981,x99981),x99984),x99983)),f866(f866(f296(x99981,x99981,x99981),x99982),f314(x99981,x99982))))+P107(f866(f866(f336(f936(x99981,x99981)),f866(f866(f260(x99981,x99981),f611(x99982,x99983,x99984,x99981)),x99983)),x99982))
% 157.60/157.52 [10033]P107(f866(f866(f336(x100331),x100332),f866(f866(f117(f937(x100331,a925)),x100333),x100334)))+~P107(f866(f866(f866(f117(f937(x100331,a925)),f866(f866(f7(x100331,f937(x100331,a925),a925),f336(x100331)),x100333)),f866(f866(f7(x100331,f937(x100331,a925),a925),f336(x100331)),x100334)),x100332))
% 157.60/157.52 [10034]P107(f866(f866(f336(x100341),x100342),f866(f866(f108(f937(x100341,a925)),x100343),x100344)))+~P107(f866(f866(f866(f108(f937(x100341,a925)),f866(f866(f7(x100341,f937(x100341,a925),a925),f336(x100341)),x100343)),f866(f866(f7(x100341,f937(x100341,a925),a925),f336(x100341)),x100344)),x100342))
% 157.60/157.52 [10305]P32(x103051,f866(f866(f7(x103051,f937(f936(x103051,x103051),a925),f937(x103051,a925)),f866(f866(f8(f937(x103051,f937(f937(f936(x103051,x103051),a925),a925)),f937(f937(f936(x103051,x103051),a925),f937(x103051,a925)),x103051),f7(x103051,f937(f936(x103051,x103051),a925),a925)),f866(f866(f8(f937(x103051,f936(x103051,x103051)),f937(x103051,f937(f937(f936(x103051,x103051),a925),a925)),x103051),f866(f8(f936(x103051,x103051),f937(f937(f936(x103051,x103051),a925),a925),x103051),f336(f936(x103051,x103051)))),f260(x103051,x103051)))),x103052),x103053,x103054)+~P107(f866(f866(f336(f936(f931(x103051),f931(x103051))),f866(f866(f260(f931(x103051),f931(x103051)),x103053),x103054)),f165(x103051,x103052)))
% 157.60/157.52 [10309]P60(x103091,f866(f866(f7(x103091,f937(f936(x103091,x103091),a925),f937(x103091,a925)),f866(f866(f8(f937(x103091,f937(f937(f936(x103091,x103091),a925),a925)),f937(f937(f936(x103091,x103091),a925),f937(x103091,a925)),x103091),f7(x103091,f937(f936(x103091,x103091),a925),a925)),f866(f866(f8(f937(x103091,f936(x103091,x103091)),f937(x103091,f937(f937(f936(x103091,x103091),a925),a925)),x103091),f866(f8(f936(x103091,x103091),f937(f937(f936(x103091,x103091),a925),a925),x103091),f336(f936(x103091,x103091)))),f260(x103091,x103091)))),x103092),x103093,x103094)+~P107(f866(f866(f336(f936(f937(x103091,a925),f937(x103091,a925))),f866(f866(f260(f937(x103091,a925),f937(x103091,a925)),x103093),x103094)),f325(x103091,x103092)))
% 157.60/157.52 [10344]E(x103441,x103442)+~E(f866(f866(f7(x103443,f937(f936(x103443,x103444),a925),f937(x103444,a925)),f866(f866(f8(f937(x103444,f937(f937(f936(x103443,x103444),a925),a925)),f937(f937(f936(x103443,x103444),a925),f937(x103444,a925)),x103443),f7(x103444,f937(f936(x103443,x103444),a925),a925)),f866(f866(f8(f937(x103444,f936(x103443,x103444)),f937(x103444,f937(f937(f936(x103443,x103444),a925),a925)),x103443),f866(f8(f936(x103443,x103444),f937(f937(f936(x103443,x103444),a925),a925),x103444),f336(f936(x103443,x103444)))),f260(x103443,x103444)))),x103441),f866(f866(f7(x103443,f937(f936(x103443,x103444),a925),f937(x103444,a925)),f866(f866(f8(f937(x103444,f937(f937(f936(x103443,x103444),a925),a925)),f937(f937(f936(x103443,x103444),a925),f937(x103444,a925)),x103443),f7(x103444,f937(f936(x103443,x103444),a925),a925)),f866(f866(f8(f937(x103444,f936(x103443,x103444)),f937(x103444,f937(f937(f936(x103443,x103444),a925),a925)),x103443),f866(f8(f936(x103443,x103444),f937(f937(f936(x103443,x103444),a925),a925),x103444),f336(f936(x103443,x103444)))),f260(x103443,x103444)))),x103442))
% 157.60/157.52 [10347]~P32(x103471,f866(f866(f7(x103471,f937(f936(x103471,x103471),a925),f937(x103471,a925)),f866(f866(f8(f937(x103471,f937(f937(f936(x103471,x103471),a925),a925)),f937(f937(f936(x103471,x103471),a925),f937(x103471,a925)),x103471),f7(x103471,f937(f936(x103471,x103471),a925),a925)),f866(f866(f8(f937(x103471,f936(x103471,x103471)),f937(x103471,f937(f937(f936(x103471,x103471),a925),a925)),x103471),f866(f8(f936(x103471,x103471),f937(f937(f936(x103471,x103471),a925),a925),x103471),f336(f936(x103471,x103471)))),f260(x103471,x103471)))),x103474),x103472,x103473)+P107(f866(f866(f336(f936(f931(x103471),f931(x103471))),f866(f866(f260(f931(x103471),f931(x103471)),x103472),x103473)),f165(x103471,x103474)))
% 157.60/157.52 [10348]~P60(x103481,f866(f866(f7(x103481,f937(f936(x103481,x103481),a925),f937(x103481,a925)),f866(f866(f8(f937(x103481,f937(f937(f936(x103481,x103481),a925),a925)),f937(f937(f936(x103481,x103481),a925),f937(x103481,a925)),x103481),f7(x103481,f937(f936(x103481,x103481),a925),a925)),f866(f866(f8(f937(x103481,f936(x103481,x103481)),f937(x103481,f937(f937(f936(x103481,x103481),a925),a925)),x103481),f866(f8(f936(x103481,x103481),f937(f937(f936(x103481,x103481),a925),a925),x103481),f336(f936(x103481,x103481)))),f260(x103481,x103481)))),x103484),x103482,x103483)+P107(f866(f866(f336(f936(f937(x103481,a925),f937(x103481,a925))),f866(f866(f260(f937(x103481,a925),f937(x103481,a925)),x103482),x103483)),f325(x103481,x103484)))
% 157.60/157.52 [7740]~P96(x77401)+E(f866(f866(f87(x77401),f866(f110(x77401),x77402)),f866(f866(f87(x77401),f866(f110(x77401),x77403)),x77404)),f866(f866(f87(x77401),f866(f110(x77401),f866(f866(f87(a1),x77402),x77403))),x77404))
% 157.60/157.52 [7741]~P96(x77411)+E(f866(f866(f86(x77411),f866(f110(x77411),x77412)),f866(f866(f23(x77411),f866(f110(x77411),x77413)),x77414)),f866(f866(f23(x77411),f866(f110(x77411),f866(f866(f86(a1),x77412),x77413))),x77414))
% 157.60/157.52 [7742]~P96(x77421)+E(f866(f866(f86(x77421),f866(f110(x77421),x77422)),f866(f866(f86(x77421),f866(f110(x77421),x77423)),x77424)),f866(f866(f86(x77421),f866(f110(x77421),f866(f866(f86(a1),x77422),x77423))),x77424))
% 157.60/157.52 [7782]~P148(x77821)+E(f866(f172(x77821),f866(f866(f161(x77822,x77821),f866(f16(x77821,x77822),x77823)),x77824)),f866(f866(f87(x77821),f866(f107(x77821),f866(f196(f931(x77822)),x77824))),x77823))
% 157.60/157.52 [8019]E(f866(f276(x80191,f866(f866(f158(f936(a106,x80191)),x80192),x80193)),x80194),f866(f264(a106,x80191),x80192))+~P107(f866(f866(f244(a106),x80194),f866(f259(a106,x80191),x80192)))
% 157.60/157.52 [8059]~P96(x80591)+E(f866(f866(f86(x80591),f866(f110(x80591),x80592)),f866(f866(f23(x80591),x80593),f866(f110(x80591),x80594))),f866(f866(f86(x80591),f866(f110(x80591),f866(f866(f86(a1),x80592),f866(f85(a1),x80594)))),x80593))
% 157.60/157.52 [8190]E(f866(f276(x81901,x81902),f866(f866(f23(a106),x81903),f866(f259(a106,x81901),x81904))),f866(f276(x81901,f866(f866(f158(f936(a106,x81901)),x81904),x81902)),x81903))+P107(f866(f866(f244(a106),x81903),f866(f259(a106,x81901),x81904)))
% 157.60/157.52 [8620]~P107(f866(f866(f336(x86201),x86202),f866(f179(x86201),f121(x86201,x86204))))+P107(f866(f866(f336(x86201),x86202),f866(f179(x86201),f121(x86201,f866(f866(f141(x86201),x86203),x86204)))))
% 157.60/157.52 [8621]~P107(f866(f866(f336(x86211),x86212),f866(f179(x86211),f121(x86211,x86213))))+P107(f866(f866(f336(x86211),x86212),f866(f179(x86211),f121(x86211,f866(f866(f141(x86211),x86213),x86214)))))
% 157.60/157.52 [8639]E(f866(f866(f117(f937(x86391,a925)),f866(f866(f108(f937(x86391,a925)),x86392),x86393)),x86394),f866(f866(f108(f937(x86391,a925)),x86392),f866(f866(f117(f937(x86391,a925)),x86393),x86394)))+~P107(f866(f866(f243(f937(x86391,a925)),x86394),x86392))
% 157.60/157.52 [8949]~E(f866(f866(f117(f937(x89491,a925)),f866(f866(f108(f937(x89491,a925)),x89493),x89494)),x89492),f866(f866(f108(f937(x89491,a925)),x89493),f866(f866(f117(f937(x89491,a925)),x89494),x89492)))+P107(f866(f866(f243(f937(x89491,a925)),x89492),x89493))
% 157.60/157.52 [9243]~P107(f866(f866(f243(f937(x92431,a925)),x92432),f866(f866(f117(f937(x92431,a925)),x92433),x92434)))+P107(f866(f866(f243(f937(x92431,a925)),f866(f866(f23(f937(x92431,a925)),x92432),x92433)),x92434))
% 157.60/157.52 [9359]~E(f866(f317(x93591,x93592,x93593),f250(f937(x93591,a925))),f250(f937(x93592,a925)))+E(f866(f317(x93591,x93592,x93593),f866(f317(x93592,x93591,f97(x93591,x93592,f250(f937(x93591,a925)),x93593)),x93594)),x93594)
% 157.60/157.52 [9364]P107(f866(f866(f243(f937(x93641,a925)),x93642),f866(f866(f117(f937(x93641,a925)),x93643),x93644)))+~P107(f866(f866(f243(f937(x93641,a925)),f866(f866(f23(f937(x93641,a925)),x93642),x93643)),x93644))
% 157.60/157.52 [9446]~P89(x94461)+E(f866(f81(x94461),f866(f866(f6(x94462,x94461),f866(f866(f8(x94461,x94461,x94462),f81(x94461)),x94463)),x94464)),f866(f866(f6(x94462,x94461),f866(f866(f8(x94461,x94461,x94462),f81(x94461)),x94463)),x94464))
% 157.60/157.52 [9619]~P89(x96191)+P107(f866(f866(f243(x96191),f2(x96191)),f866(f866(f6(x96192,x96191),f866(f866(f8(x96191,x96191,x96192),f81(x96191)),x96193)),x96194)))
% 157.60/157.52 [9623]~P3(x96231)+E(f866(f172(x96231),f866(f866(f161(x96232,x96231),f866(f78(x96231,x96231,x96232,f85(x96231)),x96233)),x96234)),f866(f85(x96231),f866(f172(x96231),f866(f866(f161(x96232,x96231),x96233),x96234))))
% 157.60/157.52 [9762]~P89(x97621)+P107(f866(f866(f243(x97621),f866(f81(x97621),f866(f866(f6(x97622,x97621),x97623),x97624))),f866(f866(f6(x97622,x97621),f866(f866(f8(x97621,x97621,x97622),f81(x97621)),x97623)),x97624)))
% 157.60/157.52 [9791]~E(f866(f866(f86(a930),x97911),x97914),f866(f866(f86(a930),x97913),x97912))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x97911),x97912)),f866(f866(f260(a930,a930),x97913),x97914))),a115))
% 157.60/157.52 [9792]~P107(f866(f866(f244(a930),x97921),x97923))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x97921),x97922)),f866(f866(f260(a930,a930),x97923),x97924))),a38))
% 157.60/157.52 [9793]~P107(f866(f866(f244(a930),x97931),x97933))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x97931),x97932)),f866(f866(f260(a930,a930),x97933),x97934))),a76))
% 157.60/157.52 [9940]E(f866(f866(f86(a930),x99401),x99402),f866(f866(f86(a930),x99403),x99404))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x99401),x99404)),f866(f866(f260(a930,a930),x99403),x99402))),a115))
% 157.60/157.52 [9972]E(f866(f866(f171(x99721),f866(f866(f145(x99721),f866(f196(f931(x99721)),f184(x99721,x99722,x99723))),x99723)),x99724),f866(f866(f171(x99721),x99723),f866(f866(f86(a930),x99724),f866(f196(f931(x99721)),f184(x99721,x99722,x99723)))))+~P107(f866(f866(f244(a930),x99724),f866(f196(f931(x99721)),f866(f866(f145(x99721),f866(f196(f931(x99721)),f184(x99721,x99722,x99723))),x99723))))
% 157.60/157.52 [9988]~P107(f866(f866(f336(x99882),x99884),f866(f866(f44(x99881,f937(x99882,a925)),f250(f937(x99881,a925))),x99883)))+P107(f866(f866(f866(f44(x99881,f937(x99882,a925)),f250(f937(x99881,a925))),f866(f866(f8(f937(x99882,a925),f937(x99882,a925),x99881),f866(f7(x99882,f937(x99882,a925),a925),f336(x99882))),x99883)),x99884))
% 157.60/157.52 [9989]~P107(f866(f866(f336(x99892),x99894),f866(f866(f45(x99891,f937(x99892,a925)),f250(f937(x99891,a925))),x99893)))+P107(f866(f866(f866(f45(x99891,f937(x99892,a925)),f250(f937(x99891,a925))),f866(f866(f8(f937(x99892,a925),f937(x99892,a925),x99891),f866(f7(x99892,f937(x99892,a925),a925),f336(x99892))),x99893)),x99894))
% 157.60/157.52 [10059]~P107(f866(f54(x100591,x100592),f866(f866(f260(a1,a1),x100594),x100593)))+P107(f866(f54(f866(f85(a1),x100591),x100592),f866(f866(f260(a1,a1),f866(f866(f866(f103(a1),f866(f866(a332,x100593),f2(a1))),f866(f85(a1),x100594)),f866(f866(f23(a1),f866(f85(a1),x100594)),f84(a1)))),f866(f866(f866(f103(a1),f866(f866(a332,x100593),f2(a1))),f2(a1)),f866(f866(f23(a1),x100592),x100593)))))
% 157.60/157.52 [10071]P107(f866(f866(f336(x100711),x100712),f866(f866(f44(x100713,f937(x100711,a925)),f250(f937(x100713,a925))),x100714)))+~P107(f866(f866(f866(f44(x100713,f937(x100711,a925)),f250(f937(x100713,a925))),f866(f866(f8(f937(x100711,a925),f937(x100711,a925),x100713),f866(f7(x100711,f937(x100711,a925),a925),f336(x100711))),x100714)),x100712))
% 157.60/157.52 [10072]P107(f866(f866(f336(x100721),x100722),f866(f866(f45(x100723,f937(x100721,a925)),f250(f937(x100723,a925))),x100724)))+~P107(f866(f866(f866(f45(x100723,f937(x100721,a925)),f250(f937(x100723,a925))),f866(f866(f8(f937(x100721,a925),f937(x100721,a925),x100723),f866(f7(x100721,f937(x100721,a925),a925),f336(x100721))),x100724)),x100722))
% 157.60/157.52 [10084]E(f866(f866(f44(a930,f937(x100841,a925)),f250(f937(a930,a925))),x100842),f866(f866(f44(a930,f937(x100841,a925)),f250(f937(a930,a925))),x100843))+~E(f866(f866(f44(a930,f937(x100841,a925)),f866(f309(a930,f2(a930)),f422(x100842,x100844,x100843,x100841))),x100843),f866(f866(f44(a930,f937(x100841,a925)),f866(f309(a930,f2(a930)),f866(f866(f86(a930),f422(x100842,x100844,x100843,x100841)),x100844))),x100842))
% 157.60/157.52 [10425]~P107(f866(f866(f243(f937(f936(x104251,x104252),a925)),x104253),x104254))+P107(f866(f866(f243(f937(x104251,f937(x104252,a925))),f866(f866(f7(x104251,f937(f936(x104251,x104252),a925),f937(x104252,a925)),f866(f866(f8(f937(x104252,f937(f937(f936(x104251,x104252),a925),a925)),f937(f937(f936(x104251,x104252),a925),f937(x104252,a925)),x104251),f7(x104252,f937(f936(x104251,x104252),a925),a925)),f866(f866(f8(f937(x104252,f936(x104251,x104252)),f937(x104252,f937(f937(f936(x104251,x104252),a925),a925)),x104251),f866(f8(f936(x104251,x104252),f937(f937(f936(x104251,x104252),a925),a925),x104252),f336(f936(x104251,x104252)))),f260(x104251,x104252)))),x104253)),f866(f866(f7(x104251,f937(f936(x104251,x104252),a925),f937(x104252,a925)),f866(f866(f8(f937(x104252,f937(f937(f936(x104251,x104252),a925),a925)),f937(f937(f936(x104251,x104252),a925),f937(x104252,a925)),x104251),f7(x104252,f937(f936(x104251,x104252),a925),a925)),f866(f866(f8(f937(x104252,f936(x104251,x104252)),f937(x104252,f937(f937(f936(x104251,x104252),a925),a925)),x104251),f866(f8(f936(x104251,x104252),f937(f937(f936(x104251,x104252),a925),a925),x104252),f336(f936(x104251,x104252)))),f260(x104251,x104252)))),x104254)))
% 157.60/157.52 [10441]P107(f866(f866(f243(f937(f936(x104411,x104412),a925)),x104413),x104414))+~P107(f866(f866(f243(f937(x104411,f937(x104412,a925))),f866(f866(f7(x104411,f937(f936(x104411,x104412),a925),f937(x104412,a925)),f866(f866(f8(f937(x104412,f937(f937(f936(x104411,x104412),a925),a925)),f937(f937(f936(x104411,x104412),a925),f937(x104412,a925)),x104411),f7(x104412,f937(f936(x104411,x104412),a925),a925)),f866(f866(f8(f937(x104412,f936(x104411,x104412)),f937(x104412,f937(f937(f936(x104411,x104412),a925),a925)),x104411),f866(f8(f936(x104411,x104412),f937(f937(f936(x104411,x104412),a925),a925),x104412),f336(f936(x104411,x104412)))),f260(x104411,x104412)))),x104413)),f866(f866(f7(x104411,f937(f936(x104411,x104412),a925),f937(x104412,a925)),f866(f866(f8(f937(x104412,f937(f937(f936(x104411,x104412),a925),a925)),f937(f937(f936(x104411,x104412),a925),f937(x104412,a925)),x104411),f7(x104412,f937(f936(x104411,x104412),a925),a925)),f866(f866(f8(f937(x104412,f936(x104411,x104412)),f937(x104412,f937(f937(f936(x104411,x104412),a925),a925)),x104411),f866(f8(f936(x104411,x104412),f937(f937(f936(x104411,x104412),a925),a925),x104412),f336(f936(x104411,x104412)))),f260(x104411,x104412)))),x104414)))
% 157.60/157.52 [9493]~P107(f866(f866(f336(f936(x94931,x94931)),x94932),f314(x94931,x94934)))+P107(f866(f866(f336(f936(x94931,x94931)),x94932),f314(x94931,f866(f866(f117(f937(f936(x94931,x94931),a925)),x94933),x94934))))
% 157.60/157.52 [9494]~P107(f866(f866(f336(f936(x94941,x94941)),x94942),f314(x94941,x94943)))+P107(f866(f866(f336(f936(x94941,x94941)),x94942),f314(x94941,f866(f866(f117(f937(f936(x94941,x94941),a925)),x94943),x94944))))
% 157.60/157.52 [10171]~P107(f866(f866(f243(a930),f866(f866(f86(a930),x101711),x101714)),f866(f866(f86(a930),x101713),x101712)))+P107(f866(f866(f243(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x101711),x101712)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x101713),x101714)),f195(f937(f936(a930,a930),a925)))))))
% 157.60/157.52 [10172]~P107(f866(f866(f244(a930),f866(f866(f86(a930),x101721),x101724)),f866(f866(f86(a930),x101723),x101722)))+P107(f866(f866(f244(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x101721),x101722)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x101723),x101724)),f195(f937(f936(a930,a930),a925)))))))
% 157.60/157.52 [10250]P107(f866(f866(f243(a930),f866(f866(f86(a930),x102501),x102502)),f866(f866(f86(a930),x102503),x102504)))+~P107(f866(f866(f243(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x102501),x102504)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x102503),x102502)),f195(f937(f936(a930,a930),a925)))))))
% 157.60/157.52 [10251]P107(f866(f866(f244(a930),f866(f866(f86(a930),x102511),x102512)),f866(f866(f86(a930),x102513),x102514)))+~P107(f866(f866(f244(a1),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x102511),x102514)),f195(f937(f936(a930,a930),a925)))))),f866(a95,f866(f293(f936(a930,a930),f936(a930,a930),a115),f866(f866(f316(f936(a930,a930)),f866(f866(f260(a930,a930),x102513),x102512)),f195(f937(f936(a930,a930),a925)))))))
% 157.60/157.52 [10291]P107(f866(f866(f243(f937(x102911,a925)),f866(f866(f44(a930,f937(x102911,a925)),f250(f937(a930,a925))),x102912)),f866(f866(f44(a930,f937(x102911,a925)),f250(f937(a930,a925))),x102913)))+~P107(f866(f866(f243(f937(x102911,a925)),f866(f866(f44(a930,f937(x102911,a925)),f866(f309(a930,f2(a930)),f419(x102913,x102914,x102912,x102911))),x102912)),f866(f866(f44(a930,f937(x102911,a925)),f866(f309(a930,f2(a930)),f866(f866(f86(a930),f419(x102913,x102914,x102912,x102911)),x102914))),x102913)))
% 157.60/157.52 [10351]P107(f866(f866(f243(a106),x103514),f2(a106)))+E(f866(f866(f267(f936(a106,a106),f936(x103511,f937(a933,a330)),f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106))),f866(x103512,x103513)),f866(f866(f8(f937(f937(a106,f937(a925,f934(f932(x103511)))),f937(f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106)))),f937(f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106))),f936(x103511,f937(a933,a330))),f866(f267(f936(a106,a106),f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106))),f285(x103511,x103512,f866(f866(f23(a106),x103514),f84(a106)),x103513))),f866(f866(f8(f937(f937(a106,f937(a925,f934(f932(x103511)))),f937(a106,f937(a925,f934(f932(x103511))))),f937(f937(a106,f937(a925,f934(f932(x103511)))),f937(f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106)))),f936(x103511,f937(a933,a330))),f866(f8(f937(a106,f937(a925,f934(f932(x103511)))),f937(f936(a106,a106),f936(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106))),f937(a106,f937(a925,f934(f932(x103511))))),f260(f937(a106,f937(a925,f934(f932(x103511)))),f936(a106,a106)))),f866(f866(f8(f937(a106,f937(a925,f934(f932(x103511)))),f937(f937(a106,f937(a925,f934(f932(x103511)))),f937(a106,f937(a925,f934(f932(x103511))))),f936(x103511,f937(a933,a330))),f49(x103511)),f866(f866(f8(x103511,f937(a106,f937(a925,f934(f932(x103511)))),f936(x103511,f937(a933,a330))),f47(x103511)),f259(x103511,f937(a933,a330))))))),f285(x103511,x103512,x103514,x103513))
% 157.60/157.52 [10413]~P107(f866(f866(f336(x104132),x104134),f866(f292(x104131,x104132),x104133)))+P107(f866(f258(x104131,x104132,f866(f866(f7(x104131,f937(f936(x104131,x104132),a925),f937(x104132,a925)),f866(f866(f8(f937(x104132,f937(f937(f936(x104131,x104132),a925),a925)),f937(f937(f936(x104131,x104132),a925),f937(x104132,a925)),x104131),f7(x104132,f937(f936(x104131,x104132),a925),a925)),f866(f866(f8(f937(x104132,f936(x104131,x104132)),f937(x104132,f937(f937(f936(x104131,x104132),a925),a925)),x104131),f866(f8(f936(x104131,x104132),f937(f937(f936(x104131,x104132),a925),a925),x104132),f336(f936(x104131,x104132)))),f260(x104131,x104132)))),x104133)),x104134))
% 157.60/157.52 [10414]~P107(f866(f866(f336(x104141),x104144),f866(f272(x104141,x104142),x104143)))+P107(f866(f257(x104141,x104142,f866(f866(f7(x104141,f937(f936(x104141,x104142),a925),f937(x104142,a925)),f866(f866(f8(f937(x104142,f937(f937(f936(x104141,x104142),a925),a925)),f937(f937(f936(x104141,x104142),a925),f937(x104142,a925)),x104141),f7(x104142,f937(f936(x104141,x104142),a925),a925)),f866(f866(f8(f937(x104142,f936(x104141,x104142)),f937(x104142,f937(f937(f936(x104141,x104142),a925),a925)),x104141),f866(f8(f936(x104141,x104142),f937(f937(f936(x104141,x104142),a925),a925),x104142),f336(f936(x104141,x104142)))),f260(x104141,x104142)))),x104143)),x104144))
% 157.60/157.52 [10428]P107(f866(f866(f336(x104281),x104282),f866(f292(x104283,x104281),x104284)))+~P107(f866(f258(x104283,x104281,f866(f866(f7(x104283,f937(f936(x104283,x104281),a925),f937(x104281,a925)),f866(f866(f8(f937(x104281,f937(f937(f936(x104283,x104281),a925),a925)),f937(f937(f936(x104283,x104281),a925),f937(x104281,a925)),x104283),f7(x104281,f937(f936(x104283,x104281),a925),a925)),f866(f866(f8(f937(x104281,f936(x104283,x104281)),f937(x104281,f937(f937(f936(x104283,x104281),a925),a925)),x104283),f866(f8(f936(x104283,x104281),f937(f937(f936(x104283,x104281),a925),a925),x104281),f336(f936(x104283,x104281)))),f260(x104283,x104281)))),x104284)),x104282))
% 157.60/157.52 [10429]P107(f866(f866(f336(x104291),x104292),f866(f272(x104291,x104293),x104294)))+~P107(f866(f257(x104291,x104293,f866(f866(f7(x104291,f937(f936(x104291,x104293),a925),f937(x104293,a925)),f866(f866(f8(f937(x104293,f937(f937(f936(x104291,x104293),a925),a925)),f937(f937(f936(x104291,x104293),a925),f937(x104293,a925)),x104291),f7(x104293,f937(f936(x104291,x104293),a925),a925)),f866(f866(f8(f937(x104293,f936(x104291,x104293)),f937(x104293,f937(f937(f936(x104291,x104293),a925),a925)),x104291),f866(f8(f936(x104291,x104293),f937(f937(f936(x104291,x104293),a925),a925),x104293),f336(f936(x104291,x104293)))),f260(x104291,x104293)))),x104294)),x104292))
% 157.60/157.52 [10095]P107(f866(f167(x100951,x100952),x100953))+~P107(f866(f167(x100951,f866(f866(f18(x100951,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100951),a333),x100954)),x100952)),x100953))
% 157.60/157.52 [10096]P107(f866(f167(x100961,x100962),x100963))+~P107(f866(f167(x100961,f866(f866(f18(x100961,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100961),a333),x100962)),x100964)),x100963))
% 157.60/157.52 [10173]~P114(x101731)+E(f866(f866(f87(x101731),f866(f866(f86(x101731),f84(x101731)),f84(x101731))),f866(f866(f6(a930,x101731),f866(f866(f8(x101731,x101731,a930),f866(f86(x101731),x101732)),f866(f866(f7(a930,x101731,x101731),f866(f866(f8(x101731,f937(x101731,x101731),a930),f87(x101731)),f107(x101731))),x101733))),f866(f290(a930),x101734))),f866(f866(f87(x101731),f866(f107(x101731),x101734)),f866(f866(f86(x101731),x101732),f866(f866(f86(x101731),x101732),f866(f866(f87(x101731),f866(f107(x101731),f866(f866(f23(a930),x101734),f84(a930)))),x101733)))))
% 157.60/157.52 [10312]P107(f866(x103121,f528(x103122,x103123,x103124,x103121)))+P37(x103122,f866(f270(f936(x103122,x103122)),f866(f265(x103122,x103122,a925),f866(f866(f8(f937(x103122,a925),f937(x103122,a925),x103122),f866(f18(x103122,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103122),a333),x103121))),f866(f866(f7(x103122,f937(x103122,x103122),f937(x103122,a925)),f866(f866(f8(f937(x103122,a925),f937(f937(x103122,x103122),f937(x103122,a925)),x103122),f8(x103122,a925,x103122)),a332)),x103123)))))
% 157.60/157.52 [10326]~P107(f866(f866(f244(a930),f866(x103264,f866(x103263,f528(x103261,x103263,x103264,x103262)))),f866(x103264,f528(x103261,x103263,x103264,x103262))))+P37(x103261,f866(f270(f936(x103261,x103261)),f866(f265(x103261,x103261,a925),f866(f866(f8(f937(x103261,a925),f937(x103261,a925),x103261),f866(f18(x103261,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103261),a333),x103262))),f866(f866(f7(x103261,f937(x103261,x103261),f937(x103261,a925)),f866(f866(f8(f937(x103261,a925),f937(f937(x103261,x103261),f937(x103261,a925)),x103261),f8(x103261,a925,x103261)),a332)),x103263)))))
% 157.60/157.52 [10398]~P5(x103981)+E(f43(x103981,f866(f270(x103981),f866(f866(f8(f937(f937(x103982,x103981),a925),a925,x103981),f93(f937(x103982,x103981))),f866(f866(f8(f937(f937(x103982,x103981),a925),f937(f937(x103982,x103981),a925),x103981),f866(f18(f937(x103982,x103981),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x103982,x103981)),a333),f866(f866(f7(f937(x103982,x103981),f937(f937(x103982,x103981),a925),a925),f336(f937(x103982,x103981))),x103983)))),f866(f866(f7(x103981,f937(f937(x103982,x103981),x103981),f937(f937(x103982,x103981),a925)),f866(f866(f8(f937(x103981,a925),f937(f937(f937(x103982,x103981),x103981),f937(f937(x103982,x103981),a925)),x103981),f8(x103981,a925,f937(x103982,x103981))),a332)),f866(f866(f7(f937(x103982,x103981),x103982,x103981),f5(f937(x103982,x103981))),x103984)))))),f866(f43(f937(x103982,x103981),x103983),x103984))
% 157.60/157.52 [10399]~P5(x103991)+E(f43(x103991,f866(f270(x103991),f866(f866(f8(f937(f937(x103992,x103991),a925),a925,x103991),f93(f937(x103992,x103991))),f866(f866(f8(f937(f937(x103992,x103991),a925),f937(f937(x103992,x103991),a925),x103991),f866(f18(f937(x103992,x103991),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x103992,x103991)),a333),f866(f866(f7(f937(x103992,x103991),f937(f937(x103992,x103991),a925),a925),f336(f937(x103992,x103991))),x103993)))),f866(f866(f7(x103991,f937(f937(x103992,x103991),x103991),f937(f937(x103992,x103991),a925)),f866(f866(f8(f937(x103991,a925),f937(f937(f937(x103992,x103991),x103991),f937(f937(x103992,x103991),a925)),x103991),f8(x103991,a925,f937(x103992,x103991))),a332)),f866(f866(f7(f937(x103992,x103991),x103992,x103991),f5(f937(x103992,x103991))),x103994)))))),f866(f43(f937(x103992,x103991),x103993),x103994))
% 157.60/157.52 [10400]~P5(x104001)+E(f42(x104001,f866(f270(x104001),f866(f866(f8(f937(f937(x104002,x104001),a925),a925,x104001),f93(f937(x104002,x104001))),f866(f866(f8(f937(f937(x104002,x104001),a925),f937(f937(x104002,x104001),a925),x104001),f866(f18(f937(x104002,x104001),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x104002,x104001)),a333),f866(f866(f7(f937(x104002,x104001),f937(f937(x104002,x104001),a925),a925),f336(f937(x104002,x104001))),x104003)))),f866(f866(f7(x104001,f937(f937(x104002,x104001),x104001),f937(f937(x104002,x104001),a925)),f866(f866(f8(f937(x104001,a925),f937(f937(f937(x104002,x104001),x104001),f937(f937(x104002,x104001),a925)),x104001),f8(x104001,a925,f937(x104002,x104001))),a332)),f866(f866(f7(f937(x104002,x104001),x104002,x104001),f5(f937(x104002,x104001))),x104004)))))),f866(f42(f937(x104002,x104001),x104003),x104004))
% 157.60/157.52 [10401]~P5(x104011)+E(f42(x104011,f866(f270(x104011),f866(f866(f8(f937(f937(x104012,x104011),a925),a925,x104011),f93(f937(x104012,x104011))),f866(f866(f8(f937(f937(x104012,x104011),a925),f937(f937(x104012,x104011),a925),x104011),f866(f18(f937(x104012,x104011),a925,a925),f866(f866(f8(a925,f937(a925,a925),f937(x104012,x104011)),a333),f866(f866(f7(f937(x104012,x104011),f937(f937(x104012,x104011),a925),a925),f336(f937(x104012,x104011))),x104013)))),f866(f866(f7(x104011,f937(f937(x104012,x104011),x104011),f937(f937(x104012,x104011),a925)),f866(f866(f8(f937(x104011,a925),f937(f937(f937(x104012,x104011),x104011),f937(f937(x104012,x104011),a925)),x104011),f8(x104011,a925,f937(x104012,x104011))),a332)),f866(f866(f7(f937(x104012,x104011),x104012,x104011),f5(f937(x104012,x104011))),x104014)))))),f866(f42(f937(x104012,x104011),x104013),x104014))
% 157.60/157.52 [10454]~P107(f866(f866(f336(f936(x104541,x104541)),f866(f866(f260(x104541,x104541),x104543),x104544)),f866(f866(f117(f937(f936(x104541,x104541),a925)),x104542),f314(x104541,f195(f937(f936(x104541,x104541),a925))))))+P107(f866(f866(f866(f866(f117(f937(x104541,f937(x104541,a925))),f866(f866(f7(x104541,f937(f936(x104541,x104541),a925),f937(x104541,a925)),f866(f866(f8(f937(x104541,f937(f937(f936(x104541,x104541),a925),a925)),f937(f937(f936(x104541,x104541),a925),f937(x104541,a925)),x104541),f7(x104541,f937(f936(x104541,x104541),a925),a925)),f866(f866(f8(f937(x104541,f936(x104541,x104541)),f937(x104541,f937(f937(f936(x104541,x104541),a925),a925)),x104541),f866(f8(f936(x104541,x104541),f937(f937(f936(x104541,x104541),a925),a925),x104541),f336(f936(x104541,x104541)))),f260(x104541,x104541)))),x104542)),a332),x104543),x104544))
% 157.60/157.52 [10464]P107(f866(f866(f336(f936(x104641,x104641)),f866(f866(f260(x104641,x104641),x104642),x104643)),f866(f866(f117(f937(f936(x104641,x104641),a925)),x104644),f314(x104641,f195(f937(f936(x104641,x104641),a925))))))+~P107(f866(f866(f866(f866(f117(f937(x104641,f937(x104641,a925))),f866(f866(f7(x104641,f937(f936(x104641,x104641),a925),f937(x104641,a925)),f866(f866(f8(f937(x104641,f937(f937(f936(x104641,x104641),a925),a925)),f937(f937(f936(x104641,x104641),a925),f937(x104641,a925)),x104641),f7(x104641,f937(f936(x104641,x104641),a925),a925)),f866(f866(f8(f937(x104641,f936(x104641,x104641)),f937(x104641,f937(f937(f936(x104641,x104641),a925),a925)),x104641),f866(f8(f936(x104641,x104641),f937(f937(f936(x104641,x104641),a925),a925),x104641),f336(f936(x104641,x104641)))),f260(x104641,x104641)))),x104644)),a332),x104642),x104643))
% 157.60/157.52 [10409]E(f866(f866(f158(f931(x104091)),f866(f866(f158(x104091),x104092),f866(f149(f931(x104091),f931(x104091),f141(x104091),f120(x104091)),f866(f866(f161(f931(x104091),f931(x104091)),f163(f931(x104091),x104091,f120(x104091),f866(f866(f8(f931(x104091),f937(f931(x104091),f931(x104091)),x104091),f16(f931(x104091),f931(x104091))),f866(f866(f7(x104091,f931(x104091),f931(x104091)),f158(x104091)),f120(x104091))))),x104093)))),f186(x104091,f866(f866(f158(f931(x104091)),x104094),f866(f149(f931(f931(x104091)),f931(f931(x104091)),f141(f931(x104091)),f120(f931(x104091))),f866(f866(f161(f931(x104091),f931(f931(x104091))),f163(f931(f931(x104091)),x104091,f120(f931(x104091)),f866(f16(f937(f931(x104091),f931(f931(x104091))),x104091),f866(f866(f7(f931(x104091),f931(f931(x104091)),f931(f931(x104091))),f158(f931(x104091))),f120(f931(x104091)))))),x104093))))),f186(x104091,f866(f866(f158(f931(x104091)),f866(f866(f158(x104091),x104092),x104094)),x104093)))+~P107(f866(f322(f931(f931(x104091)),f187(x104091)),f866(f866(f158(f931(x104091)),f866(f866(f158(x104091),x104092),x104094)),x104093)))
% 157.60/157.52 [10453]~P107(f866(f66(x104532),f866(f270(x104532),x104534)))+P107(f866(f66(x104531),f866(f270(x104531),f866(f866(f8(f937(x104532,a925),a925,x104531),f93(x104532)),f866(f866(f7(x104531,f937(x104532,a925),f937(x104532,a925)),f866(f866(f8(f937(x104532,f937(a925,a925)),f937(f937(x104532,a925),f937(x104532,a925)),x104531),f18(x104532,a925,a925)),f866(f866(f8(f937(x104532,a925),f937(x104532,f937(a925,a925)),x104531),f866(f8(a925,f937(a925,a925),x104532),a333)),f866(f866(f7(x104531,f937(x104532,x104531),f937(x104532,a925)),f866(f866(f8(f937(x104531,a925),f937(f937(x104532,x104531),f937(x104532,a925)),x104531),f8(x104531,a925,x104532)),a332)),x104533)))),x104534)))))
% 157.60/157.52 [8987]P25(x89871,x89872,x89873,x89874)+~P26(x89871,x89872,x89873,x89874,x89875)
% 157.60/157.52 [5511]E(x55111,x55112)+~E(f176(x55113,x55111,x55114),f176(x55113,x55112,x55115))
% 157.60/157.52 [5512]E(x55121,x55122)+~E(f133(x55123,x55124,x55121),f133(x55123,x55125,x55122))
% 157.60/157.52 [5513]E(x55131,x55132)+~E(f133(x55133,x55131,x55134),f133(x55133,x55132,x55135))
% 157.60/157.52 [8322]~E(f866(x83223,x83224),x83225)+E(f80(x83221,x83222,x83223,x83224,x83225),x83223)
% 157.60/157.52 [8845]~E(f80(x88454,x88455,x88451,x88452,x88453),x88451)+E(f866(x88451,x88452),x88453)
% 157.60/157.52 [9463]~P26(x94632,x94631,x94634,x94633,x94635)+P26(x94631,x94632,f83(x94632,x94631,x94633,x94634),x94635,x94633)
% 157.60/157.52 [9464]~P26(x94642,x94641,x94644,x94643,x94645)+P26(x94641,x94642,f97(x94642,x94641,x94643,x94644),x94645,x94643)
% 157.60/157.52 [6319]P107(f866(f258(x63191,x63192,x63193),x63194))+~P107(f866(f866(x63193,x63195),x63194))
% 157.60/157.52 [6321]P107(f866(f257(x63211,x63212,x63213),x63214))+~P107(f866(f866(x63213,x63214),x63215))
% 157.60/157.52 [6798]~E(x67985,f2(a106))+E(f866(f207(x67981,x67982,x67983,x67984),x67985),f122(x67982))
% 157.60/157.52 [6799]~E(x67995,f2(a106))+E(f866(f205(x67991,x67992,x67993,x67994),x67995),f131(x67992))
% 157.60/157.52 [6933]~E(x69333,f2(a106))+E(f866(f281(x69331,x69332,x69333,x69334),x69335),f866(f260(x69331,x69332),x69335))
% 157.60/157.52 [7974]~P20(x79744,x79741,x79742,x79745)+E(f866(f78(x79741,x79741,x79741,f866(x79742,x79743)),f866(x79742,x79743)),f866(x79742,x79743))
% 157.60/157.52 [8359]~P16(x83595,x83591,x83592)+E(f866(f78(x83591,x83591,x83591,f866(x83592,x83593)),f866(x83592,x83594)),f866(f78(x83591,x83591,x83591,f866(x83592,x83594)),f866(x83592,x83593)))
% 157.60/157.52 [8679]P107(f866(f866(f336(f936(x86791,x86791)),f866(f866(f260(x86791,x86791),x86792),x86793)),f328(x86791,x86794,x86795)))+~P107(f866(f866(f244(a930),f866(x86794,x86792)),f866(x86794,x86793)))
% 157.60/157.52 [8773]~P107(f866(f866(f336(x87734),x87733),f306(x87734,x87731,x87732,x87735)))+P107(f866(f866(x87731,x87732),x87733))
% 157.60/157.52 [8774]~P107(f866(f866(f336(x87744),x87743),f303(x87744,x87741,x87742,x87745)))+P107(f866(f866(x87741,x87742),x87743))
% 157.60/157.52 [8775]~P107(f866(f866(f336(x87754),x87752),f306(x87754,x87751,x87755,x87753)))+P107(f866(f866(x87751,x87752),x87753))
% 157.60/157.52 [8776]~P107(f866(f866(f336(x87764),x87762),f303(x87764,x87761,x87765,x87763)))+P107(f866(f866(x87761,x87762),x87763))
% 157.60/157.52 [8857]~P26(x88571,x88573,x88575,x88572,x88574)+E(f866(f40(x88571),x88572),f866(f40(x88573),x88574))
% 157.60/157.52 [8905]~P26(x89051,x89052,x89053,x89054,x89055)+E(f866(f317(x89051,x89052,x89053),x89054),x89055)
% 157.60/157.52 [8925]~P58(x89252,x89251,x89255,x89253,x89254)+E(f866(f317(x89251,x89252,x89253),x89254),f250(f937(x89252,a925)))
% 157.60/157.52 [9376]~P34(x93761,x93762,x93763,x93764,x93765)+P34(x93761,x93762,x93763,f866(f175(x93761),x93764),f866(f175(x93762),x93765))
% 157.60/157.52 [9378]~P34(x93781,x93782,x93783,f866(f175(x93781),x93784),x93785)+P34(x93781,x93782,x93783,x93784,f866(f175(x93782),x93785))
% 157.60/157.52 [9379]~P34(x93791,x93792,x93793,x93794,f866(f175(x93792),x93795))+P34(x93791,x93792,x93793,f866(f175(x93791),x93794),x93795)
% 157.60/157.52 [9385]P34(x93851,x93852,x93853,x93854,x93855)+~P34(x93851,x93852,x93853,f866(f175(x93851),x93854),f866(f175(x93852),x93855))
% 157.60/157.52 [9781]P107(f866(f866(f336(f936(f931(x97811),f931(x97811))),f866(f866(f260(f931(x97811),f931(x97811)),f866(f866(f158(x97811),x97812),x97813)),f866(f866(f158(x97811),x97812),x97814))),f164(x97811,x97815)))+~P107(f866(f866(f336(f936(f931(x97811),f931(x97811))),f866(f866(f260(f931(x97811),f931(x97811)),x97813),x97814)),f164(x97811,x97815)))
% 157.60/157.52 [9782]P107(f866(f866(f336(f936(f931(x97821),f931(x97821))),f866(f866(f260(f931(x97821),f931(x97821)),f866(f866(f141(x97821),x97822),x97823)),f866(f866(f141(x97821),x97822),x97824))),f154(x97821,x97825)))+~P107(f866(f866(f336(f936(f931(x97821),f931(x97821))),f866(f866(f260(f931(x97821),f931(x97821)),x97823),x97824)),f154(x97821,x97825)))
% 157.60/157.52 [9979]E(f866(f866(f158(x99791),f659(x99792,x99793,x99794,x99795,x99791)),f660(x99792,x99793,x99794,x99795,x99791)),x99795)+~P107(f866(f866(f336(f936(f931(x99791),f931(x99791))),f866(f866(f260(f931(x99791),f931(x99791)),x99795),f866(f866(f158(x99791),x99794),x99793))),f165(x99791,x99792)))
% 157.60/157.52 [10001]E(f866(f866(f158(x100011),f661(x100012,x100013,x100014,x100015,x100011)),f663(x100012,x100013,x100014,x100015,x100011)),x100013)+~P107(f866(f866(f336(f936(f931(x100011),f931(x100011))),f866(f866(f260(f931(x100011),f931(x100011)),f866(f866(f158(x100011),x100015),x100014)),x100013)),f165(x100011,x100012)))
% 157.60/157.52 [10146]~P107(f866(f866(f336(f936(f931(x101461),f931(x101461))),f866(f866(f260(f931(x101461),f931(x101461)),f866(f866(f158(x101461),x101465),x101462)),x101464)),f165(x101461,x101463)))+P107(f866(f866(f336(f936(f931(x101461),f931(x101461))),f866(f866(f260(f931(x101461),f931(x101461)),x101462),f663(x101463,x101464,x101462,x101465,x101461))),f165(x101461,x101463)))
% 157.60/157.52 [10217]~P107(f866(f866(f336(f936(f931(x102171),f931(x102171))),f866(f866(f260(f931(x102171),f931(x102171)),x102175),f866(f866(f158(x102171),x102174),x102173))),f165(x102171,x102172)))+P107(f866(f866(f336(f936(f931(x102171),f931(x102171))),f866(f866(f260(f931(x102171),f931(x102171)),f660(x102172,x102173,x102174,x102175,x102171)),x102173)),f165(x102171,x102172)))
% 157.60/157.52 [10402]P107(f866(f866(f336(f936(x104021,x104021)),f866(f866(f260(x104021,x104021),f866(x104022,f866(f866(f86(a930),x104023),x104024))),f866(x104022,x104023))),f314(x104021,x104025)))+~P107(f866(f866(f336(f936(x104021,x104021)),f866(f866(f260(x104021,x104021),f866(x104022,f866(a119,f582(x104024,x104023,x104025,x104022,x104021)))),f866(x104022,f582(x104024,x104023,x104025,x104022,x104021)))),f314(x104021,x104025)))
% 157.60/157.52 [5479]E(x54791,x54792)+~E(f866(f866(f158(x54793),x54794),x54791),f866(f866(f158(x54793),x54795),x54792))
% 157.60/157.52 [5480]E(x54801,x54802)+~E(f866(f866(f158(x54803),x54801),x54804),f866(f866(f158(x54803),x54802),x54805))
% 157.60/157.52 [5528]P107(f866(x55281,x55282))+~E(f866(f143(x55283,x55281),x55284),f866(f866(f158(x55283),x55282),x55285))
% 157.60/157.52 [5529]P107(f866(x55291,x55292))+~E(f866(f866(f158(x55293),x55292),x55294),f866(f143(x55293,x55291),x55295))
% 157.60/157.52 [5685]~E(f866(f866(f145(x56851),x56853),x56852),f866(f866(f158(x56851),x56854),x56855))+E(f866(f866(f171(x56851),x56852),x56853),x56854)
% 157.60/157.52 [5827]~P14(x58274,x58275,x58271)+E(f866(f866(x58271,x58272),f866(f866(x58271,x58272),x58273)),f866(f866(x58271,x58272),x58273))
% 157.60/157.52 [6377]~E(x63774,f2(a106))+E(f866(f866(f124(x63771,x63772,x63773),x63774),x63775),f866(f866(f260(f931(x63772),x63771),f120(x63772)),x63775))
% 157.60/157.52 [6446]~P110(x64462)+~E(f866(f866(f155(x64461,x64462,x64463),x64464),x64465),f120(x64461))
% 157.60/157.52 [6837]E(x68371,x68372)+~E(f866(f866(f141(x68373),x68374),f866(f866(f158(x68373),x68371),f120(x68373))),f866(f866(f141(x68373),x68375),f866(f866(f158(x68373),x68372),f120(x68373))))
% 157.60/157.52 [6838]E(x68381,x68382)+~E(f866(f866(f141(x68383),x68381),f866(f866(f158(x68383),x68384),f120(x68383))),f866(f866(f141(x68383),x68382),f866(f866(f158(x68383),x68385),f120(x68383))))
% 157.60/157.52 [7149]E(f866(f866(f316(x71491),f866(x71492,x71493)),f866(f317(x71494,x71491,x71492),x71495)),f866(f317(x71494,x71491,x71492),x71495))+~P107(f866(f866(f336(x71494),x71493),x71495))
% 157.60/157.52 [7155]~P107(f866(x71554,f866(x71553,x71555)))+P107(f866(f866(f318(x71551,x71552,x71553),x71554),x71555))
% 157.60/157.52 [7158]~P107(f866(f866(x71583,x71585),x71584))+P107(f866(f866(f251(x71581,x71582,x71583),x71584),x71585))
% 157.60/157.52 [7251]~E(f866(f317(x72511,x72512,x72513),x72514),x72515)+E(f866(f317(f937(x72511,a925),f937(x72512,a925),f317(x72511,x72512,x72513)),f866(f315(x72511),x72514)),f866(f315(x72512),x72515))
% 157.60/157.52 [7278]E(f866(f279(x72781,x72782,x72783,x72784),x72785),f866(x72784,x72785))+~P107(f866(f866(f336(x72781),x72785),x72783))
% 157.60/157.52 [7590]P25(x75901,x75902,x75903,x75904)+~P25(x75901,x75902,x75903,f866(f866(f316(x75901),x75905),x75904))
% 157.60/157.52 [7654]P107(f866(x76541,x76542))+~P107(f866(f866(f99(x76543,x76544,x76541),x76545),x76542))
% 157.60/157.52 [7695]~P107(f866(f866(f336(x76954),x76953),x76955))+P107(f866(f866(f336(x76951),f866(x76952,x76953)),f866(f317(x76954,x76951,x76952),x76955)))
% 157.60/157.52 [7716]~P110(x77162)+E(f157(x77161,x77162,x77163,f866(f143(x77161,x77164),x77165)),f866(f143(x77161,x77164),f157(x77161,x77162,x77163,x77165)))
% 157.60/157.52 [7746]P107(f866(x77461,f866(x77462,x77463)))+~P107(f866(f866(f318(x77464,x77465,x77462),x77461),x77463))
% 157.60/157.52 [7749]P107(f866(f866(x77491,x77492),x77493))+~P107(f866(f866(f251(x77494,x77495,x77491),x77493),x77492))
% 157.60/157.52 [7750]P107(f866(f866(x77501,x77502),x77503))+~P107(f866(f866(f99(x77504,x77501,x77505),x77502),x77503))
% 157.60/157.52 [7812]~P107(f866(f866(f336(x78123),f866(x78124,x78122)),x78125))+P107(f866(f866(f336(x78121),x78122),f866(f318(x78121,x78123,x78124),x78125)))
% 157.60/157.52 [8204]~P107(f866(f866(f336(x82045),x82043),f866(f318(x82045,x82041,x82042),x82044)))+P107(f866(f866(f336(x82041),f866(x82042,x82043)),x82044))
% 157.60/157.52 [8495]~P16(x84952,x84951,x84953)+E(f866(f149(x84951,x84952,f866(f7(x84952,x84951,x84951),x84953),x84954),f159(x84952,x84955)),f866(f866(f69(x84952,x84951,x84953),x84954),f866(f179(x84952),x84955)))
% 157.60/157.52 [8517]E(f866(x85171,f410(x85172,x85171,x85173,x85174)),x85174)+~P107(f866(f866(f336(x85175),x85174),f866(f317(x85173,x85175,x85171),x85172)))
% 157.60/157.52 [8518]E(f866(x85181,f418(x85182,x85181,x85183,x85184)),x85184)+~P107(f866(f866(f336(x85185),x85184),f866(f317(x85183,x85185,x85181),x85182)))
% 157.60/157.52 [8820]~E(x88202,f866(f866(f158(x88201),x88204),x88205))+P107(f866(f866(f336(f936(f931(x88201),f931(x88201))),f866(f866(f260(f931(x88201),f931(x88201)),f120(x88201)),x88202)),f154(x88201,x88203)))
% 157.60/157.52 [8866]E(f866(x88661,f866(f97(x88662,x88663,x88664,x88661),x88665)),x88665)+~P107(f866(f866(f336(x88663),x88665),f866(f317(x88662,x88663,x88661),x88664)))
% 157.60/157.52 [8869]P25(x88691,x88692,f97(x88692,x88691,x88693,x88694),x88695)+~P107(f866(f866(f243(f937(x88691,a925)),x88695),f866(f317(x88692,x88691,x88694),x88693)))
% 157.60/157.52 [8876]~P34(x88761,x88763,x88765,x88762,x88764)+E(f866(f196(f931(x88761)),x88762),f866(f196(f931(x88763)),x88764))
% 157.60/157.52 [8887]P107(f866(f866(f243(f937(x88871,a925)),f866(f866(f45(x88872,f937(x88871,a925)),x88873),x88874)),f866(x88874,x88875)))+~P107(f866(f866(f336(x88872),x88875),x88873))
% 157.60/157.52 [8941]~P58(x89411,x89412,x89413,x89415,x89414)+E(f866(f317(x89411,x89412,x89413),f250(f937(x89411,a925))),x89414)
% 157.60/157.52 [9170]E(f866(f143(x91701,x91702),f753(x91703,x91704,x91705,x91702,x91701)),x91703)+~E(f866(f143(x91701,x91702),x91705),f866(f866(f158(x91701),x91704),x91703))
% 157.60/157.52 [9171]E(f866(f143(x91711,x91712),f750(x91713,x91712,x91714,x91715,x91711)),x91714)+~E(f866(f866(f158(x91711),x91715),x91714),f866(f143(x91711,x91712),x91713))
% 157.60/157.52 [9264]E(f866(f196(f931(x92641)),x92642),x92643)+~P107(f866(f866(f336(f936(f931(x92641),f931(x92641))),f866(f866(f260(f931(x92641),f931(x92641)),x92644),x92642)),f866(f150(x92641,x92645),x92643)))
% 157.60/157.52 [9265]E(f866(f196(f931(x92651)),x92652),x92653)+~P107(f866(f866(f336(f936(f931(x92651),f931(x92651))),f866(f866(f260(f931(x92651),f931(x92651)),x92652),x92654)),f866(f150(x92651,x92655),x92653)))
% 157.60/157.52 [9334]P107(f866(f866(f336(x93341),f410(x93342,x93343,x93341,x93344)),x93342))+~P107(f866(f866(f336(x93345),x93344),f866(f317(x93341,x93345,x93343),x93342)))
% 157.60/157.52 [9335]P107(f866(f866(f336(x93351),f418(x93352,x93353,x93351,x93354)),x93352))+~P107(f866(f866(f336(x93355),x93354),f866(f317(x93351,x93355,x93353),x93352)))
% 157.60/157.52 [9491]E(f866(f317(x94911,x94912,x94913),f351(x94914,x94913,x94911,x94915,x94912)),x94915)+~P107(f866(f866(f243(f937(x94912,a925)),x94915),f866(f317(x94911,x94912,x94913),x94914)))
% 157.60/157.52 [9799]P107(f866(f866(f336(f936(f931(x97991),f931(x97991))),f866(f866(f260(f931(x97991),f931(x97991)),f866(f866(f158(x97991),x97992),x97993)),f866(f866(f158(x97991),x97992),x97994))),f314(f931(x97991),f164(x97991,x97995))))+~P107(f866(f866(f336(f936(f931(x97991),f931(x97991))),f866(f866(f260(f931(x97991),f931(x97991)),x97993),x97994)),f314(f931(x97991),f164(x97991,x97995))))
% 157.60/157.52 [9830]~E(f866(x98303,f702(x98305,x98304,x98303,x98302,x98301)),f866(x98305,f702(x98305,x98304,x98303,x98302,x98301)))+E(f866(f866(f161(x98301,x98302),x98303),x98304),f866(f866(f161(x98301,x98302),x98305),x98304))
% 157.60/157.52 [9906]~E(f866(f143(x99061,x99065),x99064),f866(f866(f158(x99061),x99063),x99062))+E(f866(f866(f141(x99061),f754(x99062,x99063,x99064,x99065,x99061)),f866(f866(f158(x99061),x99063),f753(x99062,x99063,x99064,x99065,x99061))),x99064)
% 157.60/157.52 [9907]~E(f866(f866(f158(x99071),x99075),x99074),f866(f143(x99071,x99073),x99072))+E(f866(f866(f141(x99071),f751(x99072,x99073,x99074,x99075,x99071)),f866(f866(f158(x99071),x99075),f750(x99072,x99073,x99074,x99075,x99071))),x99072)
% 157.60/157.52 [9911]E(f866(f866(f161(x99111,x99112),x99113),x99114),f866(f866(f161(x99111,x99112),x99115),x99114))+P107(f866(f866(f336(x99111),f702(x99113,x99114,x99115,x99112,x99111)),f866(f179(x99111),x99114)))
% 157.60/157.52 [9941]~P107(f866(f866(f336(x99415),x99414),f866(f293(x99411,x99415,x99413),x99412)))+P107(f866(f866(f336(x99411),f491(x99412,x99413,x99411,x99414,x99415)),x99412))
% 157.60/157.52 [9942]~P107(f866(f866(f336(x99425),x99424),f866(f293(x99421,x99425,x99423),x99422)))+P107(f866(f866(f336(x99421),f513(x99422,x99423,x99421,x99424,x99425)),x99422))
% 157.60/157.52 [9973]~P107(f866(f866(f243(f937(x99735,a925)),x99734),f866(f317(x99731,x99735,x99733),x99732)))+P107(f866(f866(f243(f937(x99731,a925)),f351(x99732,x99733,x99731,x99734,x99735)),x99732))
% 157.60/157.52 [10404]E(x104041,f2(a106))+E(f232(f936(f931(x104042),x104043),f936(x104042,x104043),f866(f866(f260(f931(x104042),x104043),f120(x104042)),x104044),f866(f265(x104042,x104043,f936(f931(x104042),x104043)),f866(f866(f7(x104042,f937(x104043,f936(f931(x104042),x104043)),f937(x104043,f936(f931(x104042),x104043))),f866(f866(f8(f937(f936(f931(x104042),x104043),f936(f931(x104042),x104043)),f937(f937(x104043,f936(f931(x104042),x104043)),f937(x104043,f936(f931(x104042),x104043))),x104042),f8(f936(f931(x104042),x104043),f936(f931(x104042),x104043),x104043)),f866(f866(f8(f937(f931(x104042),f937(x104043,f936(f931(x104042),x104043))),f937(f936(f931(x104042),x104043),f936(f931(x104042),x104043)),x104042),f265(f931(x104042),x104043,f936(f931(x104042),x104043))),f866(f866(f8(f937(f931(x104042),f931(x104042)),f937(f931(x104042),f937(x104043,f936(f931(x104042),x104043))),x104042),f866(f8(f931(x104042),f937(x104043,f936(f931(x104042),x104043)),f931(x104042)),f260(f931(x104042),x104043))),f158(x104042))))),f866(f124(x104043,x104042,x104045),f866(f866(f23(a106),x104041),f84(a106))))),f866(x104045,x104044)),f866(f866(f124(x104043,x104042,x104045),x104041),x104044))
% 157.60/157.52 [6258]E(x62581,x62582)+~E(f866(f264(x62583,x62584),f866(f866(f260(x62583,x62584),x62585),x62581)),x62582)
% 157.60/157.52 [6259]E(x62591,x62592)+~E(f866(f259(x62593,x62594),f866(f866(f260(x62593,x62594),x62591),x62595)),x62592)
% 157.60/157.52 [6520]~E(x65203,f866(f866(f141(x65201),x65204),f866(f866(f158(x65201),x65202),x65205)))+P107(f866(f866(f336(x65201),x65202),f866(f179(x65201),x65203)))
% 157.60/157.52 [6920]E(f866(f317(x69201,x69202,f866(f16(x69202,x69201),x69203)),x69204),f866(f866(f316(x69202),x69203),f195(f937(x69202,a925))))+~P107(f866(f866(f336(x69201),x69205),x69204))
% 157.60/157.52 [6991]E(f866(f866(f117(f937(x69911,a925)),f866(f179(x69911),x69912)),f866(f179(x69911),x69913)),f866(f179(x69911),x69914))+~E(f173(x69911,x69915,x69914),f866(f866(f260(f931(x69911),f931(x69911)),x69912),x69913))
% 157.60/157.52 [7090]~P110(x70902)+E(f866(f196(f931(x70901)),f866(f866(f155(x70901,x70902,x70903),x70904),x70905)),f866(a119,f866(f196(f931(x70901)),x70905)))
% 157.60/157.52 [7102]~P110(x71022)+E(f866(f179(x71021),f866(f866(f155(x71021,x71022,x71023),x71024),x71025)),f866(f866(f316(x71021),x71024),f866(f179(x71021),x71025)))
% 157.60/157.52 [7372]~P114(x73721)+E(f866(f866(f87(x73721),f866(f866(f87(x73721),x73722),x73723)),f866(f866(f87(x73721),x73724),x73725)),f866(f866(f87(x73721),f866(f866(f87(x73721),x73722),x73724)),f866(f866(f87(x73721),x73723),x73725)))
% 157.60/157.52 [7373]~P114(x73731)+E(f866(f866(f86(x73731),f866(f866(f86(x73731),x73732),x73733)),f866(f866(f86(x73731),x73734),x73735)),f866(f866(f86(x73731),f866(f866(f86(x73731),x73732),x73734)),f866(f866(f86(x73731),x73733),x73735)))
% 157.60/157.52 [7374]~P65(x73741)+E(f866(f866(f297(x73741),f866(f866(f87(x73741),x73742),x73743)),f866(f866(f87(x73741),x73744),x73745)),f866(f866(f87(x73741),f866(f866(f297(x73741),x73742),x73744)),f866(f866(f297(x73741),x73743),x73745)))
% 157.60/157.52 [7388]~P110(x73881)+E(f313(x73881,f866(f866(f242(x73881),x73882),x73883),f866(f866(f241(x73881),x73884),x73885)),f866(f866(f108(f937(x73881,a925)),f313(x73881,x73882,x73884)),f313(x73881,x73883,x73885)))
% 157.60/157.52 [7389]~P110(x73891)+E(f310(x73891,f866(f866(f242(x73891),x73892),x73893),f866(f866(f241(x73891),x73894),x73895)),f866(f866(f108(f937(x73891,a925)),f310(x73891,x73892,x73894)),f310(x73891,x73893,x73895)))
% 157.60/157.52 [7390]~P110(x73901)+E(f312(x73901,f866(f866(f242(x73901),x73902),x73903),f866(f866(f241(x73901),x73904),x73905)),f866(f866(f108(f937(x73901,a925)),f312(x73901,x73902,x73904)),f312(x73901,x73903,x73905)))
% 157.60/157.52 [7391]~P110(x73911)+E(f866(f866(f108(f937(x73911,a925)),f866(f309(x73911,x73912),x73913)),f866(f309(x73911,x73914),x73915)),f866(f309(x73911,f866(f866(f242(x73911),x73912),x73914)),f866(f866(f241(x73911),x73913),x73915)))
% 157.60/157.52 [7510]~P107(f866(x75101,f490(x75103,x75102,x75101)))+P107(f866(x75101,f866(f866(f260(x75102,x75103),x75104),x75105)))
% 157.60/157.52 [7620]~E(x76202,f866(x76204,x76205))+P107(f866(f866(f336(x76201),x76202),f866(f317(x76203,x76201,x76204),f250(f937(x76203,a925)))))
% 157.60/157.52 [7692]~P14(x76923,x76922,x76924)+P14(x76921,x76922,f866(f866(f8(x76923,f937(x76922,x76922),x76921),x76924),x76925))
% 157.60/157.52 [7693]~P16(x76933,x76932,x76934)+P16(x76931,x76932,f866(f866(f8(x76933,f937(x76932,x76932),x76931),x76934),x76935))
% 157.60/157.52 [7829]~P25(x78291,x78292,x78293,x78294)+P25(x78291,x78292,x78293,f866(f866(f23(f937(x78291,a925)),x78294),x78295))
% 157.60/157.52 [7983]~P107(f866(f866(x79833,x79834),x79835))+P107(f866(f866(f265(x79831,x79832,a925),x79833),f866(f866(f260(x79831,x79832),x79834),x79835)))
% 157.60/157.52 [8094]~P107(f866(x80942,x80944))+~E(f866(f866(f145(x80941),f866(f196(f931(x80941)),f184(x80941,x80942,x80943))),x80943),f866(f866(f158(x80941),x80944),x80945))
% 157.60/157.52 [8114]P25(x81141,x81142,x81143,x81144)+~P25(x81141,x81142,x81143,f866(f866(f117(f937(x81141,a925)),x81145),x81144))
% 157.60/157.52 [8115]P25(x81151,x81152,x81153,x81154)+~P25(x81151,x81152,x81153,f866(f866(f117(f937(x81151,a925)),x81154),x81155))
% 157.60/157.52 [8161]~P110(x81612)+E(f866(f866(f155(x81611,x81612,x81613),x81614),f157(x81611,x81612,x81613,x81615)),f157(x81611,x81612,x81613,f866(f866(f158(x81611),x81614),x81615)))
% 157.60/157.52 [8472]~P14(x84722,x84721,x84723)+E(f866(f149(x84721,x84722,f866(f7(x84722,x84721,x84721),x84723),x84724),x84725),f866(f866(f69(x84722,x84721,x84723),x84724),f866(f179(x84722),x84725)))
% 157.60/157.52 [8500]~E(f866(f866(f145(x85001),f866(f196(f931(x85001)),f184(x85001,x85002,x85003))),x85003),f866(f866(f158(x85001),x85004),x85005))+E(f866(f866(f141(x85001),f184(x85001,x85002,x85003)),f866(f866(f158(x85001),x85004),x85005)),x85003)
% 157.60/157.52 [8528]P107(f866(f866(x85281,x85282),x85283))+~P107(f866(f866(f265(x85284,x85285,a925),x85281),f866(f866(f260(x85284,x85285),x85282),x85283)))
% 157.60/157.52 [9004]P107(f866(f866(f243(f937(x90041,a925)),f866(f317(x90042,x90041,x90043),x90044)),f866(f317(x90042,x90041,x90043),x90045)))+~P107(f866(f866(f243(f937(x90042,a925)),x90044),x90045))
% 157.60/157.52 [9005]P107(f866(f866(f243(f937(x90051,a925)),f866(f318(x90051,x90052,x90053),x90054)),f866(f318(x90051,x90052,x90053),x90055)))+~P107(f866(f866(f243(f937(x90052,a925)),x90054),x90055))
% 157.60/157.52 [9084]E(x90841,f2(a106))+E(f866(f866(f267(x90842,x90843,x90842,f936(x90843,x90842)),f866(x90844,x90845)),f281(x90843,x90842,f866(f866(f23(a106),x90841),f84(a106)),x90844)),f866(f281(x90843,x90842,x90841,x90844),x90845))
% 157.60/157.52 [9197]P107(f866(f866(f263(x91971,x91972,a925,x91973),x91974),x91975))+~P107(f866(x91973,f866(f866(f260(x91971,x91972),x91974),x91975)))
% 157.60/157.52 [9469]~P107(f866(f866(f263(x94692,x94693,a925,x94691),x94694),x94695))+P107(f866(x94691,f866(f866(f260(x94692,x94693),x94694),x94695)))
% 157.60/157.52 [9651]~P107(f866(f866(f336(x96512),x96515),f866(f317(x96511,x96512,x96514),x96513)))+P107(f866(f866(f336(x96511),f866(f97(x96511,x96512,x96513,x96514),x96515)),x96513))
% 157.60/157.52 [9741]~P107(f866(f66(x97413),f866(f317(x97412,x97413,x97415),f250(f937(x97412,a925)))))+P107(f866(f66(x97411),f866(f317(x97412,x97411,f866(f866(f8(x97413,x97411,x97412),x97414),x97415)),f250(f937(x97412,a925)))))
% 157.60/157.52 [9766]P107(f866(f866(f243(f937(f937(x97661,a925),a925)),f866(f317(f937(x97662,a925),f937(x97661,a925),f317(x97662,x97661,x97663)),f866(f315(x97662),x97664))),f866(f315(x97661),x97665)))+~P107(f866(f866(f243(f937(x97661,a925)),f866(f317(x97662,x97661,x97663),x97664)),x97665))
% 157.60/157.52 [9838]E(x98381,x98382)+~P107(f866(f71(x98383,x98384,x98385,x98381,f195(f937(x98383,a925))),x98382))
% 157.60/157.52 [9854]E(f866(f866(f260(x98541,x98542),f539(x98543,x98544,x98545,x98542,x98541)),f541(x98543,x98544,x98545,x98542,x98541)),x98545)+~P107(f866(f866(f336(f936(x98541,x98542)),x98545),f866(f866(f262(x98541,x98542),x98544),x98543)))
% 157.60/157.52 [9947]P107(f866(f866(f336(x99471),f539(x99472,x99473,x99474,x99475,x99471)),x99473))+~P107(f866(f866(f336(f936(x99471,x99475)),x99474),f866(f866(f262(x99471,x99475),x99473),x99472)))
% 157.60/157.52 [9957]P107(f866(f866(f336(x99571),f429(x99572,x99573,x99574,x99575,x99571)),x99575))+P107(f866(f866(f243(f937(x99574,a925)),f866(f317(x99571,x99574,x99573),x99575)),x99572))
% 157.60/157.52 [10104]P107(f866(f866(f336(x101041),f541(x101042,x101043,x101044,x101041,x101045)),f866(x101042,f539(x101042,x101043,x101044,x101041,x101045))))+~P107(f866(f866(f336(f936(x101045,x101041)),x101044),f866(f866(f262(x101045,x101041),x101043),x101042)))
% 157.60/157.52 [10124]P107(f866(f866(f336(f936(x101241,x101241)),f866(f866(f260(x101241,x101241),x101242),f608(x101243,x101244,x101245,x101242,x101241))),x101243))+~P107(f866(f866(f336(f936(x101241,x101241)),f866(f866(f260(x101241,x101241),x101242),x101245)),f866(f866(f190(f936(x101241,x101241),a925),f866(a119,x101244)),x101243)))
% 157.60/157.52 [10125]P107(f866(f866(f336(f936(x101251,x101251)),f866(f866(f260(x101251,x101251),x101252),f609(x101253,x101254,x101255,x101252,x101251))),x101253))+~P107(f866(f866(f336(f936(x101251,x101251)),f866(f866(f260(x101251,x101251),x101252),x101255)),f866(f866(f190(f936(x101251,x101251),a925),f866(a119,x101254)),x101253)))
% 157.60/157.52 [10131]~P24(x101311,x101312,f866(f866(f316(f929(x101311)),f98(x101311,f99(x101311,x101313,x101314),x101315,x101313)),f195(f937(f929(x101311),a925))))+P24(x101311,x101312,f866(f866(f316(f929(x101311)),f98(x101311,x101313,f30(x101314,x101315),f99(x101311,x101313,f866(f78(a925,a925,a926,a329),x101314)))),f195(f937(f929(x101311),a925))))
% 157.60/157.52 [10143]~P107(f866(f866(f336(f936(f931(x101431),f931(x101431))),f866(f866(f260(f931(x101431),f931(x101431)),f866(f866(f158(x101431),x101432),x101435)),x101434)),f165(x101431,x101433)))+P107(f866(f866(f336(f936(x101431,x101431)),f866(f866(f260(x101431,x101431),x101432),f661(x101433,x101434,x101435,x101432,x101431))),x101433))
% 157.60/157.52 [10165]~P107(f866(f866(f336(x101651),f866(x101653,f429(x101655,x101653,x101651,x101654,x101652))),x101655))+P107(f866(f866(f243(f937(x101651,a925)),f866(f317(x101652,x101651,x101653),x101654)),x101655))
% 157.60/157.52 [6598]P107(f866(x65982,x65984))+E(f184(x65981,x65982,f866(f866(f141(x65981),x65983),f866(f866(f158(x65981),x65984),x65985))),f184(x65981,x65982,x65983))
% 157.60/157.52 [6649]~P2(x66492)+E(f866(f866(f866(f23(f937(x66491,x66492)),x66493),x66494),x66495),f866(f866(f23(x66492),f866(x66493,x66495)),f866(x66494,x66495)))
% 157.60/157.52 [6651]~P83(x66512)+E(f866(f866(f866(f117(f937(x66511,x66512)),x66513),x66514),x66515),f866(f866(f117(x66512),f866(x66513,x66515)),f866(x66514,x66515)))
% 157.60/157.52 [6653]~P83(x66532)+E(f866(f866(f866(f108(f937(x66531,x66532)),x66533),x66534),x66535),f866(f866(f108(x66532),f866(x66533,x66535)),f866(x66534,x66535)))
% 157.60/157.52 [6670]E(x66701,x66702)+E(f866(f866(f171(x66703),f866(f866(f166(x66703,x66704),x66701),x66705)),x66702),f866(f866(f171(x66703),x66704),x66702))
% 157.60/157.52 [6939]~E(x69394,f195(f937(x69393,a925)))+E(f866(f866(f23(f937(x69391,a925)),x69392),f866(f866(f44(x69393,f937(x69391,a925)),x69394),x69395)),x69392)
% 157.60/157.52 [6940]~E(x69404,f195(f937(x69403,a925)))+E(f866(f866(f117(f937(x69401,a925)),x69402),f866(f866(f44(x69403,f937(x69401,a925)),x69404),x69405)),x69402)
% 157.60/157.52 [6941]~E(x69414,f195(f937(x69413,a925)))+E(f866(f866(f108(f937(x69411,a925)),x69412),f866(f866(f45(x69413,f937(x69411,a925)),x69414),x69415)),x69412)
% 157.60/157.52 [6957]~E(x69574,f195(f937(x69573,a925)))+E(f866(f866(f316(x69571),x69572),f866(f866(f44(x69573,f937(x69571,a925)),x69574),x69575)),f866(f866(f316(x69571),x69572),f195(f937(x69571,a925))))
% 157.60/157.52 [7738]E(f866(f866(f171(x77381),f866(f866(f161(x77382,x77381),x77383),x77384)),x77385),f866(x77383,f866(f866(f171(x77382),x77384),x77385)))+~P107(f866(f866(f244(a930),x77385),f866(f196(f931(x77382)),x77384)))
% 157.60/157.52 [7800]E(f866(f866(f117(f937(x78001,a925)),f866(x78002,x78003)),f866(f866(f44(x78004,f937(x78001,a925)),x78005),x78002)),f866(f866(f44(x78004,f937(x78001,a925)),x78005),x78002))+~P107(f866(f866(f336(x78004),x78003),x78005))
% 157.76/157.52 [7801]E(f866(f866(f108(f937(x78011,a925)),f866(x78012,x78013)),f866(f866(f45(x78014,f937(x78011,a925)),x78015),x78012)),f866(f866(f45(x78014,f937(x78011,a925)),x78015),x78012))+~P107(f866(f866(f336(x78014),x78013),x78015))
% 157.76/157.52 [8395]~E(x83953,f195(f937(x83951,a925)))+E(f866(f866(f44(x83951,f937(x83952,a925)),x83953),f866(f866(f8(f937(x83952,a925),f937(x83952,a925),x83951),f866(f316(x83952),x83954)),x83955)),f195(f937(x83952,a925)))
% 157.76/157.52 [8400]~P107(f866(f866(f336(x84004),x84003),x84005))+P107(f866(f866(f243(f937(x84001,a925)),f866(x84002,x84003)),f866(f866(f44(x84004,f937(x84001,a925)),x84005),x84002)))
% 157.76/157.52 [8527]~E(f866(x85274,x85272),x85275)+P107(f866(f866(f336(x85271),x85272),f866(f318(x85271,x85273,x85274),f866(f866(f316(x85273),x85275),f195(f937(x85273,a925))))))
% 157.76/157.52 [8574]~P55(x85741,x85742,f866(f294(x85742,x85741),x85743))+E(f866(f866(f108(f937(x85741,a925)),f866(f293(x85742,x85741,x85743),x85744)),f866(f293(x85742,x85741,x85743),x85745)),f866(f293(x85742,x85741,x85743),f866(f866(f108(f937(x85742,a925)),x85744),x85745)))
% 157.76/157.52 [8648]E(x86481,f2(a106))+E(f866(f125(x86482,x86483,f866(x86484,f866(f866(f23(a106),x86481),f84(a106)))),f866(f866(f7(x86482,a106,f932(x86483)),x86485),x86481)),f866(f207(x86482,x86483,x86484,x86485),x86481))
% 157.76/157.52 [8686]E(x86861,f195(f937(x86862,a925)))+E(f866(f866(f44(x86862,f937(x86863,a925)),x86861),f866(f866(f8(f937(x86863,a925),f937(x86863,a925),x86862),f866(f316(x86863),x86864)),x86865)),f866(f866(f316(x86863),x86864),f866(f866(f44(x86862,f937(x86863,a925)),x86861),x86865)))
% 157.76/157.52 [8738]~P25(x87382,x87381,x87383,f250(f937(x87382,a925)))+E(f866(f866(f23(f937(x87381,a925)),f866(f317(x87382,x87381,x87383),x87384)),f866(f317(x87382,x87381,x87383),x87385)),f866(f317(x87382,x87381,x87383),f866(f866(f23(f937(x87382,a925)),x87384),x87385)))
% 157.76/157.52 [8739]~P25(x87392,x87391,x87393,f250(f937(x87392,a925)))+E(f866(f866(f108(f937(x87391,a925)),f866(f317(x87392,x87391,x87393),x87394)),f866(f317(x87392,x87391,x87393),x87395)),f866(f317(x87392,x87391,x87393),f866(f866(f108(f937(x87392,a925)),x87394),x87395)))
% 157.76/157.52 [8807]~P107(f866(f866(f72(x88071,x88072,x88075),x88073),x88074))+P107(f866(f866(f336(f936(x88071,x88072)),f866(f866(f260(x88071,x88072),x88073),x88074)),x88075))
% 157.76/157.52 [8839]P107(f866(f866(f336(x88391),x88392),f866(f292(x88393,x88391),x88394)))+~P107(f866(f866(f336(f936(x88393,x88391)),f866(f866(f260(x88393,x88391),x88395),x88392)),x88394))
% 157.76/157.52 [8841]P107(f866(f866(f336(x88411),x88412),f866(f272(x88411,x88413),x88414)))+~P107(f866(f866(f336(f936(x88411,x88413)),f866(f866(f260(x88411,x88413),x88412),x88415)),x88414))
% 157.76/157.52 [8988]P107(f866(f866(f72(x89881,x89882,x89883),x89884),x89885))+~P107(f866(f866(f336(f936(x89881,x89882)),f866(f866(f260(x89881,x89882),x89884),x89885)),x89883))
% 157.76/157.52 [9027]E(f866(x90271,x90272),x90273)+~P107(f866(f866(f336(x90274),x90272),f866(f318(x90274,x90275,x90271),f866(f866(f316(x90275),x90273),f195(f937(x90275,a925))))))
% 157.76/157.52 [9261]P107(f866(f866(f336(f936(x92611,x92612)),f866(f866(f260(x92611,x92612),x92613),x92614)),f866(f294(x92612,x92611),x92615)))+~P107(f866(f866(f336(f936(x92612,x92611)),f866(f866(f260(x92612,x92611),x92614),x92613)),x92615))
% 157.76/157.52 [9279]~P107(f866(f866(x92791,x92795),x92794))+P107(f866(f866(x92791,f866(f264(x92792,x92793),f866(f866(f260(x92792,x92793),x92794),x92795))),f866(f259(x92792,x92793),f866(f866(f260(x92792,x92793),x92794),x92795))))
% 157.76/157.52 [9309]~P107(f866(f866(f336(f936(x93092,x93091)),f866(f866(f260(x93092,x93091),x93094),x93093)),f866(f294(x93091,x93092),x93095)))+P107(f866(f866(f336(f936(x93091,x93092)),f866(f866(f260(x93091,x93092),x93093),x93094)),x93095))
% 157.76/157.52 [9342]~P107(f866(f866(f336(f936(x93423,x93421)),f866(f866(f260(x93423,x93421),x93425),x93422)),x93424))+P107(f866(f866(f336(x93421),x93422),f866(f293(x93423,x93421,x93424),f866(f866(f316(x93423),x93425),f195(f937(x93423,a925))))))
% 157.76/157.52 [9389]P107(f866(f866(f336(f936(x93891,x93892)),f866(f866(f260(x93891,x93892),x93893),x93894)),x93895))+~P107(f866(f866(f336(x93892),x93894),f866(f293(x93891,x93892,x93895),f866(f866(f316(x93891),x93893),f195(f937(x93891,a925))))))
% 157.76/157.52 [9476]~P72(x94761)+E(f866(f866(f6(a930,x94761),x94762),f310(a930,f866(f866(f86(a930),x94763),x94764),f866(f866(f86(a930),x94765),x94764))),f866(f866(f6(a930,x94761),f866(f866(f8(a930,x94761,a930),x94762),f866(f866(f7(a930,a930,a930),f86(a930)),x94764))),f310(a930,x94763,x94765)))
% 157.76/157.52 [9496]~P72(x94961)+E(f866(f866(f6(a930,x94961),x94962),f866(f309(a930,f866(f866(f86(a930),x94963),x94964)),f866(f866(f86(a930),x94965),x94964))),f866(f866(f6(a930,x94961),f866(f866(f8(a930,x94961,a930),x94962),f866(f866(f7(a930,a930,a930),f86(a930)),x94964))),f866(f309(a930,x94963),x94965)))
% 157.76/157.52 [9553]~P25(x95531,x95532,x95533,f250(f937(x95531,a925)))+E(f866(f866(f161(x95531,x95532),x95533),f866(f143(x95531,f866(f866(f8(a925,a925,x95531),a329),f866(a332,x95534))),x95535)),f866(f143(x95532,f866(f866(f8(a925,a925,x95532),a329),f866(a332,f866(x95533,x95534)))),f866(f866(f161(x95531,x95532),x95533),x95535)))
% 157.76/157.52 [9571]~P25(x95711,x95712,x95713,f866(f866(f316(x95711),x95714),f866(f179(x95711),x95715)))+E(f866(f866(f161(x95711,x95712),x95713),f866(f143(x95711,f866(f866(f8(a925,a925,x95711),a329),f866(a332,x95714))),x95715)),f866(f143(x95712,f866(f866(f8(a925,a925,x95712),a329),f866(a332,f866(x95713,x95714)))),f866(f866(f161(x95711,x95712),x95713),x95715)))
% 157.76/157.52 [9729]P107(f866(f866(f336(f936(f931(x97291),f931(x97291))),f866(f866(f260(f931(x97291),f931(x97291)),f866(f866(f158(x97291),x97292),x97293)),f866(f866(f158(x97291),x97294),x97293))),f164(x97291,x97295)))+~P107(f866(f866(f336(f936(x97291,x97291)),f866(f866(f260(x97291,x97291),x97292),x97294)),x97295))
% 157.76/157.52 [9849]E(f866(f866(f316(x98491),f549(x98492,x98493,x98494,x98495,x98491)),f561(x98492,x98493,x98494,x98495,x98491)),f866(f866(f316(x98491),x98494),x98493))+~P107(f866(f67(x98491,x98495,f866(f866(f316(x98491),x98494),x98493)),x98492))
% 157.76/157.52 [9850]E(f866(f866(f316(x98501),f576(x98502,x98503,x98504,x98505,x98501)),f583(x98502,x98503,x98504,x98505,x98501)),f866(f866(f316(x98501),x98504),x98503))+~P107(f866(f67(x98501,x98505,f866(f866(f316(x98501),x98504),x98503)),x98502))
% 157.76/157.52 [9932]P107(f866(f866(f336(x99321),f618(x99322,x99323,x99324,x99325,x99321)),x99324))+P107(f866(f866(f866(f45(x99321,f937(x99325,a925)),x99324),x99323),x99322))
% 157.76/157.52 [9937]P107(f866(f866(f336(x99371),f616(x99372,x99373,x99371,x99374,x99375)),x99373))+P107(f866(f866(f336(x99375),x99374),f866(f866(f45(x99371,f937(x99375,a925)),x99373),x99372)))
% 157.76/157.52 [9945]P107(f866(f866(f336(x99451),f619(x99452,x99453,x99451,x99454,x99455)),x99453))+P107(f866(f866(f243(f937(x99455,a925)),x99454),f866(f866(f45(x99451,f937(x99455,a925)),x99453),x99452)))
% 157.76/157.52 [9946]P107(f866(f866(f336(x99461),f842(x99462,x99463,x99464,x99465,x99461)),x99465))+P107(f866(f866(f243(f937(x99464,a925)),x99463),f866(f866(f45(x99461,f937(x99464,a925)),x99465),x99462)))
% 157.76/157.52 [9948]P107(f866(f866(x99481,f784(x99482,x99481,x99483,x99484,x99485)),x99482))+~P107(f866(f866(f866(f44(x99485,f937(x99484,a925)),x99483),x99481),x99482))
% 157.76/157.52 [9952]P107(f866(f866(f336(x99521),f784(x99522,x99523,x99524,x99525,x99521)),x99524))+~P107(f866(f866(f866(f44(x99521,f937(x99525,a925)),x99524),x99523),x99522))
% 157.76/157.52 [9953]P53(x99534,f866(f866(f45(x99531,f937(x99534,a925)),x99535),x99533),f866(f866(f45(x99531,f937(f936(x99534,x99534),a925)),x99535),x99532))+P107(f866(f866(f336(x99531),f785(x99532,x99533,x99534,x99535,x99531)),x99535))
% 157.76/157.52 [9954]P53(x99544,f866(f866(f44(x99541,f937(x99544,a925)),x99545),x99543),f866(f866(f44(x99541,f937(f936(x99544,x99544),a925)),x99545),x99542))+P107(f866(f866(f336(x99541),f834(x99542,x99543,x99544,x99545,x99541)),x99545))
% 157.76/157.52 [9965]P107(f866(f866(f336(x99651),f882(x99652,x99653,x99651,x99654,x99655)),x99653))+~P107(f866(f866(f336(x99655),x99654),f866(f866(f44(x99651,f937(x99655,a925)),x99653),x99652)))
% 157.76/157.52 [9971]P107(f866(f866(f336(x99711),x99712),f866(x99713,f882(x99713,x99714,x99715,x99712,x99711))))+~P107(f866(f866(f336(x99711),x99712),f866(f866(f44(x99715,f937(x99711,a925)),x99714),x99713)))
% 157.76/157.52 [10053]~P107(f866(f866(x100534,f618(x100535,x100534,x100533,x100532,x100531)),x100535))+P107(f866(f866(f866(f45(x100531,f937(x100532,a925)),x100533),x100534),x100535))
% 157.76/157.52 [10056]~P107(f866(f866(f336(x100561),x100562),f866(x100565,f616(x100565,x100564,x100563,x100562,x100561))))+P107(f866(f866(f336(x100561),x100562),f866(f866(f45(x100563,f937(x100561,a925)),x100564),x100565)))
% 157.76/157.52 [10060]~P53(x100601,f866(x100604,f834(x100605,x100604,x100601,x100603,x100602)),f866(x100605,f834(x100605,x100604,x100601,x100603,x100602)))+P53(x100601,f866(f866(f44(x100602,f937(x100601,a925)),x100603),x100604),f866(f866(f44(x100602,f937(f936(x100601,x100601),a925)),x100603),x100605))
% 157.76/157.52 [10061]~P53(x100611,f866(x100614,f785(x100615,x100614,x100611,x100613,x100612)),f866(x100615,f785(x100615,x100614,x100611,x100613,x100612)))+P53(x100611,f866(f866(f45(x100612,f937(x100611,a925)),x100613),x100614),f866(f866(f45(x100612,f937(f936(x100611,x100611),a925)),x100613),x100615))
% 157.76/157.52 [10062]~P107(f866(f866(f243(f937(x100621,a925)),x100622),f866(x100625,f619(x100625,x100624,x100623,x100622,x100621))))+P107(f866(f866(f243(f937(x100621,a925)),x100622),f866(f866(f45(x100623,f937(x100621,a925)),x100624),x100625)))
% 157.76/157.52 [10063]~P107(f866(f866(f243(f937(x100631,a925)),x100632),f866(x100635,f842(x100635,x100632,x100631,x100634,x100633))))+P107(f866(f866(f243(f937(x100631,a925)),x100632),f866(f866(f45(x100633,f937(x100631,a925)),x100634),x100635)))
% 157.76/157.52 [10128]~P107(f866(f866(f336(x101281),f549(x101285,x101284,x101283,x101282,x101281)),f561(x101285,x101284,x101283,x101282,x101281)))+~P107(f866(f67(x101281,x101282,f866(f866(f316(x101281),x101283),x101284)),x101285))
% 157.76/157.52 [10129]~P107(f866(f866(f336(x101291),f576(x101295,x101294,x101293,x101292,x101291)),f583(x101295,x101294,x101293,x101292,x101291)))+~P107(f866(f67(x101291,x101292,f866(f866(f316(x101291),x101293),x101294)),x101295))
% 157.76/157.52 [10130]~P107(f866(f866(f336(f936(x101301,x101301)),f866(f866(f260(x101301,x101301),x101302),x101305)),f866(f866(f190(f936(x101301,x101301),a925),f866(a119,x101304)),x101303)))+P107(f866(f866(f336(f936(x101301,x101301)),f866(f866(f260(x101301,x101301),x101302),f610(x101303,x101304,x101305,x101302,x101301))),f866(f866(f190(f936(x101301,x101301),a925),x101304),x101303)))
% 157.76/157.52 [10137]P107(f866(f71(x101371,x101371,x101372,f549(x101373,x101374,x101375,x101372,x101371),f561(x101373,x101374,x101375,x101372,x101371)),x101373))+~P107(f866(f67(x101371,x101372,f866(f866(f316(x101371),x101375),x101374)),x101373))
% 157.76/157.52 [10138]P107(f866(f71(x101381,x101381,x101382,f576(x101383,x101384,x101385,x101382,x101381),f583(x101383,x101384,x101385,x101382,x101381)),x101383))+~P107(f866(f67(x101381,x101382,f866(f866(f316(x101381),x101385),x101384)),x101383))
% 157.76/157.52 [10148]~P110(x101481)+P13(x101481,f866(f866(f161(x101482,x101481),x101483),f866(f143(x101482,f866(f866(f7(x101482,x101481,a925),f866(f866(f8(x101481,f937(x101481,a925),x101482),a332),x101483)),f866(x101484,x101485))),x101485)))
% 157.76/157.52 [10189]~P107(f866(f866(f336(x101892),x101895),f866(f293(x101891,x101892,x101894),x101893)))+P107(f866(f866(f336(f936(x101891,x101892)),f866(f866(f260(x101891,x101892),f491(x101893,x101894,x101891,x101895,x101892)),x101895)),x101894))
% 157.76/157.52 [10190]~P107(f866(f866(f336(x101902),x101905),f866(f293(x101901,x101902,x101904),x101903)))+P107(f866(f866(f336(f936(x101901,x101902)),f866(f866(f260(x101901,x101902),f513(x101903,x101904,x101901,x101905,x101902)),x101905)),x101904))
% 157.76/157.52 [10210]~P107(f866(f866(f336(f936(x102101,x102101)),f866(f866(f260(x102101,x102101),x102105),x102104)),f866(f866(f190(f936(x102101,x102101),a925),f866(a119,x102103)),x102102)))+P107(f866(f866(f336(f936(x102101,x102101)),f866(f866(f260(x102101,x102101),f610(x102102,x102103,x102104,x102105,x102101)),x102104)),x102102))
% 157.76/157.52 [10213]~P107(f866(f866(f336(f936(x102131,x102131)),f866(f866(f260(x102131,x102131),x102135),x102134)),f866(f866(f190(f936(x102131,x102131),a925),f866(a119,x102133)),x102132)))+P107(f866(f866(f336(f936(x102131,x102131)),f866(f866(f260(x102131,x102131),f608(x102132,x102133,x102134,x102135,x102131)),x102134)),f866(f866(f190(f936(x102131,x102131),a925),x102133),x102132)))
% 157.76/157.52 [10214]~P107(f866(f866(f336(f936(x102141,x102141)),f866(f866(f260(x102141,x102141),x102145),x102144)),f866(f866(f190(f936(x102141,x102141),a925),f866(a119,x102143)),x102142)))+P107(f866(f866(f336(f936(x102141,x102141)),f866(f866(f260(x102141,x102141),f609(x102142,x102143,x102144,x102145,x102141)),x102144)),f866(f866(f190(f936(x102141,x102141),a925),x102143),x102142)))
% 157.76/157.52 [10215]~P107(f866(f866(f336(f936(f931(x102151),f931(x102151))),f866(f866(f260(f931(x102151),f931(x102151)),x102155),f866(f866(f158(x102151),x102154),x102153))),f165(x102151,x102152)))+P107(f866(f866(f336(f936(x102151,x102151)),f866(f866(f260(x102151,x102151),f659(x102152,x102153,x102154,x102155,x102151)),x102154)),x102152))
% 157.76/157.52 [7821]~E(x78213,f195(f937(x78212,a925)))+E(f866(f866(f117(f937(x78211,a925)),f866(f866(f44(x78212,f937(x78211,a925)),x78213),x78214)),x78215),x78215)
% 157.76/157.52 [7822]~E(x78223,f195(f937(x78222,a925)))+E(f866(f866(f108(f937(x78221,a925)),f866(f866(f45(x78222,f937(x78221,a925)),x78223),x78224)),x78225),x78225)
% 157.76/157.52 [8243]~E(x82433,f195(f937(x82432,a925)))+E(f866(f866(f23(f937(x82431,a925)),f866(f866(f45(x82432,f937(x82431,a925)),x82433),x82434)),x82435),f866(f866(f23(f937(x82431,a925)),f250(f937(x82431,a925))),x82435))
% 157.76/157.52 [8369]E(f866(f866(f166(x83691,f866(f866(f141(x83691),x83692),x83693)),x83694),x83695),f866(f866(f141(x83691),f866(f866(f166(x83691,x83692),x83694),x83695)),x83693))+~P107(f866(f866(f244(a930),x83694),f866(f196(f931(x83691)),x83692)))
% 157.76/157.52 [8638]E(f866(f866(f171(x86381),f866(f866(f161(a930,x86381),x86382),f146(a930,f866(f309(a930,x86383),x86384)))),x86385),f866(x86382,f866(f866(f86(a930),x86383),x86385)))+~P107(f866(f866(f244(a930),x86385),f866(f866(f23(a930),x86384),x86383)))
% 157.76/157.52 [8652]E(x86521,f2(a106))+E(f129(x86522,x86523,f866(x86524,f866(f866(f23(a106),x86521),f84(a106))),f866(f866(f7(x86522,a106,f932(f934(x86523))),x86525),x86521)),f866(f205(x86522,x86523,x86524,x86525),x86521))
% 157.76/157.52 [8676]~E(x86763,f195(f937(x86761,a925)))+E(f866(f866(f44(x86761,f937(x86762,a925)),x86763),f866(f866(f8(f937(x86762,a925),f937(x86762,a925),x86761),f866(f117(f937(x86762,a925)),x86764)),x86765)),f195(f937(x86762,a925)))
% 157.76/157.52 [8677]~E(x86773,f195(f937(x86771,a925)))+E(f866(f866(f45(x86771,f937(x86772,a925)),x86773),f866(f866(f8(f937(x86772,a925),f937(x86772,a925),x86771),f866(f23(f937(x86772,a925)),x86774)),x86775)),f250(f937(x86772,a925)))
% 157.76/157.52 [8678]~E(x86783,f195(f937(x86781,a925)))+E(f866(f866(f45(x86781,f937(x86782,a925)),x86783),f866(f866(f8(f937(x86782,a925),f937(x86782,a925),x86781),f866(f108(f937(x86782,a925)),x86784)),x86785)),f250(f937(x86782,a925)))
% 157.76/157.52 [8680]~P147(x86802)+E(f866(f866(f6(x86801,x86802),f866(f866(f8(x86802,x86802,x86801),f866(f87(x86802),x86803)),x86804)),x86805),f866(f866(f87(x86802),x86803),f866(f866(f6(x86801,x86802),x86804),x86805)))
% 157.76/157.52 [8972]E(x89721,f195(f937(x89722,a925)))+E(f866(f866(f44(x89722,f937(x89723,a925)),x89721),f866(f866(f8(f937(x89723,a925),f937(x89723,a925),x89722),f866(f117(f937(x89723,a925)),x89724)),x89725)),f866(f866(f117(f937(x89723,a925)),x89724),f866(f866(f44(x89722,f937(x89723,a925)),x89721),x89725)))
% 157.76/157.52 [8973]E(x89731,f195(f937(x89732,a925)))+E(f866(f866(f45(x89732,f937(x89733,a925)),x89731),f866(f866(f8(f937(x89733,a925),f937(x89733,a925),x89732),f866(f23(f937(x89733,a925)),x89734)),x89735)),f866(f866(f23(f937(x89733,a925)),x89734),f866(f866(f44(x89732,f937(x89733,a925)),x89731),x89735)))
% 157.76/157.52 [8974]E(x89741,f195(f937(x89742,a925)))+E(f866(f866(f45(x89742,f937(x89743,a925)),x89741),f866(f866(f8(f937(x89743,a925),f937(x89743,a925),x89742),f866(f108(f937(x89743,a925)),x89744)),x89745)),f866(f866(f108(f937(x89743,a925)),x89744),f866(f866(f45(x89742,f937(x89743,a925)),x89741),x89745)))
% 157.76/157.52 [9179]~P107(f866(f866(f244(a930),f866(x91794,x91792)),f866(x91794,x91793)))+P107(f866(f866(f336(f936(x91791,x91791)),f866(f866(f260(x91791,x91791),x91792),x91793)),f160(x91791,f866(f866(f158(f937(x91791,a930)),x91794),x91795))))
% 157.76/157.52 [9442]~P25(x94422,x94421,x94423,f866(f866(f117(f937(x94422,a925)),x94424),x94425))+E(f866(f866(f108(f937(x94421,a925)),f866(f317(x94422,x94421,x94423),f866(f866(f23(f937(x94422,a925)),x94424),x94425))),f866(f317(x94422,x94421,x94423),f866(f866(f23(f937(x94422,a925)),x94425),x94424))),f195(f937(x94421,a925)))
% 157.76/157.52 [9695]~P25(x96953,x96951,x96955,f250(f937(x96953,a925)))+E(f866(f78(x96951,x96952,x96953,f866(f78(x96953,x96952,x96951,x96954),f97(x96953,x96951,f250(f937(x96953,a925)),x96955))),x96955),x96954)
% 157.76/157.52 [9725]~P107(f866(f866(f243(f937(x97253,a925)),f866(f293(x97251,x97253,x97254),x97252)),x97255))+P107(f866(f866(f243(f937(x97251,a925)),x97252),f866(f85(f937(x97251,a925)),f866(f293(x97253,x97251,f866(f294(x97251,x97253),x97254)),f866(f85(f937(x97253,a925)),x97255)))))
% 157.76/157.52 [9750]~P25(x97501,x97502,x97503,f866(f866(f316(x97501),x97504),x97505))+~P107(f866(f866(f336(x97502),f866(x97503,x97504)),f866(f317(x97501,x97502,x97503),f866(f866(f23(f937(x97501,a925)),x97505),f866(f866(f316(x97501),x97504),f195(f937(x97501,a925)))))))
% 157.76/157.52 [9803]P107(f866(f866(f243(f937(x98031,a925)),f866(f293(x98032,x98031,x98033),x98034)),x98035))+~P107(f866(f866(f243(f937(x98032,a925)),x98034),f866(f85(f937(x98032,a925)),f866(f293(x98031,x98032,f866(f294(x98032,x98031),x98033)),f866(f85(f937(x98031,a925)),x98035)))))
% 157.76/157.52 [9876]~P89(x98761)+P107(f866(f866(f243(x98761),f866(f81(x98761),f866(f866(f23(x98761),f866(f866(f86(x98761),x98762),x98763)),f866(f866(f86(x98761),x98764),x98765)))),f866(f866(f86(x98761),f866(f81(x98761),f866(f866(f23(x98761),x98762),x98764))),f866(f81(x98761),f866(f866(f23(x98761),x98763),x98765)))))
% 157.76/157.52 [9986]P107(f866(f866(f336(x99861),f889(x99862,x99863,x99864,x99861,x99865)),x99864))+P107(f866(f866(f243(f937(x99865,a925)),f866(f866(f44(x99861,f937(x99865,a925)),x99864),x99863)),x99862))
% 157.76/157.52 [10167]~P107(f866(f866(f243(f937(x101671,a925)),f866(x101674,f889(x101675,x101674,x101673,x101672,x101671))),x101675))+P107(f866(f866(f243(f937(x101671,a925)),f866(f866(f44(x101672,f937(x101671,a925)),x101673),x101674)),x101675))
% 157.76/157.52 [8786]E(f866(f866(f141(x87861),x87862),f866(f866(f166(x87861,x87863),f866(f866(f23(a930),x87864),f866(f196(f931(x87861)),x87862))),x87865)),f866(f866(f166(x87861,f866(f866(f141(x87861),x87862),x87863)),x87864),x87865))+P107(f866(f866(f244(a930),x87864),f866(f196(f931(x87861)),x87862)))
% 157.76/157.52 [8814]~P145(x88141)+E(f866(f866(f86(x88141),f866(f866(f87(x88141),x88142),x88143)),f866(f866(f86(x88141),f866(f866(f87(x88141),x88144),x88143)),x88145)),f866(f866(f86(x88141),f866(f866(f87(x88141),f866(f866(f86(x88141),x88142),x88144)),x88143)),x88145))
% 157.76/157.52 [9398]~P147(x93981)+E(f866(f172(x93981),f866(f866(f161(x93982,x93981),f866(f866(f8(x93981,x93981,x93982),f866(f87(x93981),x93983)),x93984)),x93985)),f866(f866(f87(x93981),x93983),f866(f172(x93981),f866(f866(f161(x93982,x93981),x93984),x93985))))
% 157.76/157.52 [9570]E(f866(f196(f931(x95701)),f866(f866(f182(x95701),f866(f866(f241(a930),f866(f196(f931(x95701)),x95702)),f866(f196(f931(x95703)),x95704))),x95702)),f866(f196(f931(x95703)),f866(f866(f182(x95703),f866(f866(f241(a930),f866(f196(f931(x95701)),x95702)),f866(f196(f931(x95703)),x95704))),x95704)))+P107(f866(x95705,f866(f866(f188(x95701,x95703),x95702),x95704)))
% 157.76/157.52 [9813]~P147(x98132)+E(f866(f866(f6(x98131,x98132),f866(f866(f7(x98131,x98132,x98132),f866(f866(f8(x98132,f937(x98132,x98132),x98131),f87(x98132)),x98133)),x98134)),x98135),f866(f866(f87(x98132),f866(f866(f6(x98131,x98132),x98133),x98135)),x98134))
% 157.76/157.52 [9814]~P66(x98142)+E(f866(f866(f6(x98141,x98142),f866(f866(f7(x98141,x98142,x98142),f866(f866(f8(x98142,f937(x98142,x98142),x98141),f297(x98142)),x98143)),x98144)),x98145),f866(f866(f297(x98142),f866(f866(f6(x98141,x98142),x98143),x98145)),x98144))
% 157.76/157.52 [9821]~P71(x98212)+E(f866(f866(f9(x98211,x98212),f866(f866(f18(x98211,x98212,x98212),f866(f866(f8(x98212,f937(x98212,x98212),x98211),f87(x98212)),x98213)),x98214)),x98215),f866(f866(f87(x98212),f866(f866(f9(x98211,x98212),x98213),x98215)),f866(f866(f9(x98211,x98212),x98214),x98215)))
% 157.76/157.52 [9822]~P3(x98222)+E(f866(f866(f6(x98221,x98222),f866(f866(f18(x98221,x98222,x98222),f866(f866(f8(x98222,f937(x98222,x98222),x98221),f23(x98222)),x98223)),x98224)),x98225),f866(f866(f23(x98222),f866(f866(f6(x98221,x98222),x98223),x98225)),f866(f866(f6(x98221,x98222),x98224),x98225)))
% 157.76/157.52 [9823]~P72(x98232)+E(f866(f866(f6(x98231,x98232),f866(f866(f18(x98231,x98232,x98232),f866(f866(f8(x98232,f937(x98232,x98232),x98231),f86(x98232)),x98233)),x98234)),x98235),f866(f866(f86(x98232),f866(f866(f6(x98231,x98232),x98233),x98235)),f866(f866(f6(x98231,x98232),x98234),x98235)))
% 157.76/157.52 [9861]~E(x98613,f195(f937(x98611,a925)))+E(f866(f866(f44(x98611,f937(x98612,a925)),x98613),f866(f866(f7(x98611,f937(x98612,a925),f937(x98612,a925)),f866(f866(f8(f937(x98612,a925),f937(f937(x98612,a925),f937(x98612,a925)),x98611),f117(f937(x98612,a925))),x98614)),x98615)),f195(f937(x98612,a925)))
% 157.76/157.52 [9862]~E(x98623,f195(f937(x98621,a925)))+E(f866(f866(f45(x98621,f937(x98622,a925)),x98623),f866(f866(f7(x98621,f937(x98622,a925),f937(x98622,a925)),f866(f866(f8(f937(x98622,a925),f937(f937(x98622,a925),f937(x98622,a925)),x98621),f23(f937(x98622,a925))),x98624)),x98625)),f250(f937(x98622,a925)))
% 157.76/157.52 [9863]~E(x98633,f195(f937(x98631,a925)))+E(f866(f866(f45(x98631,f937(x98632,a925)),x98633),f866(f866(f7(x98631,f937(x98632,a925),f937(x98632,a925)),f866(f866(f8(f937(x98632,a925),f937(f937(x98632,a925),f937(x98632,a925)),x98631),f108(f937(x98632,a925))),x98634)),x98635)),f250(f937(x98632,a925)))
% 157.76/157.52 [9884]E(x98841,f195(f937(x98842,a925)))+E(f866(f866(f44(x98842,f937(x98843,a925)),x98841),f866(f866(f7(x98842,f937(x98843,a925),f937(x98843,a925)),f866(f866(f8(f937(x98843,a925),f937(f937(x98843,a925),f937(x98843,a925)),x98842),f117(f937(x98843,a925))),x98844)),x98845)),f866(f866(f117(f937(x98843,a925)),f866(f866(f44(x98842,f937(x98843,a925)),x98841),x98844)),x98845))
% 157.76/157.52 [9885]E(x98851,f195(f937(x98852,a925)))+E(f866(f866(f45(x98852,f937(x98853,a925)),x98851),f866(f866(f7(x98852,f937(x98853,a925),f937(x98853,a925)),f866(f866(f8(f937(x98853,a925),f937(f937(x98853,a925),f937(x98853,a925)),x98852),f23(f937(x98853,a925))),x98854)),x98855)),f866(f866(f23(f937(x98853,a925)),f866(f866(f45(x98852,f937(x98853,a925)),x98851),x98854)),x98855))
% 157.76/157.52 [9886]E(x98861,f195(f937(x98862,a925)))+E(f866(f866(f45(x98862,f937(x98863,a925)),x98861),f866(f866(f7(x98862,f937(x98863,a925),f937(x98863,a925)),f866(f866(f8(f937(x98863,a925),f937(f937(x98863,a925),f937(x98863,a925)),x98862),f108(f937(x98863,a925))),x98864)),x98865)),f866(f866(f108(f937(x98863,a925)),f866(f866(f45(x98862,f937(x98863,a925)),x98861),x98864)),x98865))
% 157.76/157.52 [9447]~P107(f866(f866(f243(a930),x94471),x94474))+E(f866(f866(f23(a930),f866(f866(f86(a930),f866(f866(f87(a930),x94471),x94472)),x94473)),f866(f866(f86(a930),f866(f866(f87(a930),x94474),x94472)),x94475)),f866(f866(f23(a930),x94473),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x94474),x94471)),x94472)),x94475)))
% 157.76/157.52 [10036]~P147(x100361)+E(f866(f172(x100361),f866(f866(f161(x100362,x100361),f866(f866(f7(x100362,x100361,x100361),f866(f866(f8(x100361,f937(x100361,x100361),x100362),f87(x100361)),x100363)),x100364)),x100365)),f866(f866(f87(x100361),f866(f172(x100361),f866(f866(f161(x100362,x100361),x100363),x100365))),x100364))
% 157.76/157.52 [10042]~P3(x100421)+E(f866(f172(x100421),f866(f866(f161(x100422,x100421),f866(f866(f18(x100422,x100421,x100421),f866(f866(f8(x100421,f937(x100421,x100421),x100422),f23(x100421)),x100423)),x100424)),x100425)),f866(f866(f23(x100421),f866(f172(x100421),f866(f866(f161(x100422,x100421),x100423),x100425))),f866(f172(x100421),f866(f866(f161(x100422,x100421),x100424),x100425))))
% 157.76/157.52 [10043]~P72(x100431)+E(f866(f172(x100431),f866(f866(f161(x100432,x100431),f866(f866(f18(x100432,x100431,x100431),f866(f866(f8(x100431,f937(x100431,x100431),x100432),f86(x100431)),x100433)),x100434)),x100435)),f866(f866(f86(x100431),f866(f172(x100431),f866(f866(f161(x100432,x100431),x100433),x100435))),f866(f172(x100431),f866(f866(f161(x100432,x100431),x100434),x100435))))
% 157.76/157.52 [10181]P107(f866(x101811,f866(f866(f188(x101812,x101813),x101814),x101815)))+~P107(f866(x101811,f866(f866(f188(x101812,x101813),f866(f866(f182(x101812),f866(f866(f241(a930),f866(f196(f931(x101812)),x101814)),f866(f196(f931(x101813)),x101815))),x101814)),f866(f866(f182(x101813),f866(f866(f241(a930),f866(f196(f931(x101812)),x101814)),f866(f196(f931(x101813)),x101815))),x101815))))
% 157.76/157.52 [10440]~P107(f866(f866(f336(f936(x104402,x104401)),f866(f866(f260(x104402,x104401),x104404),x104405)),f866(f294(x104401,x104402),x104403)))+P107(f866(f866(f251(x104401,x104402,f866(f866(f7(x104401,f937(f936(x104401,x104402),a925),f937(x104402,a925)),f866(f866(f8(f937(x104402,f937(f937(f936(x104401,x104402),a925),a925)),f937(f937(f936(x104401,x104402),a925),f937(x104402,a925)),x104401),f7(x104402,f937(f936(x104401,x104402),a925),a925)),f866(f866(f8(f937(x104402,f936(x104401,x104402)),f937(x104402,f937(f937(f936(x104401,x104402),a925),a925)),x104401),f866(f8(f936(x104401,x104402),f937(f937(f936(x104401,x104402),a925),a925),x104402),f336(f936(x104401,x104402)))),f260(x104401,x104402)))),x104403)),x104404),x104405))
% 157.76/157.52 [10450]P107(f866(f866(f336(f936(x104501,x104502)),f866(f866(f260(x104501,x104502),x104503),x104504)),f866(f294(x104502,x104501),x104505)))+~P107(f866(f866(f251(x104502,x104501,f866(f866(f7(x104502,f937(f936(x104502,x104501),a925),f937(x104501,a925)),f866(f866(f8(f937(x104501,f937(f937(f936(x104502,x104501),a925),a925)),f937(f937(f936(x104502,x104501),a925),f937(x104501,a925)),x104502),f7(x104501,f937(f936(x104502,x104501),a925),a925)),f866(f866(f8(f937(x104501,f936(x104502,x104501)),f937(x104501,f937(f937(f936(x104502,x104501),a925),a925)),x104502),f866(f8(f936(x104502,x104501),f937(f937(f936(x104502,x104501),a925),a925),x104501),f336(f936(x104502,x104501)))),f260(x104502,x104501)))),x104505)),x104503),x104504))
% 157.76/157.52 [9694]~P107(f866(f866(f243(a930),x96944),x96941))+E(f866(f866(f23(a930),f866(f866(f86(a930),f866(f866(f87(a930),x96941),x96942)),x96943)),f866(f866(f86(a930),f866(f866(f87(a930),x96944),x96942)),x96945)),f866(f866(f23(a930),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x96941),x96944)),x96942)),x96943)),x96945))
% 157.76/157.52 [5505]E(x55051,x55052)+~E(f28(x55053,x55054,x55051),f28(x55055,x55056,x55052))
% 157.76/157.52 [5506]E(x55061,x55062)+~E(f28(x55063,x55061,x55064),f28(x55065,x55062,x55066))
% 157.76/157.52 [5507]E(x55071,x55072)+~E(f28(x55071,x55073,x55074),f28(x55072,x55075,x55076))
% 157.76/157.52 [5508]E(x55081,x55082)+~E(f27(x55083,x55084,x55081),f27(x55085,x55086,x55082))
% 157.76/157.52 [5509]E(x55091,x55092)+~E(f27(x55093,x55091,x55094),f27(x55095,x55092,x55096))
% 157.76/157.52 [5510]E(x55101,x55102)+~E(f27(x55101,x55103,x55104),f27(x55102,x55105,x55106))
% 157.76/157.52 [7521]E(x75211,x75212)+~E(f229(x75213,x75214,x75215,x75211),f229(x75213,x75214,x75216,x75212))
% 157.76/157.52 [7522]E(x75221,x75222)+~E(f229(x75223,x75224,x75221,x75225),f229(x75223,x75224,x75222,x75226))
% 157.76/157.52 [8623]~P19(x86235,x86231,x86232,x86236)+E(f866(f78(x86231,x86231,x86231,f866(x86232,x86233)),f866(x86232,x86234)),f866(f78(x86231,x86231,x86231,f866(x86232,x86234)),f866(x86232,x86233)))
% 157.76/157.52 [8858]~P58(x88584,x88585,x88582,x88581,x88586)+E(f866(x88581,f866(x88582,x88583)),x88583)
% 157.76/157.52 [9025]P25(x90251,x90252,x90253,x90254)+~P25(x90251,x90255,f866(f78(x90252,x90255,x90251,x90256),x90253),x90254)
% 157.76/157.52 [9098]~E(x90986,x90984)+E(f866(f80(x90981,x90982,x90983,x90984,x90985),x90986),x90985)
% 157.76/157.52 [9106]E(x91061,x91062)+E(f866(f80(x91063,x91064,x91065,x91062,x91066),x91061),f866(x91065,x91061))
% 157.76/157.52 [9118]~P25(x91184,x91182,f866(f78(x91181,x91182,x91184,x91183),x91185),x91186)+P25(x91181,x91182,x91183,f866(f317(x91184,x91181,x91185),x91186))
% 157.76/157.52 [9824]P107(f866(f66(x98241),x98242))+~P107(f866(f71(x98241,x98243,x98244,x98245,x98242),x98246))
% 157.76/157.52 [9833]~P107(f866(f866(f336(x98334),x98333),f307(x98334,x98335,x98331,x98332,x98336)))+P107(f866(f866(x98331,x98332),x98333))
% 157.76/157.52 [9834]~P107(f866(f866(f336(x98344),x98343),f304(x98344,x98341,x98345,x98342,x98346)))+P107(f866(f866(x98341,x98342),x98343))
% 157.76/157.52 [9835]~P107(f866(f866(f336(x98354),x98352),f307(x98354,x98351,x98355,x98356,x98353)))+P107(f866(f866(x98351,x98352),x98353))
% 157.76/157.52 [9836]~P107(f866(f866(f336(x98364),x98362),f304(x98364,x98365,x98361,x98366,x98363)))+P107(f866(f866(x98361,x98362),x98363))
% 157.76/157.52 [10327]P12(x103271,x103272,x103273,x103274,x103275,x103276)+~E(f866(f866(x103276,f857(x103273,x103276,x103275,x103272,x103274,x103271)),f859(x103273,x103276,x103275,x103272,x103274,x103271)),f866(f866(x103276,f858(x103273,x103276,x103275,x103272,x103274,x103271)),f860(x103273,x103276,x103275,x103272,x103274,x103271)))
% 157.76/157.52 [6022]E(x60221,x60222)+~E(f866(f866(f260(x60223,x60224),x60225),x60221),f866(f866(f260(x60223,x60224),x60226),x60222))
% 157.76/157.52 [6024]E(x60241,x60242)+~E(f866(f866(f260(x60243,x60244),x60241),x60245),f866(f866(f260(x60243,x60244),x60242),x60246))
% 157.76/157.52 [6159]~P16(x61595,x61596,x61591)+E(f866(f866(x61591,x61592),f866(f866(x61591,x61593),x61594)),f866(f866(x61591,x61593),f866(f866(x61591,x61592),x61594)))
% 157.76/157.52 [7584]~P32(x75844,x75841,f866(f866(f158(x75844),x75842),x75845),f866(f866(f158(x75844),x75843),x75846))+P107(f866(f866(x75841,x75842),x75843))
% 157.76/157.52 [7935]P32(x79351,x79352,x79353,x79354)+~P32(x79351,x79352,f866(f866(f158(x79351),x79355),x79353),f866(f866(f158(x79351),x79356),x79354))
% 157.76/157.52 [8962]~P58(x89625,x89621,x89622,x89626,x89624)+P107(f866(f866(f336(x89621),f866(x89622,x89623)),x89624))
% 157.76/157.52 [9146]E(f866(f82(x91461,x91462,x91463,x91464,x91465),x91466),f866(x91463,x91466))+P107(f866(f866(f336(x91461),x91466),x91465))
% 157.76/157.52 [9168]~E(x91683,f866(f866(f158(x91681),x91685),x91686))+P107(f866(f866(f336(f936(f931(x91681),f931(x91681))),f866(f866(f260(f931(x91681),f931(x91681)),x91682),f866(f866(f141(x91681),x91682),x91683))),f154(x91681,x91684)))
% 157.76/157.52 [9173]E(f866(f82(x91731,x91732,x91733,x91734,x91735),x91736),f866(x91734,x91736))+~P107(f866(f866(f336(x91731),x91736),x91735))
% 157.76/157.52 [9404]~P34(x94041,x94042,x94043,x94045,x94046)+P34(x94041,x94042,x94043,f866(f866(f182(x94041),x94044),x94045),f866(f866(f182(x94042),x94044),x94046))
% 157.76/157.52 [9405]~P34(x94051,x94052,x94053,x94055,x94056)+P34(x94051,x94052,x94053,f866(f866(f145(x94051),x94054),x94055),f866(f866(f145(x94052),x94054),x94056))
% 157.76/157.52 [9661]E(f866(f317(x96611,x96612,f80(x96611,x96612,x96613,x96614,x96615)),x96616),f866(f317(x96611,x96612,x96613),x96616))+P107(f866(f866(f336(x96611),x96614),x96616))
% 157.76/157.52 [9664]E(f866(f866(f161(x96641,x96642),f80(x96641,x96642,x96643,x96644,x96645)),x96646),f866(f866(f161(x96641,x96642),x96643),x96646))+P107(f866(f866(f336(x96641),x96644),f866(f179(x96641),x96646)))
% 157.76/157.52 [9896]~P23(x98964,x98962,x98965,x98963,x98966,x98961)+E(f866(x98961,f195(f937(x98962,a925))),x98963)
% 157.76/157.52 [10132]~E(f866(x101324,f866(f259(x101321,x101323),x101325)),f866(x101326,f866(f259(x101321,x101323),x101325)))+E(f866(f266(x101321,x101322,x101323,x101323,x101324,f32(x101323)),x101325),f866(f266(x101321,x101322,x101323,x101323,x101326,f32(x101323)),x101325))
% 157.76/157.52 [10133]~E(f866(x101334,f866(f264(x101331,x101332),x101335)),f866(x101336,f866(f264(x101331,x101332),x101335)))+E(f866(f266(x101331,x101331,x101332,x101333,f32(x101331),x101334),x101335),f866(f266(x101331,x101331,x101332,x101333,f32(x101331),x101336),x101335))
% 157.76/157.52 [10176]~E(f866(f266(x101762,x101766,x101763,x101763,x101761,f32(x101763)),x101764),f866(f266(x101762,x101766,x101763,x101763,x101765,f32(x101763)),x101764))+E(f866(x101761,f866(f259(x101762,x101763),x101764)),f866(x101765,f866(f259(x101762,x101763),x101764)))
% 157.76/157.52 [10177]~E(f866(f266(x101772,x101772,x101773,x101776,f32(x101772),x101771),x101774),f866(f266(x101772,x101772,x101773,x101776,f32(x101772),x101775),x101774))+E(f866(x101771,f866(f264(x101772,x101773),x101774)),f866(x101775,f866(f264(x101772,x101773),x101774)))
% 157.76/157.52 [9065]P107(f866(f866(f336(x90651),x90652),x90653))+~P107(f866(f866(f336(f936(x90651,x90654)),f866(f866(f260(x90651,x90654),x90652),x90655)),f866(f866(f262(x90651,x90654),x90653),x90656)))
% 157.76/157.52 [9081]P107(f866(f866(f336(x90811),x90812),f866(x90813,x90814)))+~P107(f866(f866(f336(f936(x90815,x90811)),f866(f866(f260(x90815,x90811),x90814),x90812)),f866(f866(f262(x90815,x90811),x90816),x90813)))
% 157.76/157.52 [9520]P107(f866(f866(f336(f936(x95201,x95201)),f866(f866(f260(x95201,x95201),f866(x95202,x95203)),f866(x95202,x95204))),x95205))+~P107(f866(f866(f336(f936(x95206,x95206)),f866(f866(f260(x95206,x95206),x95203),x95204)),f866(f866(f295(x95201,x95206),x95205),x95202)))
% 157.76/157.52 [9540]~P107(f866(f866(f336(f936(x95404,x95404)),f866(f866(f260(x95404,x95404),f866(x95406,x95402)),f866(x95406,x95403))),x95405))+P107(f866(f866(f336(f936(x95401,x95401)),f866(f866(f260(x95401,x95401),x95402),x95403)),f866(f866(f295(x95404,x95401),x95405),x95406)))
% 157.76/157.52 [10179]E(f866(f866(f260(x101791,x101792),f653(x101793,x101794,x101795,x101796,x101792,x101791)),f654(x101793,x101794,x101795,x101796,x101792,x101791)),x101796)+~P107(f866(f866(f336(f936(x101791,x101792)),x101796),f866(f866(f296(x101791,x101795,x101792),x101794),x101793)))
% 157.76/157.52 [10394]~P107(f866(f866(f336(f936(x103941,x103946)),x103945),f866(f866(f296(x103941,x103942,x103946),x103944),x103943)))+P107(f866(f866(f336(f936(x103941,x103942)),f866(f866(f260(x103941,x103942),f653(x103943,x103944,x103942,x103945,x103946,x103941)),f655(x103943,x103944,x103942,x103945,x103946,x103941))),x103944))
% 157.76/157.52 [10395]~P107(f866(f866(f336(f936(x103956,x103952)),x103955),f866(f866(f296(x103956,x103951,x103952),x103954),x103953)))+P107(f866(f866(f336(f936(x103951,x103952)),f866(f866(f260(x103951,x103952),f655(x103953,x103954,x103951,x103955,x103952,x103956)),f654(x103953,x103954,x103951,x103955,x103952,x103956))),x103953))
% 157.76/157.52 [10396]P12(x103961,x103962,x103963,x103964,x103965,x103966)+P107(f866(f866(f336(f936(x103962,x103962)),f866(f866(f260(x103962,x103962),f860(x103963,x103966,x103965,x103962,x103964,x103961)),f859(x103963,x103966,x103965,x103962,x103964,x103961))),x103965))
% 157.76/157.52 [10397]P12(x103971,x103972,x103973,x103974,x103975,x103976)+P107(f866(f866(f336(f936(x103971,x103971)),f866(f866(f260(x103971,x103971),f858(x103973,x103976,x103975,x103972,x103974,x103971)),f857(x103973,x103976,x103975,x103972,x103974,x103971))),x103974))
% 157.76/157.52 [8007]~P5(x80072)+E(f866(f866(f44(x80071,x80072),x80073),f866(f866(f7(x80071,x80074,x80072),x80075),x80076)),f866(f866(f866(f44(x80071,f937(x80074,x80072)),x80073),x80075),x80076))
% 157.76/157.52 [8008]~P5(x80082)+E(f866(f866(f45(x80081,x80082),x80083),f866(f866(f7(x80081,x80084,x80082),x80085),x80086)),f866(f866(f866(f45(x80081,f937(x80084,x80082)),x80083),x80085),x80086))
% 157.76/157.52 [8768]E(f866(f866(f44(x87681,f937(x87682,a925)),x87683),f866(f866(f8(f937(x87682,a925),f937(x87682,a925),x87681),f866(f316(x87682),x87684)),x87685)),f866(f866(f316(x87682),x87684),f866(f866(f44(x87681,f937(x87682,a925)),x87683),x87685)))+~P107(f866(f866(f336(x87681),x87686),x87683))
% 157.76/157.52 [9223]~P5(x92232)+E(f866(f866(f44(x92231,x92232),x92233),f866(f866(f8(f937(x92234,x92232),x92232,x92231),f866(f44(x92234,x92232),x92235)),f866(f7(x92234,x92231,x92232),x92236))),f866(f866(f44(x92234,x92232),x92235),f866(f866(f8(f937(x92231,x92232),x92232,x92234),f866(f44(x92231,x92232),x92233)),x92236)))
% 157.76/157.52 [9224]~P5(x92242)+E(f866(f866(f45(x92241,x92242),x92243),f866(f866(f8(f937(x92244,x92242),x92242,x92241),f866(f45(x92244,x92242),x92245)),f866(f7(x92244,x92241,x92242),x92246))),f866(f866(f45(x92244,x92242),x92245),f866(f866(f8(f937(x92241,x92242),x92242,x92244),f866(f45(x92241,x92242),x92243)),x92246)))
% 157.76/157.52 [9429]P107(f866(f866(f336(x94291),x94292),f866(f179(x94291),x94293)))+~P107(f866(f866(f336(f936(x94294,x94291)),f866(f866(f260(x94294,x94291),x94295),x94292)),f866(f179(f936(x94294,x94291)),f866(f866(f188(x94294,x94291),x94296),x94293))))
% 157.76/157.52 [9430]P107(f866(f866(f336(x94301),x94302),f866(f179(x94301),x94303)))+~P107(f866(f866(f336(f936(x94301,x94304)),f866(f866(f260(x94301,x94304),x94302),x94305)),f866(f179(f936(x94301,x94304)),f866(f866(f188(x94301,x94304),x94303),x94306))))
% 157.76/157.52 [9536]P107(f866(f866(f243(f937(x95361,a925)),f866(f293(x95362,x95361,x95363),x95364)),x95365))+~P107(f866(f866(f243(f937(f936(x95362,x95361),a925)),x95363),f866(f866(f262(x95362,x95361),x95366),f866(f16(f937(x95361,a925),x95362),x95365))))
% 157.76/157.52 [9541]~P26(x95414,x95412,x95415,f250(f937(x95414,a925)),f250(f937(x95412,a925)))+E(f866(f866(f45(x95411,f937(x95412,a925)),x95413),f866(f866(f8(f937(x95414,a925),f937(x95412,a925),x95411),f317(x95414,x95412,x95415)),x95416)),f866(f317(x95414,x95412,x95415),f866(f866(f45(x95411,f937(x95414,a925)),x95413),x95416)))
% 157.76/157.52 [9728]P107(f866(f866(f336(f936(f931(x97281),f931(x97281))),f866(f866(f260(f931(x97281),f931(x97281)),f866(f866(f158(x97281),x97282),x97283)),f866(f866(f158(x97281),x97284),x97285))),f154(x97281,x97286)))+~P107(f866(f866(f336(f936(x97281,x97281)),f866(f866(f260(x97281,x97281),x97282),x97284)),x97286))
% 157.76/157.52 [10175]E(f866(f866(f260(x101751,x101752),f563(x101753,x101754,x101755,x101752,x101751,x101756)),f564(x101753,x101754,x101755,x101752,x101751,x101756)),x101756)+P107(f866(f866(f336(x101755),x101754),f866(f866(f265(x101751,x101752,f937(x101755,a925)),x101753),x101756)))
% 157.76/157.52 [10182]E(f866(f866(f260(x101821,x101822),f565(x101823,x101824,x101822,x101821,x101825,x101826)),f566(x101823,x101824,x101822,x101821,x101825,x101826)),x101823)+~P107(f866(f866(f336(x101826),x101825),f866(f866(f265(x101821,x101822,f937(x101826,a925)),x101824),x101823)))
% 157.76/157.52 [10342]P107(f866(f866(f336(x103421),x103422),f866(f866(x103423,f565(x103424,x103423,x103425,x103426,x103422,x103421)),f566(x103424,x103423,x103425,x103426,x103422,x103421))))+~P107(f866(f866(f336(x103421),x103422),f866(f866(f265(x103426,x103425,f937(x103421,a925)),x103423),x103424)))
% 157.76/157.52 [10367]~P107(f866(f866(f336(x103671),x103672),f866(f866(x103675,f563(x103675,x103672,x103671,x103674,x103673,x103676)),f564(x103675,x103672,x103671,x103674,x103673,x103676))))+P107(f866(f866(f336(x103671),x103672),f866(f866(f265(x103673,x103674,f937(x103671,a925)),x103675),x103676)))
% 157.76/157.52 [8668]E(x86681,x86682)+E(f866(f866(f166(x86683,f866(f866(f166(x86683,x86684),x86681),x86685)),x86682),x86686),f866(f866(f166(x86683,f866(f866(f166(x86683,x86684),x86682),x86686)),x86681),x86685))
% 157.76/157.52 [9788]~P107(f866(f866(f336(x97883),x97886),x97885))+E(f866(f866(f316(x97881),x97882),f866(f317(x97883,x97881,x97884),f866(f866(f23(f937(x97883,a925)),x97885),f866(f866(f316(x97883),x97886),f195(f937(x97883,a925)))))),f866(f317(x97883,x97881,f80(x97883,x97881,x97884,x97886,x97882)),x97885))
% 157.76/157.52 [9302]~P107(f866(f866(x93024,x93025),x93026))+P107(f866(f866(f866(f866(f117(f937(x93021,f937(x93022,a925))),x93023),x93024),x93025),x93026))
% 157.76/157.52 [9304]~P107(f866(f866(x93043,x93045),x93046))+P107(f866(f866(f866(f866(f117(f937(x93041,f937(x93042,a925))),x93043),x93044),x93045),x93046))
% 157.76/157.52 [9591]P107(f866(f866(x95911,x95912),x95913))+~P107(f866(f866(f866(f866(f108(f937(x95914,f937(x95915,a925))),x95916),x95911),x95912),x95913))
% 157.76/157.52 [9592]P107(f866(f866(x95921,x95922),x95923))+~P107(f866(f866(f866(f866(f108(f937(x95924,f937(x95925,a925))),x95921),x95926),x95922),x95923))
% 157.76/157.52 [10024]~P71(x100242)+E(f866(f866(f9(x100241,x100242),f866(f866(f7(x100241,f937(x100243,a925),x100242),f866(f866(f8(f937(x100243,x100242),f937(f937(x100243,a925),x100242),x100241),f9(x100243,x100242)),x100244)),x100245)),x100246),f866(f866(f9(f936(x100241,x100243),x100242),f866(f265(x100241,x100243,x100242),x100244)),f866(f866(f262(x100241,x100243),x100246),f866(f16(f937(x100243,a925),x100241),x100245))))
% 157.76/157.52 [10025]~P72(x100252)+E(f866(f866(f6(x100251,x100252),f866(f866(f7(x100251,f937(x100253,a925),x100252),f866(f866(f8(f937(x100253,x100252),f937(f937(x100253,a925),x100252),x100251),f6(x100253,x100252)),x100254)),x100255)),x100256),f866(f866(f6(f936(x100251,x100253),x100252),f866(f265(x100251,x100253,x100252),x100254)),f866(f866(f262(x100251,x100253),x100256),f866(f16(f937(x100253,a925),x100251),x100255))))
% 157.76/157.52 [10157]~P72(x101572)+E(f866(f866(f6(x101571,x101572),f866(f866(f7(x101571,f937(x101573,a925),x101572),f866(f866(f8(f937(x101573,x101572),f937(f937(x101573,a925),x101572),x101571),f6(x101573,x101572)),f866(f7(x101573,x101571,x101572),x101574))),x101575)),x101576),f866(f866(f6(x101573,x101572),f866(f866(f7(x101573,f937(x101571,a925),x101572),f866(f866(f8(f937(x101571,x101572),f937(f937(x101571,a925),x101572),x101573),f6(x101571,x101572)),x101574)),x101576)),x101575))
% 157.76/157.52 [10462]~P107(f866(f866(f336(f936(x104621,x104622)),f866(f866(f260(x104621,x104622),x104625),x104626)),f866(f866(f117(f937(f936(x104621,x104622),a925)),x104623),x104624)))+P107(f866(f866(f866(f866(f117(f937(x104621,f937(x104622,a925))),f866(f866(f7(x104621,f937(f936(x104621,x104622),a925),f937(x104622,a925)),f866(f866(f8(f937(x104622,f937(f937(f936(x104621,x104622),a925),a925)),f937(f937(f936(x104621,x104622),a925),f937(x104622,a925)),x104621),f7(x104622,f937(f936(x104621,x104622),a925),a925)),f866(f866(f8(f937(x104622,f936(x104621,x104622)),f937(x104622,f937(f937(f936(x104621,x104622),a925),a925)),x104621),f866(f8(f936(x104621,x104622),f937(f937(f936(x104621,x104622),a925),a925),x104622),f336(f936(x104621,x104622)))),f260(x104621,x104622)))),x104623)),f866(f866(f7(x104621,f937(f936(x104621,x104622),a925),f937(x104622,a925)),f866(f866(f8(f937(x104622,f937(f937(f936(x104621,x104622),a925),a925)),f937(f937(f936(x104621,x104622),a925),f937(x104622,a925)),x104621),f7(x104622,f937(f936(x104621,x104622),a925),a925)),f866(f866(f8(f937(x104622,f936(x104621,x104622)),f937(x104622,f937(f937(f936(x104621,x104622),a925),a925)),x104621),f866(f8(f936(x104621,x104622),f937(f937(f936(x104621,x104622),a925),a925),x104622),f336(f936(x104621,x104622)))),f260(x104621,x104622)))),x104624)),x104625),x104626))
% 157.76/157.52 [10463]~P107(f866(f866(f336(f936(x104631,x104632)),f866(f866(f260(x104631,x104632),x104635),x104636)),f866(f866(f108(f937(f936(x104631,x104632),a925)),x104633),x104634)))+P107(f866(f866(f866(f866(f108(f937(x104631,f937(x104632,a925))),f866(f866(f7(x104631,f937(f936(x104631,x104632),a925),f937(x104632,a925)),f866(f866(f8(f937(x104632,f937(f937(f936(x104631,x104632),a925),a925)),f937(f937(f936(x104631,x104632),a925),f937(x104632,a925)),x104631),f7(x104632,f937(f936(x104631,x104632),a925),a925)),f866(f866(f8(f937(x104632,f936(x104631,x104632)),f937(x104632,f937(f937(f936(x104631,x104632),a925),a925)),x104631),f866(f8(f936(x104631,x104632),f937(f937(f936(x104631,x104632),a925),a925),x104632),f336(f936(x104631,x104632)))),f260(x104631,x104632)))),x104633)),f866(f866(f7(x104631,f937(f936(x104631,x104632),a925),f937(x104632,a925)),f866(f866(f8(f937(x104632,f937(f937(f936(x104631,x104632),a925),a925)),f937(f937(f936(x104631,x104632),a925),f937(x104632,a925)),x104631),f7(x104632,f937(f936(x104631,x104632),a925),a925)),f866(f866(f8(f937(x104632,f936(x104631,x104632)),f937(x104632,f937(f937(f936(x104631,x104632),a925),a925)),x104631),f866(f8(f936(x104631,x104632),f937(f937(f936(x104631,x104632),a925),a925),x104632),f336(f936(x104631,x104632)))),f260(x104631,x104632)))),x104634)),x104635),x104636))
% 157.76/157.52 [10472]P107(f866(f866(f336(f936(x104721,x104722)),f866(f866(f260(x104721,x104722),x104723),x104724)),f866(f866(f117(f937(f936(x104721,x104722),a925)),x104725),x104726)))+~P107(f866(f866(f866(f866(f117(f937(x104721,f937(x104722,a925))),f866(f866(f7(x104721,f937(f936(x104721,x104722),a925),f937(x104722,a925)),f866(f866(f8(f937(x104722,f937(f937(f936(x104721,x104722),a925),a925)),f937(f937(f936(x104721,x104722),a925),f937(x104722,a925)),x104721),f7(x104722,f937(f936(x104721,x104722),a925),a925)),f866(f866(f8(f937(x104722,f936(x104721,x104722)),f937(x104722,f937(f937(f936(x104721,x104722),a925),a925)),x104721),f866(f8(f936(x104721,x104722),f937(f937(f936(x104721,x104722),a925),a925),x104722),f336(f936(x104721,x104722)))),f260(x104721,x104722)))),x104725)),f866(f866(f7(x104721,f937(f936(x104721,x104722),a925),f937(x104722,a925)),f866(f866(f8(f937(x104722,f937(f937(f936(x104721,x104722),a925),a925)),f937(f937(f936(x104721,x104722),a925),f937(x104722,a925)),x104721),f7(x104722,f937(f936(x104721,x104722),a925),a925)),f866(f866(f8(f937(x104722,f936(x104721,x104722)),f937(x104722,f937(f937(f936(x104721,x104722),a925),a925)),x104721),f866(f8(f936(x104721,x104722),f937(f937(f936(x104721,x104722),a925),a925),x104722),f336(f936(x104721,x104722)))),f260(x104721,x104722)))),x104726)),x104723),x104724))
% 157.76/157.52 [10473]P107(f866(f866(f336(f936(x104731,x104732)),f866(f866(f260(x104731,x104732),x104733),x104734)),f866(f866(f108(f937(f936(x104731,x104732),a925)),x104735),x104736)))+~P107(f866(f866(f866(f866(f108(f937(x104731,f937(x104732,a925))),f866(f866(f7(x104731,f937(f936(x104731,x104732),a925),f937(x104732,a925)),f866(f866(f8(f937(x104732,f937(f937(f936(x104731,x104732),a925),a925)),f937(f937(f936(x104731,x104732),a925),f937(x104732,a925)),x104731),f7(x104732,f937(f936(x104731,x104732),a925),a925)),f866(f866(f8(f937(x104732,f936(x104731,x104732)),f937(x104732,f937(f937(f936(x104731,x104732),a925),a925)),x104731),f866(f8(f936(x104731,x104732),f937(f937(f936(x104731,x104732),a925),a925),x104732),f336(f936(x104731,x104732)))),f260(x104731,x104732)))),x104735)),f866(f866(f7(x104731,f937(f936(x104731,x104732),a925),f937(x104732,a925)),f866(f866(f8(f937(x104732,f937(f937(f936(x104731,x104732),a925),a925)),f937(f937(f936(x104731,x104732),a925),f937(x104732,a925)),x104731),f7(x104732,f937(f936(x104731,x104732),a925),a925)),f866(f866(f8(f937(x104732,f936(x104731,x104732)),f937(x104732,f937(f937(f936(x104731,x104732),a925),a925)),x104731),f866(f8(f936(x104731,x104732),f937(f937(f936(x104731,x104732),a925),a925),x104732),f336(f936(x104731,x104732)))),f260(x104731,x104732)))),x104736)),x104733),x104734))
% 157.76/157.52 [10456]~P107(f866(f866(f336(f936(x104562,x104563)),f866(f866(f260(x104562,x104563),x104565),x104566)),f866(f866(f44(x104561,f937(f936(x104562,x104563),a925)),f250(f937(x104561,a925))),x104564)))+P107(f866(f866(f866(f866(f44(x104561,f937(x104562,f937(x104563,a925))),f250(f937(x104561,a925))),f866(f866(f8(f937(f936(x104562,x104563),a925),f937(x104562,f937(x104563,a925)),x104561),f866(f7(x104562,f937(f936(x104562,x104563),a925),f937(x104563,a925)),f866(f866(f8(f937(x104563,f937(f937(f936(x104562,x104563),a925),a925)),f937(f937(f936(x104562,x104563),a925),f937(x104563,a925)),x104562),f7(x104563,f937(f936(x104562,x104563),a925),a925)),f866(f866(f8(f937(x104563,f936(x104562,x104563)),f937(x104563,f937(f937(f936(x104562,x104563),a925),a925)),x104562),f866(f8(f936(x104562,x104563),f937(f937(f936(x104562,x104563),a925),a925),x104563),f336(f936(x104562,x104563)))),f260(x104562,x104563))))),x104564)),x104565),x104566))
% 157.76/157.52 [10457]~P107(f866(f866(f336(f936(x104572,x104573)),f866(f866(f260(x104572,x104573),x104575),x104576)),f866(f866(f45(x104571,f937(f936(x104572,x104573),a925)),f250(f937(x104571,a925))),x104574)))+P107(f866(f866(f866(f866(f45(x104571,f937(x104572,f937(x104573,a925))),f250(f937(x104571,a925))),f866(f866(f8(f937(f936(x104572,x104573),a925),f937(x104572,f937(x104573,a925)),x104571),f866(f7(x104572,f937(f936(x104572,x104573),a925),f937(x104573,a925)),f866(f866(f8(f937(x104573,f937(f937(f936(x104572,x104573),a925),a925)),f937(f937(f936(x104572,x104573),a925),f937(x104573,a925)),x104572),f7(x104573,f937(f936(x104572,x104573),a925),a925)),f866(f866(f8(f937(x104573,f936(x104572,x104573)),f937(x104573,f937(f937(f936(x104572,x104573),a925),a925)),x104572),f866(f8(f936(x104572,x104573),f937(f937(f936(x104572,x104573),a925),a925),x104573),f336(f936(x104572,x104573)))),f260(x104572,x104573))))),x104574)),x104575),x104576))
% 157.76/157.52 [10466]P107(f866(f866(f336(f936(x104661,x104662)),f866(f866(f260(x104661,x104662),x104663),x104664)),f866(f866(f44(x104665,f937(f936(x104661,x104662),a925)),f250(f937(x104665,a925))),x104666)))+~P107(f866(f866(f866(f866(f44(x104665,f937(x104661,f937(x104662,a925))),f250(f937(x104665,a925))),f866(f866(f8(f937(f936(x104661,x104662),a925),f937(x104661,f937(x104662,a925)),x104665),f866(f7(x104661,f937(f936(x104661,x104662),a925),f937(x104662,a925)),f866(f866(f8(f937(x104662,f937(f937(f936(x104661,x104662),a925),a925)),f937(f937(f936(x104661,x104662),a925),f937(x104662,a925)),x104661),f7(x104662,f937(f936(x104661,x104662),a925),a925)),f866(f866(f8(f937(x104662,f936(x104661,x104662)),f937(x104662,f937(f937(f936(x104661,x104662),a925),a925)),x104661),f866(f8(f936(x104661,x104662),f937(f937(f936(x104661,x104662),a925),a925),x104662),f336(f936(x104661,x104662)))),f260(x104661,x104662))))),x104666)),x104663),x104664))
% 157.76/157.52 [10467]P107(f866(f866(f336(f936(x104671,x104672)),f866(f866(f260(x104671,x104672),x104673),x104674)),f866(f866(f45(x104675,f937(f936(x104671,x104672),a925)),f250(f937(x104675,a925))),x104676)))+~P107(f866(f866(f866(f866(f45(x104675,f937(x104671,f937(x104672,a925))),f250(f937(x104675,a925))),f866(f866(f8(f937(f936(x104671,x104672),a925),f937(x104671,f937(x104672,a925)),x104675),f866(f7(x104671,f937(f936(x104671,x104672),a925),f937(x104672,a925)),f866(f866(f8(f937(x104672,f937(f937(f936(x104671,x104672),a925),a925)),f937(f937(f936(x104671,x104672),a925),f937(x104672,a925)),x104671),f7(x104672,f937(f936(x104671,x104672),a925),a925)),f866(f866(f8(f937(x104672,f936(x104671,x104672)),f937(x104672,f937(f937(f936(x104671,x104672),a925),a925)),x104671),f866(f8(f936(x104671,x104672),f937(f937(f936(x104671,x104672),a925),a925),x104672),f336(f936(x104671,x104672)))),f260(x104671,x104672))))),x104676)),x104673),x104674))
% 157.76/157.52 [7518]E(x75181,x75182)+~E(f98(x75183,x75184,x75185,x75181),f98(x75183,x75186,x75187,x75182))
% 157.76/157.52 [7519]E(x75191,x75192)+~E(f98(x75193,x75194,x75191,x75195),f98(x75193,x75196,x75192,x75197))
% 157.76/157.52 [7520]E(x75201,x75202)+~E(f98(x75203,x75201,x75204,x75205),f98(x75203,x75202,x75206,x75207))
% 157.76/157.52 [7688]E(f866(x76881,f866(x76882,x76883)),f866(x76884,x76883))+~E(f866(f78(x76885,x76886,x76887,x76881),x76882),x76884)
% 157.76/157.52 [9804]E(x98041,x98042)+E(f80(x98043,x98044,f80(x98043,x98044,x98045,x98041,x98046),x98042,x98047),f80(x98043,x98044,f80(x98043,x98044,x98045,x98042,x98047),x98041,x98046))
% 157.76/157.52 [9895]~P22(x98953,x98954,x98951,x98955,x98956,x98957)+E(f866(f866(x98951,x98952),x98952),x98952)
% 157.76/157.52 [6262]~E(f866(f866(f161(x62621,x62625),x62626),x62622),f866(f866(f161(x62623,x62625),x62627),x62624))+E(f866(f196(f931(x62621)),x62622),f866(f196(f931(x62623)),x62624))
% 157.76/157.52 [8699]E(f866(x86991,f866(x86992,x86993)),f866(x86994,x86993))+~E(f866(f78(x86995,x86996,x86997,x86991),x86992),f866(f78(x86996,x86996,x86997,f32(x86996)),x86994))
% 157.76/157.52 [9054]~P34(x90544,x90545,x90541,f866(f866(f158(x90544),x90542),x90546),f866(f866(f158(x90545),x90543),x90547))+P107(f866(f866(x90541,x90542),x90543))
% 157.76/157.52 [9436]P34(x94361,x94362,x94363,x94364,x94365)+~P34(x94361,x94362,x94363,f866(f866(f158(x94361),x94366),x94364),f866(f866(f158(x94362),x94367),x94365))
% 157.76/157.52 [10057]P107(f866(f866(x100571,x100572),f523(x100573,x100572,x100574,x100571)))+~P107(f866(f866(f261(x100575,x100576,x100577,x100571,x100574),x100572),x100573))
% 157.76/157.52 [10081]P107(f866(f866(x100811,f523(x100812,x100813,x100811,x100814)),x100812))+~P107(f866(f866(f261(x100815,x100816,x100817,x100814,x100811),x100813),x100812))
% 157.76/157.52 [9177]~P20(x91776,x91771,x91773,x91777)+E(f866(f78(x91771,x91771,x91772,f866(x91773,x91774)),f866(f78(x91771,x91771,x91772,f866(x91773,x91774)),x91775)),f866(f78(x91771,x91771,x91772,f866(x91773,x91774)),x91775))
% 157.76/157.52 [9544]~P34(x95443,x95442,x95444,f866(f866(f161(x95441,x95443),x95445),x95446),x95447)+P34(x95441,x95442,f866(f866(f8(x95443,f937(x95442,a925),x95441),x95444),x95445),x95446,x95447)
% 157.76/157.52 [9567]P34(x95671,x95672,x95673,f866(f866(f161(x95674,x95671),x95675),x95676),x95677)+~P34(x95674,x95672,f866(f866(f8(x95671,f937(x95672,a925),x95674),x95673),x95675),x95676,x95677)
% 157.76/157.52 [9176]~P107(f866(f866(f336(x91761),x91762),f866(f866(x91765,x91766),x91767)))+P107(f866(f866(f336(x91761),x91762),f866(f866(f265(x91763,x91764,f937(x91761,a925)),x91765),f866(f866(f260(x91763,x91764),x91766),x91767))))
% 157.76/157.52 [9459]P107(f866(f866(f866(x94591,x94592),x94593),x94594))+~P107(f866(f866(f866(f265(x94595,x94596,f937(x94597,a925)),x94591),f866(f866(f260(x94595,x94596),x94592),x94593)),x94594))
% 157.76/157.52 [9606]P107(f866(f866(f336(x96061),f866(f866(x96062,x96063),x96064)),f866(f317(f936(x96065,x96066),x96061,f866(f265(x96065,x96066,x96061),x96062)),x96067)))+~P107(f866(f866(f336(f936(x96065,x96066)),f866(f866(f260(x96065,x96066),x96063),x96064)),x96067))
% 157.76/157.52 [9943]P107(f866(f866(f336(f936(f931(x99431),f931(x99431))),f866(f866(f260(f931(x99431),f931(x99431)),f866(f866(f141(x99431),x99432),f866(f866(f158(x99431),x99433),x99434))),f866(f866(f141(x99431),x99432),f866(f866(f158(x99431),x99435),x99436)))),f154(x99431,x99437)))+~P107(f866(f866(f336(f936(x99431,x99431)),f866(f866(f260(x99431,x99431),x99433),x99435)),x99437))
% 157.76/157.52 [10009]~P34(x100091,x100093,x100094,x100096,f866(f866(f161(x100092,x100093),x100095),x100097))+P34(x100091,x100092,f866(f866(f7(x100091,f937(x100092,x100093),f937(x100092,a925)),f866(f866(f8(f937(x100093,a925),f937(f937(x100092,x100093),f937(x100092,a925)),x100091),f8(x100093,a925,x100092)),x100094)),x100095),x100096,x100097)
% 157.76/157.52 [10085]P34(x100851,x100852,x100853,x100854,f866(f866(f161(x100855,x100852),x100856),x100857))+~P34(x100851,x100855,f866(f866(f7(x100851,f937(x100855,x100852),f937(x100855,a925)),f866(f866(f8(f937(x100852,a925),f937(f937(x100855,x100852),f937(x100855,a925)),x100851),f8(x100852,a925,x100855)),x100853)),x100856),x100854,x100857)
% 157.76/157.52 [10381]P107(f866(f866(f336(x103811),f620(x103812,x103813,x103814,x103815,x103816,x103817,x103811)),x103815))+P107(f866(f866(f866(f866(f45(x103811,f937(x103817,f937(x103816,a925))),x103815),x103814),x103813),x103812))
% 157.76/157.52 [10382]P107(f866(f866(f336(x103821),f797(x103822,x103823,x103824,x103825,x103826,x103827,x103821)),x103827))+P107(f866(f866(f866(f866(f45(x103821,f937(x103823,f937(x103822,a925))),x103827),x103826),x103825),x103824))
% 157.76/157.52 [10383]P107(f866(f866(f336(x103831),f891(x103832,x103833,x103834,x103835,x103836,x103837,x103831)),x103835))+~P107(f866(f866(f866(f866(f44(x103831,f937(x103837,f937(x103836,a925))),x103835),x103834),x103833),x103832))
% 157.76/157.52 [10384]P107(f866(f866(f336(x103841),f798(x103842,x103843,x103844,x103845,x103846,x103847,x103841)),x103845))+~P107(f866(f866(f866(f866(f44(x103841,f937(x103847,f937(x103846,a925))),x103845),x103844),x103843),x103842))
% 157.76/157.52 [10420]P107(f866(f866(f866(x104201,f891(x104202,x104203,x104201,x104204,x104205,x104206,x104207)),x104203),x104202))+~P107(f866(f866(f866(f866(f44(x104207,f937(x104206,f937(x104205,a925))),x104204),x104201),x104203),x104202))
% 157.76/157.52 [10421]P107(f866(f866(f866(x104211,f798(x104212,x104213,x104211,x104214,x104215,x104216,x104217)),x104213),x104212))+~P107(f866(f866(f866(f866(f44(x104217,f937(x104216,f937(x104215,a925))),x104214),x104211),x104213),x104212))
% 157.76/157.52 [10437]~P107(f866(f866(f866(x104375,f620(x104377,x104376,x104375,x104374,x104373,x104372,x104371)),x104376),x104377))+P107(f866(f866(f866(f866(f45(x104371,f937(x104372,f937(x104373,a925))),x104374),x104375),x104376),x104377))
% 157.76/157.52 [10438]~P107(f866(f866(f866(x104385,f797(x104383,x104382,x104387,x104386,x104385,x104384,x104381)),x104386),x104387))+P107(f866(f866(f866(f866(f45(x104381,f937(x104382,f937(x104383,a925))),x104384),x104385),x104386),x104387))
% 157.76/157.52 [10455]~P107(f866(f866(f336(f936(x104551,x104553)),f866(f866(f260(x104551,x104553),x104556),x104557)),f866(f866(f296(x104551,x104552,x104553),x104554),x104555)))+P107(f866(f866(f261(x104551,x104552,x104553,f866(f866(f7(x104551,f937(f936(x104551,x104552),a925),f937(x104552,a925)),f866(f866(f8(f937(x104552,f937(f937(f936(x104551,x104552),a925),a925)),f937(f937(f936(x104551,x104552),a925),f937(x104552,a925)),x104551),f7(x104552,f937(f936(x104551,x104552),a925),a925)),f866(f866(f8(f937(x104552,f936(x104551,x104552)),f937(x104552,f937(f937(f936(x104551,x104552),a925),a925)),x104551),f866(f8(f936(x104551,x104552),f937(f937(f936(x104551,x104552),a925),a925),x104552),f336(f936(x104551,x104552)))),f260(x104551,x104552)))),x104554),f866(f866(f7(x104552,f937(f936(x104552,x104553),a925),f937(x104553,a925)),f866(f866(f8(f937(x104553,f937(f937(f936(x104552,x104553),a925),a925)),f937(f937(f936(x104552,x104553),a925),f937(x104553,a925)),x104552),f7(x104553,f937(f936(x104552,x104553),a925),a925)),f866(f866(f8(f937(x104553,f936(x104552,x104553)),f937(x104553,f937(f937(f936(x104552,x104553),a925),a925)),x104552),f866(f8(f936(x104552,x104553),f937(f937(f936(x104552,x104553),a925),a925),x104553),f336(f936(x104552,x104553)))),f260(x104552,x104553)))),x104555)),x104556),x104557))
% 157.76/157.52 [10465]P107(f866(f866(f336(f936(x104651,x104652)),f866(f866(f260(x104651,x104652),x104653),x104654)),f866(f866(f296(x104651,x104655,x104652),x104656),x104657)))+~P107(f866(f866(f261(x104651,x104655,x104652,f866(f866(f7(x104651,f937(f936(x104651,x104655),a925),f937(x104655,a925)),f866(f866(f8(f937(x104655,f937(f937(f936(x104651,x104655),a925),a925)),f937(f937(f936(x104651,x104655),a925),f937(x104655,a925)),x104651),f7(x104655,f937(f936(x104651,x104655),a925),a925)),f866(f866(f8(f937(x104655,f936(x104651,x104655)),f937(x104655,f937(f937(f936(x104651,x104655),a925),a925)),x104651),f866(f8(f936(x104651,x104655),f937(f937(f936(x104651,x104655),a925),a925),x104655),f336(f936(x104651,x104655)))),f260(x104651,x104655)))),x104656),f866(f866(f7(x104655,f937(f936(x104655,x104652),a925),f937(x104652,a925)),f866(f866(f8(f937(x104652,f937(f937(f936(x104655,x104652),a925),a925)),f937(f937(f936(x104655,x104652),a925),f937(x104652,a925)),x104655),f7(x104652,f937(f936(x104655,x104652),a925),a925)),f866(f866(f8(f937(x104652,f936(x104655,x104652)),f937(x104652,f937(f937(f936(x104655,x104652),a925),a925)),x104655),f866(f8(f936(x104655,x104652),f937(f937(f936(x104655,x104652),a925),a925),x104652),f336(f936(x104655,x104652)))),f260(x104655,x104652)))),x104657)),x104653),x104654))
% 157.76/157.52 [10393]~P147(x103932)+E(f866(f866(f6(x103931,x103932),f866(f866(f7(x103931,f937(x103933,a925),x103932),f866(f866(f8(f937(x103933,x103932),f937(f937(x103933,a925),x103932),x103931),f6(x103933,x103932)),f866(f866(f7(x103931,f937(x103933,x103932),f937(x103933,x103932)),f866(f866(f8(f937(x103932,x103932),f937(f937(x103933,x103932),f937(x103933,x103932)),x103931),f8(x103932,x103932,x103933)),f866(f866(f8(x103932,f937(x103932,x103932),x103931),f87(x103932)),x103934))),x103935))),x103936)),x103937),f866(f866(f87(x103932),f866(f866(f6(x103931,x103932),x103934),x103937)),f866(f866(f6(x103933,x103932),x103935),x103936)))
% 157.76/157.52 [9492]~P19(x94927,x94921,x94923,x94928)+E(f866(f78(x94921,x94921,x94922,f866(x94923,x94924)),f866(f78(x94921,x94921,x94922,f866(x94923,x94925)),x94926)),f866(f78(x94921,x94921,x94922,f866(x94923,x94925)),f866(f78(x94921,x94921,x94922,f866(x94923,x94924)),x94926)))
% 157.76/157.52 [10419]~P24(x104191,x104192,f866(f866(f316(f929(x104191)),f98(x104191,x104194,x104197,f866(f866(f7(x104191,f937(a926,a926),f937(a926,a925)),f866(f866(f8(f937(a926,a925),f937(f937(a926,a926),f937(a926,a925)),x104191),f8(a926,a925,a926)),x104198)),f866(f866(f7(a926,a930,a926),f866(f866(f7(a926,a928,f937(a930,a926)),a203),f33(x104195))),f204(x104193,x104195))))),f195(f937(f929(x104191),a925))))+P24(x104191,x104192,f866(f866(f316(f929(x104191)),f98(x104191,f866(f866(f8(f937(a926,a925),f937(a926,a925),x104191),f866(f18(a926,a925,a925),f866(f866(f8(a925,f937(a925,a925),a926),a333),f866(a332,x104193)))),f866(f866(f7(x104191,f937(a926,a926),f937(a926,a925)),f866(f866(f8(f937(a926,a925),f937(f937(a926,a926),f937(a926,a925)),x104191),f8(a926,a925,a926)),x104194)),f866(f866(f18(a926,a930,a926),f866(f866(f7(a926,a928,f937(a930,a926)),a203),f33(x104195))),x104196))),f27(x104195,x104196,x104197),x104198)),f195(f937(f929(x104191),a925))))
% 157.76/157.52 [10460]E(f866(f866(f260(x104601,x104602),f866(x104603,f546(x104604,x104605,x104603,x104606,x104607,x104608,x104602,x104601))),f866(x104605,f547(x104604,x104605,x104603,x104606,x104607,x104608,x104602,x104601))),x104608)+~P107(f866(f866(f336(f936(x104601,x104602)),x104608),f866(f317(f936(x104607,x104606),f936(x104601,x104602),f266(x104607,x104601,x104606,x104602,x104603,x104605)),x104604)))
% 157.76/157.52 [10478]~P107(f866(f866(f336(f936(x104788,x104787)),x104786),f866(f317(f936(x104781,x104782),f936(x104788,x104787),f266(x104781,x104788,x104782,x104787,x104785,x104784)),x104783)))+P107(f866(f866(f336(f936(x104781,x104782)),f866(f866(f260(x104781,x104782),f546(x104783,x104784,x104785,x104782,x104781,x104786,x104787,x104788)),f547(x104783,x104784,x104785,x104782,x104781,x104786,x104787,x104788))),x104783))
% 157.76/157.52 [9933]P107(f866(f866(f336(f936(f936(x99331,x99332),f936(x99331,x99332))),f866(f866(f260(f936(x99331,x99332),f936(x99331,x99332)),f866(f866(f260(x99331,x99332),x99333),x99334)),f866(f866(f260(x99331,x99332),x99335),x99336))),f326(x99331,x99332,x99337,x99338)))+~P107(f866(f866(f336(f936(x99331,x99331)),f866(f866(f260(x99331,x99331),x99333),x99335)),x99337))
% 157.76/157.52 [10449]E(f866(f149(x104491,x104492,f866(f7(x104492,x104491,x104491),x104493),f866(x104494,x104495)),x104496),f866(x104494,f866(f149(x104497,x104492,f866(f7(x104492,x104497,x104497),x104498),x104495),x104496)))+P107(f866(f866(f336(x104492),f741(x104495,x104498,x104494,x104493,x104497,x104491,x104496,x104492)),f866(f179(x104492),x104496)))
% 157.76/157.52 [10468]~E(f866(f78(x104681,x104681,x104687,f866(x104683,f741(x104685,x104688,x104684,x104683,x104687,x104681,x104686,x104682))),x104684),f866(f78(x104687,x104681,x104687,x104684),f866(x104688,f741(x104685,x104688,x104684,x104683,x104687,x104681,x104686,x104682))))+E(f866(f149(x104681,x104682,f866(f7(x104682,x104681,x104681),x104683),f866(x104684,x104685)),x104686),f866(x104684,f866(f149(x104687,x104682,f866(f7(x104682,x104687,x104687),x104688),x104685),x104686)))
% 157.76/157.52 [8704]E(f866(x87041,f866(x87042,x87043)),f866(x87044,f866(x87045,x87043)))+~E(f866(f78(x87046,x87047,x87048,x87041),x87042),f866(f78(x87049,x87047,x87048,x87044),x87045))
% 157.76/157.52 [10306]P107(f866(f866(f336(f936(x103061,x103062)),f866(f866(f260(x103061,x103062),f866(x103063,x103064)),f866(x103065,x103066))),f866(f317(f936(x103067,x103068),f936(x103061,x103062),f266(x103067,x103061,x103068,x103062,x103063,x103065)),x103069)))+~P107(f866(f866(f336(f936(x103067,x103068)),f866(f866(f260(x103067,x103068),x103064),x103066)),x103069))
% 157.76/157.52 [9000]~E(f866(x90004,f866(x90005,x90006)),f866(x90009,f866(x900010,x900011)))+E(f866(f866(f78(x90001,x90002,x90003,x90004),x90005),x90006),f866(f866(f78(x90007,x90002,x90008,x90009),x900010),x900011))
% 157.76/157.52 [4822]~P110(x48221)+~P103(x48221)+E(f108(x48221),f241(x48221))
% 157.76/157.52 [4823]~P110(x48231)+~P102(x48231)+E(f117(x48231),f242(x48231))
% 157.76/157.52 [5075]~P128(x50751)+~P96(x50751)+E(f866(f81(x50751),f866(f110(x50751),a104)),f84(x50751))
% 157.76/157.52 [5360]E(x53601,f2(a1))+E(f88(a1,x53601),f866(f85(a1),f84(a1)))+P107(f866(f866(f244(a1),f2(a1)),x53601))
% 157.76/157.52 [5571]E(x55711,f2(a1))+E(f88(a1,x55711),f84(a1))+~P107(f866(f866(f244(a1),f2(a1)),x55711))
% 157.76/157.52 [7588]~P40(x75881)+P107(f866(f66(a1),x75881))+~P107(f866(f66(a930),f866(f317(a1,a930,a111),x75881)))
% 157.76/157.52 [9894]E(x98941,f195(f937(f936(a930,a930),a925)))+~P107(f866(f66(f936(a930,a930)),x98941))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f195(f937(f936(a930,a930),a925))),x98941)),a39))
% 157.76/157.52 [10058]E(x100581,f2(a930))+E(x100581,f866(a119,f2(a930)))+~P107(f866(f866(f244(a930),x100581),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.76/157.52 [10337]E(x103371,f2(a106))+E(f866(f866(f86(a1),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(a22,f866(f866(f41(a106),x103371),f866(f110(a106),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))),f84(a1)),f866(a22,x103371))+E(f50(a106,x103371,f866(f110(a106),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f2(a106))
% 157.76/157.52 [10186]E(x101861,f2(a106))+~E(f50(a106,x101861,f866(f110(a106),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f2(a106))+E(f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(a22,f866(f866(f41(a106),x101861),f866(f110(a106),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f866(a22,x101861))
% 157.76/157.52 [4903]~P59(x49031,x49032)+P43(x49031,x49032)+~P44(a925)
% 157.76/157.52 [4832]~P148(x48321)+P28(x48321,x48322)+~E(x48322,f2(x48321))
% 157.76/157.52 [4833]~P110(x48331)+P13(x48331,x48332)+~E(x48332,f120(x48331))
% 157.76/157.52 [4842]~P128(x48421)+~E(x48422,f2(x48421))+E(f88(x48421,x48422),f2(x48421))
% 157.76/157.52 [4843]~P93(x48431)+~E(x48432,f2(x48431))+E(f88(x48431,x48432),f2(x48431))
% 157.76/157.52 [4851]~P148(x48512)+~P28(x48512,x48511)+E(x48511,f2(x48512))
% 157.76/157.52 [4896]~P128(x48962)+~E(f88(x48962,x48961),f2(x48962))+E(x48961,f2(x48962))
% 157.76/157.52 [4910]~P4(x49102)+~P4(x49101)+P4(f937(x49101,x49102))
% 157.76/157.52 [4911]~P4(x49112)+~P4(x49111)+P4(f936(x49111,x49112))
% 157.76/157.52 [4912]~P4(x49122)+~P4(x49121)+P4(f938(x49121,x49122))
% 157.76/157.52 [4913]~P6(x49132)+~P6(x49131)+P6(f201(x49131,x49132))
% 157.76/157.52 [4914]~P64(x49142)+~P64(x49141)+P64(f937(x49141,x49142))
% 157.76/157.52 [4915]~P64(x49152)+~P64(x49151)+P64(f936(x49151,x49152))
% 157.76/157.52 [4916]~P64(x49162)+~P64(x49161)+P64(f938(x49161,x49162))
% 157.76/157.52 [4917]~P105(x49172)+~P105(x49171)+P105(f936(x49171,x49172))
% 157.76/157.52 [5047]~P110(x50471)+~P13(x50471,x50472)+P13(x50471,f159(x50471,x50472))
% 157.76/157.52 [5289]~P6(x52892)+~P6(x52891)+P6(f50(a1,x52891,x52892))
% 157.76/157.52 [4853]~P76(x48531)+~E(x48532,f2(x48531))+E(f866(f85(x48531),x48532),x48532)
% 157.76/157.52 [4868]~P142(x48681)+~E(x48682,f2(a1))+E(f866(f109(x48681),x48682),f2(x48681))
% 157.76/157.52 [4869]~P95(x48691)+~E(x48692,f2(a1))+E(f866(f109(x48691),x48692),f2(x48691))
% 157.76/157.52 [4893]~P77(x48931)+~E(f2(x48931),x48932)+E(f866(f85(x48931),x48932),f2(x48931))
% 157.76/157.52 [4894]~P89(x48941)+~E(x48942,f2(x48941))+E(f866(f81(x48941),x48942),f2(x48941))
% 157.76/157.52 [4895]~P77(x48951)+~E(x48952,f2(x48951))+E(f866(f85(x48951),x48952),f2(x48951))
% 157.76/157.52 [4919]~P76(x49192)+E(x49191,f2(x49192))+~E(f866(f85(x49192),x49191),x49191)
% 157.76/157.52 [4927]E(x49271,f866(a111,x49272))+~E(x49271,f2(a930))+~E(x49272,f866(f107(a1),x49271))
% 157.76/157.52 [4928]E(f866(a111,x49281),x49282)+~E(x49282,f2(a930))+~E(x49281,f866(f107(a1),x49282))
% 157.76/157.52 [4932]~P95(x49322)+E(x49321,f2(a1))+~E(f866(f109(x49322),x49321),f2(x49322))
% 157.76/157.52 [4936]~P89(x49362)+E(x49361,f2(x49362))+~E(f866(f81(x49362),x49361),f2(x49362))
% 157.76/157.52 [4937]~P77(x49372)+E(x49371,f2(x49372))+~E(f866(f85(x49372),x49371),f2(x49372))
% 157.76/157.52 [4938]~P77(x49381)+E(f2(x49381),x49382)+~E(f866(f85(x49381),x49382),f2(x49381))
% 157.76/157.52 [5122]~P110(x51221)+~P13(x51221,x51222)+P13(x51221,f866(f178(x51221),x51222))
% 157.76/157.52 [5149]~P107(x51492)+~P107(x51491)+P107(f866(f866(a333,x51491),x51492))
% 157.76/157.52 [5183]~E(f84(a930),f2(a930))+E(f866(f40(x51831),x51832),f2(a930))+~P107(f866(f66(x51831),x51832))
% 157.76/157.52 [5219]~P116(x52191)+~P147(x52191)+E(f866(f866(f252(x52191),f2(x52191)),f866(a119,x52192)),f2(x52191))
% 157.76/157.52 [5257]~P110(x52571)+P13(x52571,f146(x52571,x52572))+~P107(f866(f66(x52571),x52572))
% 157.76/157.52 [5258]~P110(x52581)+P13(x52581,f733(x52582,x52581))+~P107(f866(f66(x52581),x52582))
% 157.76/157.52 [5281]~P110(x52811)+E(f866(f179(x52811),f146(x52811,x52812)),x52812)+~P107(f866(f66(x52811),x52812))
% 157.76/157.52 [5282]~P110(x52821)+E(f866(f179(x52821),f733(x52822,x52821)),x52822)+~P107(f866(f66(x52821),x52822))
% 157.76/157.52 [5310]P107(x53101)+P107(x53102)+~P107(f866(f866(a334,x53102),x53101))
% 157.76/157.52 [5323]E(x53231,f195(f937(x53232,a925)))+~E(f866(f40(x53232),x53231),f2(a930))+~P107(f866(f66(x53232),x53231))
% 157.76/157.52 [5328]P107(x53281)+~P107(x53282)+~P107(f866(f866(a337,x53282),x53281))
% 157.76/157.52 [5379]~P75(x53791)+E(f866(f81(x53791),x53792),x53792)+P107(f866(f866(f244(x53791),x53792),f2(x53791)))
% 157.76/157.52 [5439]~P64(x54392)+~P107(f866(f61(x54392),x54391))+P107(f866(x54391,f734(x54391,x54392)))
% 157.76/157.52 [5440]~P64(x54402)+~P107(f866(f61(x54402),x54401))+P107(f866(x54401,f742(x54401,x54402)))
% 157.76/157.52 [5483]E(x54831,f120(x54832))+P107(f866(f144(x54832),f121(x54832,x54831)))+~P107(f866(f144(x54832),x54831))
% 157.76/157.52 [5488]~P110(x54881)+~P107(f866(f66(x54881),x54882))+P107(f866(f144(x54881),f146(x54881,x54882)))
% 157.76/157.52 [5489]~P110(x54891)+~P107(f866(f66(x54891),x54892))+P107(f866(f144(x54891),f733(x54892,x54891)))
% 157.76/157.52 [5494]~P142(x54941)+E(f866(f107(x54941),f866(a111,x54942)),f866(f109(x54941),x54942))+P107(f866(f866(f244(a1),x54942),f2(a1)))
% 157.76/157.52 [5521]P7(x55212,x55211)+E(f866(x55211,f451(x55211)),f866(x55211,f512(x55211)))+P107(f866(f866(x55211,f451(x55211)),f512(x55211)))
% 157.76/157.52 [5533]E(f866(f107(a1),f430(x55331,x55332)),x55331)+P107(f866(x55332,f866(a111,x55331)))+~P107(f866(x55332,f2(a930)))
% 157.76/157.52 [5545]~P64(x55451)+~P107(f866(x55452,f747(x55452,x55451)))+P107(f866(f62(x55451),x55452))
% 157.76/157.52 [5546]~P64(x55461)+~P107(f866(x55462,f757(x55462,x55461)))+P107(f866(f62(x55461),x55462))
% 157.76/157.52 [5581]~P128(x55811)+~E(f88(x55811,x55812),f866(f85(x55811),f84(x55811)))+P107(f866(f866(f244(x55811),x55812),f2(x55811)))
% 157.76/157.52 [5654]~E(x56542,f2(a1))+E(f224(x56541,x56542),f866(f866(f260(a1,a1),f2(a1)),f84(a1)))+P107(f866(f866(f244(a1),x56542),f2(a1)))
% 157.76/157.52 [5655]~E(x56551,f2(a1))+E(f224(x56551,x56552),f866(f866(f260(a1,a1),f2(a1)),f84(a1)))+P107(f866(f866(f244(a1),x56552),f2(a1)))
% 157.76/157.52 [5707]E(f866(f107(a1),f430(x57071,x57072)),x57071)+P107(f866(x57072,f866(a111,x57071)))+P107(f866(f866(f244(a1),x57071),f2(a1)))
% 157.76/157.52 [5774]~P128(x57741)+E(f88(x57741,x57742),f866(f85(x57741),f84(x57741)))+~P107(f866(f866(f244(x57741),x57742),f2(x57741)))
% 157.76/157.52 [5775]~P89(x57751)+E(f866(f81(x57751),x57752),f866(f85(x57751),x57752))+~P107(f866(f866(f243(x57751),x57752),f2(x57751)))
% 157.76/157.52 [5776]~P89(x57761)+E(f866(f81(x57761),x57762),f866(f85(x57761),x57762))+~P107(f866(f866(f244(x57761),x57762),f2(x57761)))
% 157.76/157.52 [5777]~P75(x57771)+E(f866(f81(x57771),x57772),f866(f85(x57771),x57772))+~P107(f866(f866(f244(x57771),x57772),f2(x57771)))
% 157.76/157.52 [5883]~P107(f866(x58831,f430(x58832,x58831)))+P107(f866(x58831,f866(a111,x58832)))+~P107(f866(x58831,f2(a930)))
% 157.76/157.52 [5890]E(x58901,f2(a930))+E(f866(a119,f901(x58902,x58901)),x58901)+~P107(f866(f866(f244(a930),x58901),f866(a119,x58902)))
% 157.76/157.52 [5894]P7(x58941,x58942)+~E(f866(x58942,f451(x58942)),f866(x58942,f512(x58942)))+~P107(f866(f866(x58942,f451(x58942)),f512(x58942)))
% 157.76/157.52 [5912]~P110(x59121)+P13(x59121,x59122)+P107(f866(f866(f243(a930),f716(x59122,x59121)),f717(x59122,x59121)))
% 157.76/157.52 [5913]~P110(x59131)+P13(x59131,x59132)+P107(f866(f866(f243(a930),f724(x59132,x59131)),f728(x59132,x59131)))
% 157.76/157.52 [6001]~P89(x60011)+~E(x60012,f2(x60011))+P107(f866(f866(f243(x60011),f866(f81(x60011),x60012)),f2(x60011)))
% 157.76/157.52 [6089]~P107(f866(x60891,f430(x60892,x60891)))+P107(f866(x60891,f866(a111,x60892)))+P107(f866(f866(f244(a1),x60892),f2(a1)))
% 157.76/157.52 [6116]~P107(f866(x61161,f866(a111,x61162)))+P107(f866(x61161,f2(a930)))+~P107(f866(f866(f244(a1),x61162),f2(a1)))
% 157.76/157.52 [6456]~P128(x64561)+~P107(f866(f866(f244(x64561),x64562),f2(x64561)))+P107(f866(f866(f244(x64561),f88(x64561,x64562)),f2(x64561)))
% 157.76/157.52 [6570]~P128(x65701)+P107(f866(f866(f243(x65701),f866(f109(x65701),x65702)),f2(x65701)))+~P107(f866(f866(f243(a1),x65702),f2(a1)))
% 157.76/157.52 [6571]~P128(x65711)+P107(f866(f866(f244(x65711),f866(f109(x65711),x65712)),f2(x65711)))+~P107(f866(f866(f244(a1),x65712),f2(a1)))
% 157.76/157.52 [6581]~P89(x65812)+E(x65811,f2(x65812))+~P107(f866(f866(f243(x65812),f866(f81(x65812),x65811)),f2(x65812)))
% 157.76/157.52 [6659]~P142(x66591)+~P107(f866(f866(f336(x66591),x66592),f116(x66591)))+P107(f866(f866(f336(x66591),f866(f85(x66591),x66592)),f116(x66591)))
% 157.76/157.52 [6694]~P128(x66941)+~P107(f866(f866(f244(x66941),f88(x66941,x66942)),f2(x66941)))+P107(f866(f866(f244(x66941),x66942),f2(x66941)))
% 157.76/157.52 [6867]~P128(x68672)+~P107(f866(f866(f243(x68672),f866(f109(x68672),x68671)),f2(x68672)))+P107(f866(f866(f243(a1),x68671),f2(a1)))
% 157.76/157.52 [6868]~P128(x68682)+~P107(f866(f866(f244(x68682),f866(f109(x68682),x68681)),f2(x68682)))+P107(f866(f866(f244(a1),x68681),f2(a1)))
% 157.76/157.52 [7364]~P76(x73641)+~P107(f866(f866(f243(x73641),x73642),f2(x73641)))+P107(f866(f866(f243(x73641),f866(f866(f86(x73641),x73642),x73642)),f2(x73641)))
% 157.76/157.52 [7366]~P76(x73661)+~P107(f866(f866(f244(x73661),x73662),f2(x73661)))+P107(f866(f866(f244(x73661),f866(f866(f86(x73661),x73662),x73662)),f2(x73661)))
% 157.76/157.52 [7367]~P128(x73671)+~P107(f866(f866(f244(x73671),x73672),f2(x73671)))+P107(f866(f866(f244(x73671),f866(f866(f86(x73671),x73672),x73672)),f2(x73671)))
% 157.76/157.52 [7929]~P76(x79291)+~P107(f866(f866(f243(x79291),f866(f866(f86(x79291),x79292),x79292)),f2(x79291)))+P107(f866(f866(f243(x79291),x79292),f2(x79291)))
% 157.76/157.52 [7930]~P76(x79301)+~P107(f866(f866(f244(x79301),f866(f866(f86(x79301),x79302),x79302)),f2(x79301)))+P107(f866(f866(f244(x79301),x79302),f2(x79301)))
% 157.76/157.52 [7931]~P128(x79311)+~P107(f866(f866(f244(x79311),f866(f866(f86(x79311),x79312),x79312)),f2(x79311)))+P107(f866(f866(f244(x79311),x79312),f2(x79311)))
% 157.76/157.52 [4973]~E(x49732,f84(a930))+~E(x49731,f84(a930))+E(f866(f866(f87(a930),x49731),x49732),f84(a930))
% 157.76/157.52 [4974]~E(x49742,f84(a1))+~E(x49741,f84(a1))+E(f866(f866(f87(a1),x49741),x49742),f84(a1))
% 157.76/157.52 [4975]~E(x49752,f2(a930))+~E(x49751,f2(a930))+E(f866(f866(f86(a930),x49751),x49752),f2(a930))
% 157.76/157.52 [5031]~P62(x50312)+E(x50311,f2(x50312))+E(f866(f866(f41(x50312),x50311),x50311),f84(x50312))
% 157.76/157.52 [5032]~P125(x50322)+E(x50321,f2(x50322))+E(f866(f866(f297(x50322),x50321),x50321),f84(x50322))
% 157.76/157.52 [5033]~P126(x50332)+E(x50331,f2(x50332))+E(f866(f866(f297(x50332),x50331),x50331),f84(x50332))
% 157.76/157.52 [5053]~P143(x50531)+~E(x50532,f84(x50531))+E(f866(f866(f87(x50531),x50532),x50532),f84(x50531))
% 157.76/157.52 [5054]~P76(x50541)+~E(x50542,f2(x50541))+E(f866(f866(f86(x50541),x50542),x50542),f2(x50541))
% 157.76/157.52 [5055]~P126(x50551)+~E(x50552,f2(x50551))+E(f866(f866(f297(x50551),x50552),x50552),f2(x50551))
% 157.76/157.52 [5100]~E(x51002,f2(a930))+~E(x51001,f2(a930))+E(f866(f85(a1),f866(f107(a1),x51001)),f866(f107(a1),x51002))
% 157.76/157.52 [5119]E(x51191,f84(a930))+E(x51192,f2(a930))+~E(f866(f866(f87(a930),x51192),x51191),x51192)
% 157.76/157.52 [5131]E(x51311,f2(a930))+E(x51312,f2(a930))+~E(f866(f866(f87(a930),x51312),x51311),f2(a930))
% 157.76/157.52 [5158]~E(x51582,f2(a930))+~E(x51581,f866(a119,f2(a930)))+E(f866(f866(f86(a930),x51581),x51582),f866(a119,f2(a930)))
% 157.76/157.52 [5159]~E(x51591,f2(a930))+~E(x51592,f866(a119,f2(a930)))+E(f866(f866(f86(a930),x51591),x51592),f866(a119,f2(a930)))
% 157.76/157.52 [5166]E(x51661,f84(a1))+E(x51662,f866(f110(a1),a104))+~E(f866(f866(f87(a1),x51661),x51662),f84(a1))
% 157.76/157.52 [5167]E(x51671,f84(a1))+E(x51672,f866(f110(a1),a104))+~E(f866(f866(f87(a1),x51672),x51671),f84(a1))
% 157.76/157.52 [5168]E(x51681,f84(a1))+E(x51681,f866(f110(a1),a104))+~E(f866(f866(f87(a1),x51682),x51681),f84(a1))
% 157.76/157.52 [5170]E(x51701,f84(a1))+E(x51701,f866(f110(a1),a104))+~E(f866(f866(f87(a1),x51701),x51702),f84(a1))
% 157.76/157.52 [5191]~P76(x51912)+E(x51911,f2(x51912))+~E(f866(f866(f86(x51912),x51911),x51911),f2(x51912))
% 157.76/157.52 [5197]~E(x51971,f866(f110(a1),a104))+~E(x51972,f866(f110(a1),a104))+E(f866(f866(f87(a1),x51971),x51972),f84(a1))
% 157.76/157.52 [5208]E(x52081,f2(a930))+E(x52082,f2(a930))+~E(f866(f866(f86(a930),x52082),x52081),f866(a119,f2(a930)))
% 157.76/157.52 [5218]~P65(x52181)+~P96(x52181)+E(f866(f866(f297(x52181),x52182),f866(f110(x52181),a89)),f2(x52181))
% 157.76/157.52 [5224]~P143(x52241)+~E(x52242,f866(f85(x52241),f84(x52241)))+E(f866(f866(f87(x52241),x52242),x52242),f84(x52241))
% 157.76/157.52 [5229]~P6(x52292)+~P6(x52291)+P6(f866(f866(f87(a1),x52291),x52292))
% 157.76/157.52 [5230]~P6(x52302)+~P6(x52301)+P6(f866(f866(f86(a1),x52301),x52302))
% 157.76/157.52 [5231]~P6(x52312)+~P6(x52311)+P6(f866(f866(f41(a1),x52311),x52312))
% 157.76/157.52 [5233]~E(x52332,f2(a1))+E(x52331,f2(a1))+E(f51(x52331,x52332),f866(f866(f260(a1,a1),f2(a1)),x52331))
% 157.76/157.52 [5255]~E(x52552,f866(a119,f2(a930)))+~E(x52551,f866(a119,f2(a930)))+E(f866(f866(f87(a930),x52551),x52552),f866(a119,f2(a930)))
% 157.76/157.52 [5272]E(x52721,f2(a930))+E(x52722,f866(a119,f2(a930)))+~E(f866(f866(f252(a930),x52722),x52721),f866(a119,f2(a930)))
% 157.76/157.52 [5273]E(x52731,f2(a930))+E(x52731,f866(a119,f2(a930)))+~E(f866(f866(f86(a930),x52732),x52731),f866(a119,f2(a930)))
% 157.76/157.52 [5274]E(x52741,f2(a930))+E(x52741,f866(a119,f2(a930)))+~E(f866(f866(f86(a930),x52741),x52742),f866(a119,f2(a930)))
% 157.76/157.52 [5283]~P65(x52831)+~P96(x52831)+E(f866(f866(f297(x52831),x52832),f866(f110(x52831),a104)),f866(f85(x52831),x52832))
% 157.76/157.52 [5302]E(x53021,f866(a111,x53022))+~E(x53021,f2(a930))+P107(f866(f866(f243(a1),f2(a1)),x53022))
% 157.76/157.52 [5303]E(f866(a111,x53031),x53032)+~E(x53032,f2(a930))+P107(f866(f866(f243(a1),f2(a1)),x53031))
% 157.76/157.52 [5319]E(x53191,f866(a119,f2(a930)))+E(x53192,f866(a119,f2(a930)))+~E(f866(f866(f86(a930),x53191),x53192),f866(a119,f2(a930)))
% 157.76/157.52 [5330]~E(x53301,f866(a111,x53302))+E(x53301,f2(a930))+P107(f866(f866(f243(a1),f2(a1)),x53302))
% 157.76/157.52 [5331]~E(f866(a111,x53312),x53311)+E(x53311,f2(a930))+P107(f866(f866(f243(a1),f2(a1)),x53312))
% 157.76/157.52 [5353]~P83(x53531)+E(f866(f68(x53531,f117(x53531)),x53532),f13(x53531,x53532))+~P107(f866(f66(x53531),x53532))
% 157.76/157.52 [5354]~P83(x53541)+E(f866(f68(x53541,f108(x53541)),x53542),f10(x53541,x53542))+~P107(f866(f66(x53541),x53542))
% 157.76/157.52 [5355]~P110(x53551)+E(f866(f68(x53551,f242(x53551)),x53552),f14(x53551,x53552))+~P107(f866(f66(x53551),x53552))
% 157.76/157.52 [5356]~P110(x53561)+E(f866(f68(x53561,f241(x53561)),x53562),f15(x53561,x53562))+~P107(f866(f66(x53561),x53562))
% 157.76/157.52 [5434]E(x54341,x54342)+~E(f866(f866(f23(a930),x54342),x54341),f2(a930))+~E(f866(f866(f23(a930),x54341),x54342),f2(a930))
% 157.76/157.52 [5452]P6(x54521)+~P40(x54522)+~P107(f866(f866(f336(a1),x54521),x54522))
% 157.76/157.52 [5484]~P128(x54841)+~E(f88(x54841,x54842),f84(x54841))+P107(f866(f866(f244(x54841),f2(x54841)),x54842))
% 157.76/157.52 [5495]~P96(x54951)+E(f866(f107(x54951),f866(f110(a930),x54952)),f866(f110(x54951),x54952))+P107(f866(a200,f866(f110(a1),x54952)))
% 157.76/157.52 [5500]~P43(x55001,x55002)+P44(a925)+P107(f866(f66(f936(x55001,x55001)),x55002))
% 157.76/157.52 [5573]~P110(x55731)+E(f866(f68(x55731,f241(x55731)),x55732),f11(x55731,f241(x55731),x55732))+~P107(f866(f66(x55731),x55732))
% 157.76/157.52 [5574]~P110(x55741)+E(f866(f68(x55741,f242(x55741)),x55742),f12(x55741,f242(x55741),x55742))+~P107(f866(f66(x55741),x55742))
% 157.76/157.52 [5588]E(x55881,x55882)+P107(f866(f866(f244(a930),x55882),x55881))+P107(f866(f866(f244(a930),x55881),x55882))
% 157.76/157.52 [5589]E(x55891,x55892)+P107(f866(f866(f244(a1),x55892),x55891))+P107(f866(f866(f244(a1),x55891),x55892))
% 157.76/157.52 [5641]~P96(x56411)+E(f866(f107(x56411),f866(f110(a930),x56412)),f2(x56411))+~P107(f866(a200,f866(f110(a1),x56412)))
% 157.76/157.52 [5644]~E(x56442,f866(a111,x56441))+E(x56441,f866(f107(a1),x56442))+~P107(f866(f866(f243(a1),f2(a1)),x56441))
% 157.76/157.52 [5645]~E(f866(a111,x56451),x56452)+E(x56451,f866(f107(a1),x56452))+~P107(f866(f866(f243(a1),f2(a1)),x56451))
% 157.76/157.52 [5646]~E(x56461,f866(a111,x56462))+E(f866(f107(a1),x56461),x56462)+~P107(f866(f866(f243(a1),f2(a1)),x56462))
% 157.76/157.52 [5656]E(x56561,f866(a111,x56562))+~E(x56562,f866(f107(a1),x56561))+~P107(f866(f866(f243(a1),f2(a1)),x56562))
% 157.76/157.52 [5657]E(f866(a111,x56571),x56572)+~E(x56571,f866(f107(a1),x56572))+~P107(f866(f866(f243(a1),f2(a1)),x56571))
% 157.76/157.52 [5698]~P89(x56982)+E(x56981,f2(x56982))+P107(f866(f866(f244(x56982),f2(x56982)),f866(f81(x56982),x56981)))
% 157.76/157.52 [5763]~P128(x57631)+E(f88(x57631,x57632),f84(x57631))+~P107(f866(f866(f244(x57631),f2(x57631)),x57632))
% 157.76/157.52 [5767]~P96(x57671)+E(f866(f107(x57671),f866(f110(a930),x57672)),f2(x57671))+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x57672)))
% 157.76/157.52 [5778]~P89(x57781)+E(f866(f81(x57781),x57782),x57782)+~P107(f866(f866(f243(x57781),f2(x57781)),x57782))
% 157.76/157.52 [5779]~P89(x57791)+E(f866(f81(x57791),x57792),x57792)+~P107(f866(f866(f244(x57791),f2(x57791)),x57792))
% 157.76/157.52 [5788]E(x57881,f2(a930))+~E(f146(a930,f866(f309(a930,x57882),x57881)),f120(a930))+P107(f866(f866(f243(a930),x57881),x57882))
% 157.76/157.52 [5801]~P72(x58011)+E(f866(f866(f6(x58011,x58011),f5(x58011)),f866(f179(x58011),x58012)),f866(f172(x58011),x58012))+~P107(f866(f144(x58011),x58012))
% 157.76/157.52 [5804]~P142(x58041)+E(f866(f107(x58041),f866(a111,x58042)),f866(f109(x58041),x58042))+~P107(f866(f866(f243(a1),f2(a1)),x58042))
% 157.76/157.52 [5832]E(x58321,x58322)+P107(f866(f866(f244(a930),x58321),x58322))+~P107(f866(f866(f243(a930),x58321),x58322))
% 157.76/157.52 [5833]E(x58331,x58332)+P107(f866(f866(f244(a1),x58331),x58332))+~P107(f866(f866(f243(a1),x58331),x58332))
% 157.76/157.52 [5836]E(x58361,f84(a1))+~E(f866(f866(f87(a1),x58362),x58361),f84(a1))+~P107(f866(f866(f244(a1),f2(a1)),x58362))
% 157.76/157.52 [5837]E(x58371,f84(a1))+~E(f866(f866(f87(a1),x58371),x58372),f84(a1))+~P107(f866(f866(f244(a1),f2(a1)),x58371))
% 157.76/157.52 [5880]~P40(x58802)+P107(f866(f866(f243(a1),f2(a1)),x58801))+~P107(f866(f866(f336(a1),x58801),x58802))
% 157.76/157.52 [5899]~P59(x58991,x58992)+P37(x58991,x58992)+~P107(f866(f66(f936(x58991,x58991)),x58992))
% 157.76/157.52 [5901]~P59(x59011,x59012)+P43(x59011,x59012)+~P107(f866(f66(f936(x59011,x59011)),x59012))
% 157.76/157.52 [5945]E(x59451,f195(f937(x59452,a925)))+~P107(f866(f66(x59452),x59451))+P107(f866(f866(f244(a930),f2(a930)),f866(f40(x59452),x59451)))
% 157.76/157.52 [5972]~P107(f866(x59721,x59722))+P107(f866(x59721,f2(a930)))+P107(f866(f866(f244(a930),f906(x59722,x59721)),x59722))
% 157.76/157.52 [5995]E(x59951,f2(a930))+~E(f866(f172(a930),x59952),f2(a930))+~P107(f866(f866(f336(a930),x59951),f866(f179(a930),x59952)))
% 157.76/157.52 [6063]E(x60631,x60632)+~P107(f866(f866(f243(a930),x60632),x60631))+~P107(f866(f866(f243(a930),x60631),x60632))
% 157.76/157.52 [6064]E(x60641,x60642)+~P107(f866(f866(f243(a1),x60642),x60641))+~P107(f866(f866(f243(a1),x60641),x60642))
% 157.76/157.52 [6066]E(f866(f40(x60661),x60662),f2(a930))+~P107(f866(f66(x60661),x60662))+P107(f866(f866(f336(x60661),f482(x60662,x60661)),x60662))
% 157.76/157.52 [6075]E(f55(x60751,x60752),f51(x60751,x60752))+P107(f866(f866(f243(a1),f2(a1)),x60751))+~P107(f866(f866(f244(a1),f2(a1)),x60752))
% 157.76/157.52 [6103]~P107(f866(x61031,f427(x61031)))+P107(f866(x61031,f866(a111,x61032)))+~P107(f866(f866(f243(a1),f2(a1)),x61032))
% 157.76/157.52 [6106]P107(f866(f866(f243(a930),x61061),f759(x61062)))+~P107(f866(f66(a930),x61062))+~P107(f866(f866(f336(a930),x61061),x61062))
% 157.76/157.52 [6107]P107(f866(f866(f244(a930),x61071),f804(x61072)))+~P107(f866(f66(a930),x61072))+~P107(f866(f866(f336(a930),x61071),x61072))
% 157.76/157.52 [6139]E(x61391,x61392)+~P107(f866(f866(f244(a930),x61391),f866(a119,x61392)))+P107(f866(f866(f244(a930),x61391),x61392))
% 157.76/157.52 [6171]E(x61711,f866(a119,x61712))+~P107(f866(f866(f243(a930),x61711),f866(a119,x61712)))+P107(f866(f866(f243(a930),x61711),x61712))
% 157.76/157.52 [6187]P107(f866(x61871,f428(x61871)))+~P107(f866(x61871,f866(a111,x61872)))+~P107(f866(f866(f243(a1),f2(a1)),x61872))
% 157.76/157.52 [6202]~P107(f866(x62021,x62022))+~P107(f866(f866(f243(a1),f2(a1)),x62022))+P107(f866(x62021,f866(f107(a1),f399(x62021))))
% 157.76/157.52 [6213]~P89(x62132)+~E(x62131,f2(x62132))+~P107(f866(f866(f244(x62132),f2(x62132)),f866(f81(x62132),x62131)))
% 157.76/157.52 [6237]~P59(x62371,x62372)+P37(x62371,f866(f294(x62371,x62371),x62372))+~P107(f866(f66(f936(x62371,x62371)),x62372))
% 157.76/157.52 [6238]~P57(a930,x62381,x62382)+~P107(f866(f866(f244(a930),f2(a930)),x62382))+P107(f866(f866(f243(a930),x62381),x62382))
% 157.76/157.52 [6246]~P96(x62461)+E(f866(f107(x62461),f866(f110(a930),x62462)),f866(f110(x62461),x62462))+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x62462)))
% 157.76/157.52 [6249]E(f866(a119,x62491),x62492)+~P107(f866(f866(f244(a930),x62491),x62492))+P107(f866(f866(f244(a930),f866(a119,x62491)),x62492))
% 157.76/157.52 [6268]E(f866(f866(f41(a1),x62681),x62682),f2(a1))+~P107(f866(f866(f243(a1),x62681),f2(a1)))+~P107(f866(f866(f244(a1),x62682),x62681))
% 157.76/157.52 [6278]E(f50(a1,x62781,x62782),x62781)+~P107(f866(f866(f243(a1),x62781),f2(a1)))+~P107(f866(f866(f244(a1),x62782),x62781))
% 157.76/157.52 [6292]E(f52(x62921,x62922),f51(x62921,x62922))+~P107(f866(f866(f243(a1),f2(a1)),x62921))+~P107(f866(f866(f243(a1),f2(a1)),x62922))
% 157.76/157.52 [6302]E(f866(f866(f41(a1),x63021),x63022),f2(a1))+~P107(f866(f866(f243(a1),f2(a1)),x63021))+~P107(f866(f866(f244(a1),x63021),x63022))
% 157.76/157.52 [6311]E(f50(a930,f866(f110(a930),x63111),f866(f110(a930),x63112)),f866(f110(a930),x63111))+P107(f866(a200,f866(f110(a1),x63111)))+~P107(f866(a200,f866(f110(a1),x63112)))
% 157.76/157.52 [6313]E(f50(a1,x63131,x63132),x63131)+~P107(f866(f866(f243(a1),f2(a1)),x63131))+~P107(f866(f866(f244(a1),x63131),x63132))
% 157.76/157.52 [6314]E(x63141,x63142)+~P107(f866(f866(f244(a930),x63141),f866(a119,x63142)))+~P107(f866(f866(f243(a930),x63142),x63141))
% 157.76/157.52 [6328]~P76(x63281)+~P107(f866(f866(f243(x63281),x63282),f2(x63281)))+P107(f866(f866(f243(x63281),x63282),f866(f85(x63281),x63282)))
% 157.76/157.52 [6329]~P128(x63291)+~P107(f866(f866(f244(x63291),x63292),f2(x63291)))+P107(f866(f866(f244(x63291),x63292),f866(f85(x63291),x63292)))
% 157.76/157.52 [6338]~P5(x63381)+E(f866(f866(f69(x63381,x63381,f108(x63381)),f250(x63381)),x63382),f43(x63381,x63382))+~P107(f866(f66(x63381),x63382))
% 157.76/157.52 [6339]~P5(x63391)+E(f866(f866(f69(x63391,x63391,f117(x63391)),f195(x63391)),x63392),f42(x63391,x63392))+~P107(f866(f66(x63391),x63392))
% 157.76/157.52 [6356]~P128(x63561)+~P107(f866(f866(f243(a1),f2(a1)),x63562))+P107(f866(f866(f243(x63561),f2(x63561)),f866(f109(x63561),x63562)))
% 157.76/157.52 [6357]~P113(x63571)+~P107(f866(f866(f244(a930),f2(a930)),x63572))+P107(f866(f866(f244(x63571),f2(x63571)),f866(f107(x63571),x63572)))
% 157.76/157.52 [6358]~P128(x63581)+~P107(f866(f866(f244(a1),f2(a1)),x63582))+P107(f866(f866(f244(x63581),f2(x63581)),f866(f109(x63581),x63582)))
% 157.76/157.52 [6361]~P6(x63612)+~P6(x63611)+E(f866(f317(a930,a1,f107(a1)),f310(a930,f866(a111,x63611),f866(a111,x63612))),f310(a1,x63611,x63612))
% 157.76/157.52 [6367]P107(f866(x63671,x63672))+~P107(f866(f866(f243(a1),f2(a1)),x63672))+~P107(f866(x63671,f866(f107(a1),f409(x63671))))
% 157.76/157.52 [6396]E(f866(f866(f86(a930),f866(f110(a930),x63961)),f866(f110(a930),x63962)),f866(f110(a930),x63961))+P107(f866(f866(f244(a1),x63961),a89))+~P107(f866(f866(f244(a1),x63962),a89))
% 157.76/157.52 [6400]~P128(x64001)+P107(f866(f866(f244(x64001),f2(x64001)),f88(x64001,x64002)))+~P107(f866(f866(f244(x64001),f2(x64001)),x64002))
% 157.76/157.52 [6412]~P79(x64121)+~P107(f866(f866(f243(x64121),x64122),f2(x64121)))+P107(f866(f866(f243(x64121),f2(x64121)),f866(f85(x64121),x64122)))
% 157.76/157.52 [6413]~P79(x64131)+~P107(f866(f866(f244(x64131),x64132),f2(x64131)))+P107(f866(f866(f244(x64131),f2(x64131)),f866(f85(x64131),x64132)))
% 157.76/157.52 [6416]E(x64161,f250(f937(x64162,a925)))+~E(f866(f40(x64162),x64161),f866(f40(x64162),f250(f937(x64162,a925))))+~P107(f866(f66(x64162),f250(f937(x64162,a925))))
% 157.76/157.52 [6448]~P76(x64481)+P107(f866(f866(f243(x64481),x64482),f2(x64481)))+~P107(f866(f866(f243(x64481),x64482),f866(f85(x64481),x64482)))
% 157.76/157.52 [6449]~P128(x64491)+P107(f866(f866(f244(x64491),x64492),f2(x64491)))+~P107(f866(f866(f244(x64491),x64492),f866(f85(x64491),x64492)))
% 157.76/157.52 [6458]~P96(x64581)+P107(f866(f866(f336(x64581),f866(f110(x64581),x64582)),f193(x64581)))+~P107(f866(f866(f243(a1),a89),x64582))
% 157.76/157.52 [6487]E(x64871,f2(a930))+~P107(f866(f866(f244(a930),x64871),f866(a119,x64872)))+P107(f866(f866(f244(a930),f901(x64872,x64871)),x64872))
% 157.76/157.52 [6510]~P128(x65101)+~P107(f866(f866(f244(x65101),f2(x65101)),f88(x65101,x65102)))+P107(f866(f866(f244(x65101),f2(x65101)),x65102))
% 157.76/157.52 [6512]~E(f866(f110(a930),x65122),f866(f110(a930),x65121))+P107(f866(f866(f243(a1),f866(f110(a1),x65121)),f2(a1)))+~P107(f866(a200,f866(f110(a1),x65122)))
% 157.76/157.52 [6541]E(f866(f259(a1,a1),f55(x65411,x65412)),f866(f866(f41(a1),x65411),x65412))+~P107(f866(f866(f244(a1),x65411),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x65412))
% 157.76/157.52 [6578]E(f866(f264(a1,a1),f55(x65781,x65782)),f50(a1,x65781,x65782))+~P107(f866(f866(f244(a1),x65781),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x65782))
% 157.76/157.52 [6582]~P128(x65822)+~P107(f866(f866(f243(x65822),f2(x65822)),f866(f109(x65822),x65821)))+P107(f866(f866(f243(a1),f2(a1)),x65821))
% 157.76/157.52 [6583]~P113(x65832)+~P107(f866(f866(f244(x65832),f2(x65832)),f866(f107(x65832),x65831)))+P107(f866(f866(f244(a930),f2(a930)),x65831))
% 157.76/157.52 [6584]~P128(x65842)+~P107(f866(f866(f244(x65842),f2(x65842)),f866(f109(x65842),x65841)))+P107(f866(f866(f244(a1),f2(a1)),x65841))
% 157.76/157.52 [6588]E(f866(f259(a1,a1),f52(x65881,x65882)),f866(f866(f41(a1),x65881),x65882))+~P107(f866(f866(f243(a1),f2(a1)),x65882))+~P107(f866(f866(f244(a1),f2(a1)),x65881))
% 157.76/157.52 [6602]E(f866(f264(a1,a1),f52(x66021,x66022)),f50(a1,x66021,x66022))+~P107(f866(f866(f243(a1),f2(a1)),x66022))+~P107(f866(f866(f244(a1),f2(a1)),x66021))
% 157.76/157.52 [6617]~P79(x66171)+P107(f866(f866(f243(x66171),x66172),f2(x66171)))+~P107(f866(f866(f243(x66171),f2(x66171)),f866(f85(x66171),x66172)))
% 157.76/157.52 [6618]~P79(x66181)+P107(f866(f866(f244(x66181),x66182),f2(x66181)))+~P107(f866(f866(f244(x66181),f2(x66181)),f866(f85(x66181),x66182)))
% 157.76/157.52 [6647]P107(f866(f54(x66471,x66472),f55(x66471,x66472)))+~P107(f866(f866(f244(a1),x66471),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x66472))
% 157.76/157.52 [6671]P107(f866(f54(x66711,x66712),f52(x66711,x66712)))+~P107(f866(f866(f243(a1),f2(a1)),x66711))+~P107(f866(f866(f244(a1),f2(a1)),x66712))
% 157.76/157.52 [6717]~P79(x67171)+P107(f866(f866(f243(x67171),f866(f85(x67171),x67172)),f2(x67171)))+~P107(f866(f866(f243(x67171),f2(x67171)),x67172))
% 157.76/157.52 [6718]~P79(x67181)+P107(f866(f866(f244(x67181),f866(f85(x67181),x67182)),f2(x67181)))+~P107(f866(f866(f244(x67181),f2(x67181)),x67182))
% 157.76/157.52 [6734]E(f866(f866(f23(a930),f866(a111,x67341)),f866(a111,x67342)),f866(a111,f201(x67341,x67342)))+~P107(f866(f866(f243(a1),f2(a1)),x67342))+~P107(f866(f866(f243(a1),f2(a1)),x67341))
% 157.76/157.52 [6752]P107(f866(f866(f243(a1),f2(a1)),f201(x67521,x67522)))+~P107(f866(f866(f243(a1),f2(a1)),x67522))+~P107(f866(f866(f243(a1),f2(a1)),x67521))
% 157.76/157.52 [6792]~P107(f866(x67921,x67922))+P107(f866(x67921,f2(a930)))+P107(f866(x67921,f866(f866(f86(a930),f906(x67922,x67921)),f84(a930))))
% 157.76/157.52 [6874]E(f866(f110(a930),x68741),f866(f110(a930),x68742))+~P107(f866(f866(f243(a1),f866(f110(a1),x68742)),f2(a1)))+~P107(f866(a200,f866(f110(a1),x68741)))
% 157.76/157.52 [6884]~E(x68841,f2(a930))+~E(f683(x68842,x68841),f2(a930))+E(f866(f149(a930,a930,f86(a930),x68841),x68842),f2(a930))
% 157.76/157.52 [6908]~P107(f866(f66(x69081),f591(x69082,x69081)))+~P107(f866(f66(f937(x69081,a925)),x69082))+P107(f866(f66(x69081),f42(f937(x69081,a925),x69082)))
% 157.76/157.52 [6914]E(x69141,x69142)+P107(f866(f866(f244(a1),x69141),x69142))+~P107(f866(f866(f244(a1),x69141),f866(f866(f86(a1),x69142),f84(a1))))
% 157.76/157.52 [6915]P107(f866(f866(f243(a930),f866(a111,x69151)),f866(a111,x69152)))+~P107(f866(f866(f243(a1),f2(a1)),x69152))+~P107(f866(f866(f243(a1),x69151),x69152))
% 157.76/157.52 [6916]P107(f866(f866(f243(a930),f866(a111,x69161)),f866(a111,x69162)))+~P107(f866(f866(f244(a1),f2(a1)),x69161))+~P107(f866(f866(f243(a1),x69161),x69162))
% 157.76/157.52 [6918]P107(f866(f866(f244(a930),f866(a111,x69181)),f866(a111,x69182)))+~P107(f866(f866(f243(a1),f2(a1)),x69181))+~P107(f866(f866(f244(a1),x69181),x69182))
% 157.76/157.52 [6919]P107(f866(f866(f244(a930),f866(a111,x69191)),f866(a111,x69192)))+~P107(f866(f866(f244(a1),f2(a1)),x69192))+~P107(f866(f866(f244(a1),x69191),x69192))
% 157.76/157.52 [6930]E(f50(a930,f866(a111,x69301),f866(a111,x69302)),f866(a111,f50(a1,x69301,x69302)))+~P107(f866(f866(f243(a1),f2(a1)),x69302))+~P107(f866(f866(f243(a1),f2(a1)),x69301))
% 157.76/157.52 [6955]~P79(x69551)+~P107(f866(f866(f243(x69551),f866(f85(x69551),x69552)),f2(x69551)))+P107(f866(f866(f243(x69551),f2(x69551)),x69552))
% 157.76/157.52 [6956]~P79(x69561)+~P107(f866(f866(f244(x69561),f866(f85(x69561),x69562)),f2(x69561)))+P107(f866(f866(f244(x69561),f2(x69561)),x69562))
% 157.76/157.52 [6970]~P107(f866(f866(f244(a1),a89),x69702))+~P107(f866(f866(f244(a1),x69701),x69702))+P107(f866(f866(f244(a930),f866(f110(a930),x69701)),f866(f110(a930),x69702)))
% 157.76/157.52 [7058]~P107(f866(f866(f243(a1),f2(a1)),x70581))+P107(f866(f866(f244(a930),f866(a111,x70581)),x70582))+~P107(f866(f866(f244(a1),x70581),f866(f107(a1),x70582)))
% 157.76/157.52 [7063]P107(f866(x70631,x70632))+~P107(f866(x70631,f866(a20,f820(x70631,x70632))))+~P107(f866(f866(f336(a930),x70632),f250(f937(a930,a925))))
% 157.76/157.52 [7075]E(x70751,f2(a1))+E(f50(a1,x70752,x70751),f2(a1))+E(f866(f866(f23(a1),f866(f85(a1),f866(f866(f41(a1),x70752),x70751))),f84(a1)),f866(f866(f41(a1),x70752),f866(f85(a1),x70751)))
% 157.76/157.52 [7089]~P107(f866(f866(f243(a1),f2(a1)),x70891))+~P107(f866(f866(f244(a930),f866(a111,x70891)),x70892))+P107(f866(f866(f244(a1),x70891),f866(f107(a1),x70892)))
% 157.76/157.52 [7123]~P107(f866(f866(f243(a930),f866(a111,x71231)),f866(a111,x71232)))+~P107(f866(f866(f243(a1),f2(a1)),x71232))+P107(f866(f866(f243(a1),x71231),x71232))
% 157.76/157.52 [7124]~P107(f866(f866(f243(a930),f866(a111,x71241)),f866(a111,x71242)))+~P107(f866(f866(f244(a1),f2(a1)),x71241))+P107(f866(f866(f243(a1),x71241),x71242))
% 157.76/157.52 [7154]P107(f866(f866(f243(a1),x71541),x71542))+~P107(f866(f866(f243(a930),f866(f110(a930),x71541)),f866(f110(a930),x71542)))+P107(f866(f866(f243(a1),x71541),a89))
% 157.76/157.52 [7179]P107(f866(f866(f243(a1),f2(a1)),f50(a1,x71791,x71792)))+~P107(f866(f866(f243(a1),f2(a1)),x71792))+~P107(f866(f866(f243(a1),f2(a1)),x71791))
% 157.76/157.52 [7274]P107(f866(f866(f244(a1),a89),x72741))+~P107(f866(f866(f244(a1),x72742),x72741))+~P107(f866(f866(f244(a930),f866(f110(a930),x72742)),f866(f110(a930),x72741)))
% 157.76/157.52 [7327]E(f866(f866(f260(a1,a1),f866(f866(f41(a1),x73271),x73272)),f50(a1,x73271,x73272)),f55(x73271,x73272))+~P107(f866(f866(f244(a1),x73271),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x73272))
% 157.76/157.52 [7347]E(f866(f866(f260(a1,a1),f866(f866(f41(a1),x73471),x73472)),f50(a1,x73471,x73472)),f52(x73471,x73472))+~P107(f866(f866(f243(a1),f2(a1)),x73472))+~P107(f866(f866(f243(a1),f2(a1)),x73471))
% 157.76/157.52 [7399]~P99(x73992)+E(x73991,f120(x73992))+E(f866(f149(x73992,x73992,f87(x73992),f866(f148(x73992),x73991)),f866(f178(x73992),x73991)),f866(f68(x73992,f87(x73992)),f866(f179(x73992),x73991)))
% 157.76/157.52 [7515]~E(x75151,f2(a930))+E(f866(f149(a930,a930,f86(a930),x75151),x75152),f2(a930))+P107(f866(f866(f336(a930),f683(x75152,x75151)),f866(f179(a930),x75152)))
% 157.76/157.52 [7568]~P107(f866(f866(f243(a1),x75681),f2(a1)))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x75681),x75682)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x75682))
% 157.76/157.52 [7569]~P107(f866(f866(f244(a1),x75692),f2(a1)))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x75691),x75692)),f2(a1)))+~P107(f866(f866(f243(a1),f2(a1)),x75691))
% 157.76/157.52 [7570]~P107(f866(f866(f244(a1),x75702),f2(a1)))+P107(f866(f866(f244(a1),f866(f866(f41(a1),x75701),x75702)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x75701))
% 157.76/157.52 [7572]~P107(f866(f866(f244(a1),x75721),f2(a1)))+P107(f866(f866(f244(a1),f866(f866(f41(a1),x75721),x75722)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x75722))
% 157.76/157.52 [7578]P107(f866(f866(f336(f937(x75781,a925)),f591(x75782,x75781)),x75782))+~P107(f866(f66(f937(x75781,a925)),x75782))+P107(f866(f66(x75781),f42(f937(x75781,a925),x75782)))
% 157.76/157.52 [7667]P25(x76671,x76671,x76672,f250(f937(x76671,a925)))+~E(f866(f317(x76671,x76671,x76672),f250(f937(x76671,a925))),f250(f937(x76671,a925)))+~P107(f866(f66(x76671),f250(f937(x76671,a925))))
% 157.76/157.52 [7786]~P25(x77861,x77861,x77862,f250(f937(x77861,a925)))+E(f866(f317(x77861,x77861,x77862),f250(f937(x77861,a925))),f250(f937(x77861,a925)))+~P107(f866(f66(x77861),f250(f937(x77861,a925))))
% 157.76/157.52 [7923]E(f866(f866(f41(a1),x79231),x79232),f866(f110(a1),a104))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x79231),x79232)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x79231))
% 157.76/157.52 [7980]~P107(f866(f866(f244(a1),x79802),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f41(a1),x79801),x79802)),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x79801))
% 157.76/157.52 [7986]E(f866(f866(f86(a1),x79861),x79862),f50(a1,x79861,x79862))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),x79861),x79862)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x79861))
% 157.76/157.52 [7989]P107(f866(f866(f244(a1),x79891),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f41(a1),x79891),x79892)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x79892))
% 157.76/157.52 [8673]~P110(x86731)+P13(x86731,x86732)+~P107(f866(f866(f243(x86731),f866(f866(f171(x86731),x86732),f716(x86732,x86731))),f866(f866(f171(x86731),x86732),f717(x86732,x86731))))
% 157.76/157.52 [8674]~P110(x86741)+P13(x86741,x86742)+~P107(f866(f866(f243(x86741),f866(f866(f171(x86741),x86742),f724(x86742,x86741))),f866(f866(f171(x86741),x86742),f728(x86742,x86741))))
% 157.76/157.52 [5938]E(x59381,f2(a1))+~E(f50(a1,x59382,x59381),f2(a1))+E(f866(f866(f41(a1),x59382),f866(f85(a1),x59381)),f866(f85(a1),f866(f866(f41(a1),x59382),x59381)))
% 157.76/157.52 [5956]~P40(x59562)+~P40(x59561)+P40(f866(f866(f117(f937(a1,a925)),x59561),x59562))
% 157.76/157.52 [5957]~P40(x59572)+~P40(x59571)+P40(f866(f866(f108(f937(a1,a925)),x59571),x59572))
% 157.76/157.52 [5975]~P65(x59751)+~P96(x59751)+E(f866(f85(x59751),f866(f866(f297(x59751),f84(x59751)),x59752)),f866(f866(f297(x59751),f866(f110(x59751),a104)),x59752))
% 157.76/157.52 [6093]E(x60931,f2(a1))+~E(f50(a1,x60932,x60931),f2(a1))+E(f866(f866(f41(a1),f866(f85(a1),x60932)),x60931),f866(f85(a1),f866(f866(f41(a1),x60932),x60931)))
% 157.76/157.52 [6231]~P110(x62311)+P13(x62311,x62312)+P107(f866(f866(f244(a930),f717(x62312,x62311)),f866(f196(f931(x62311)),x62312)))
% 157.76/157.52 [6232]~P110(x62321)+P13(x62321,x62322)+P107(f866(f866(f244(a930),f728(x62322,x62321)),f866(f196(f931(x62321)),x62322)))
% 157.76/157.52 [6390]~P96(x63901)+~E(f866(f110(x63901),x63902),f2(x63901))+P28(x63901,f866(f110(x63901),f866(f866(f86(a1),x63902),f866(f85(a1),a89))))
% 157.76/157.52 [6391]~P96(x63911)+~E(f866(f110(x63911),x63912),f2(x63911))+P28(x63911,f866(f110(x63911),f866(f866(f86(a1),a89),f866(f85(a1),x63912))))
% 157.76/157.52 [6393]E(f866(a56,f52(f866(f85(a1),x63931),f866(f85(a1),x63932))),f51(x63931,x63932))+P107(f866(f866(f243(a1),f2(a1)),x63931))+P107(f866(f866(f244(a1),f2(a1)),x63932))
% 157.76/157.52 [6518]~E(x65182,f2(a930))+~E(x65181,f2(a930))+P107(f866(f866(f243(a1),f866(f107(a1),x65181)),f866(f85(a1),f866(f107(a1),x65182))))
% 157.76/157.52 [6547]E(f866(f866(f86(a930),f866(f110(a930),x65471)),f866(f110(a930),x65472)),f866(f110(a930),f866(f866(f86(a1),x65471),x65472)))+P107(f866(f866(f244(a1),x65471),a89))+P107(f866(f866(f244(a1),x65472),a89))
% 157.76/157.52 [6681]~P76(x66811)+~P107(f866(f866(f243(x66811),f2(x66811)),x66812))+P107(f866(f866(f243(x66811),f866(f85(x66811),x66812)),x66812))
% 157.76/157.52 [6682]~P76(x66821)+~P107(f866(f866(f244(x66821),f2(x66821)),x66822))+P107(f866(f866(f244(x66821),f866(f85(x66821),x66822)),x66822))
% 157.76/157.52 [6860]E(f866(f866(f23(a930),f866(a111,x68601)),f866(a111,x68602)),f866(a111,f866(f866(f23(a1),x68601),x68602)))+~P107(f866(f866(f243(a1),f2(a1)),x68602))+~P107(f866(f866(f243(a1),x68602),x68601))
% 157.76/157.52 [6892]E(f866(a111,f50(a1,f866(f110(a1),x68921),f866(f110(a1),x68922))),f50(a930,f866(f110(a930),x68921),f866(f110(a930),x68922)))+P107(f866(a200,f866(f110(a1),x68921)))+P107(f866(a200,f866(f110(a1),x68922)))
% 157.76/157.52 [6909]~P76(x69091)+P107(f866(f866(f243(x69091),f2(x69091)),x69092))+~P107(f866(f866(f243(x69091),f866(f85(x69091),x69092)),x69092))
% 157.76/157.52 [6910]~P76(x69101)+P107(f866(f866(f244(x69101),f2(x69101)),x69102))+~P107(f866(f866(f244(x69101),f866(f85(x69101),x69102)),x69102))
% 157.76/157.52 [6922]~P76(x69221)+~P107(f866(f866(f243(x69221),f2(x69221)),x69222))+P107(f866(f866(f243(x69221),f2(x69221)),f866(f866(f86(x69221),x69222),x69222)))
% 157.76/157.52 [6924]~P76(x69241)+~P107(f866(f866(f244(x69241),f2(x69241)),x69242))+P107(f866(f866(f244(x69241),f2(x69241)),f866(f866(f86(x69241),x69242),x69242)))
% 157.76/157.52 [6937]E(f866(f866(f86(a930),f866(a111,x69371)),f866(a111,x69372)),f866(a111,f866(f866(f86(a1),x69371),x69372)))+~P107(f866(f866(f243(a1),f2(a1)),x69372))+~P107(f866(f866(f243(a1),f2(a1)),x69371))
% 157.76/157.52 [6949]E(x69491,f2(a930))+P107(f866(f866(f244(a930),f2(a930)),x69492))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f252(a930),x69492),x69491)))
% 157.76/157.52 [6980]~P96(x69801)+E(f866(f110(x69801),x69802),f2(x69801))+~P28(x69801,f866(f110(x69801),f866(f866(f86(a1),a89),f866(f85(a1),x69802))))
% 157.76/157.52 [6981]~P96(x69811)+E(f866(f110(x69811),x69812),f2(x69811))+~P28(x69811,f866(f110(x69811),f866(f866(f86(a1),x69812),f866(f85(a1),a89))))
% 157.76/157.52 [7036]~P107(f866(f66(x70361),x70362))+~P107(f866(f66(x70361),f250(f937(x70361,a925))))+P107(f866(f66(x70361),f866(f85(f937(x70361,a925)),x70362)))
% 157.76/157.52 [7059]~P107(f866(f866(f244(a1),f2(a1)),x70592))+~P107(f866(f866(f243(a1),x70592),x70591))+P107(f866(f866(f244(a1),f2(a1)),f866(f866(f41(a1),x70591),x70592)))
% 157.76/157.52 [7060]~P107(f866(f866(f243(a1),x70601),f2(a1)))+~P107(f866(f866(f244(a1),x70602),f2(a1)))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f41(a1),x70601),x70602)))
% 157.76/157.52 [7097]~P107(f866(f866(f243(a1),f2(a1)),x70972))+~P107(f866(f866(f243(a1),f2(a1)),x70971))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f87(a1),x70971),x70972)))
% 157.76/157.52 [7098]~P107(f866(f866(f243(a1),f2(a1)),x70982))+~P107(f866(f866(f243(a1),f2(a1)),x70981))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),x70981),x70982)))
% 157.76/157.52 [7099]~P107(f866(f866(f243(a1),f2(a1)),x70992))+~P107(f866(f866(f243(a1),f2(a1)),x70991))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f41(a1),x70991),x70992)))
% 157.76/157.52 [7100]~P107(f866(f866(f243(a1),f2(a1)),x71001))+~P107(f866(f866(f244(a1),f2(a1)),x71002))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f41(a1),x71001),x71002)))
% 157.76/157.52 [7101]~P107(f866(f866(f244(a930),f2(a930)),x71012))+~P107(f866(f866(f244(a930),f2(a930)),x71011))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f87(a930),x71011),x71012)))
% 157.76/157.52 [7166]E(x71661,f2(a1))+E(f50(a1,x71662,x71661),f2(a1))+E(f866(f866(f23(a1),f866(f85(a1),f866(f866(f41(a1),x71662),x71661))),f84(a1)),f866(f866(f41(a1),f866(f85(a1),x71662)),x71661))
% 157.76/157.52 [7220]P107(f866(f866(f244(a930),f2(a930)),x72201))+P107(f866(f866(f244(a930),f2(a930)),x72202))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f86(a930),x72202),x72201)))
% 157.76/157.52 [7224]~P76(x72241)+P107(f866(f866(f243(x72241),f2(x72241)),x72242))+~P107(f866(f866(f243(x72241),f2(x72241)),f866(f866(f86(x72241),x72242),x72242)))
% 157.76/157.52 [7225]~P76(x72251)+P107(f866(f866(f244(x72251),f2(x72251)),x72252))+~P107(f866(f866(f244(x72251),f2(x72251)),f866(f866(f86(x72251),x72252),x72252)))
% 157.76/157.52 [7275]~P107(f866(f66(x72751),x72752))+P107(f866(f66(x72751),f250(f937(x72751,a925))))+~P107(f866(f66(x72751),f866(f85(f937(x72751,a925)),x72752)))
% 157.76/157.52 [7339]P107(f866(f866(f243(a1),x73391),f2(a1)))+~P107(f866(f866(f244(a1),x73392),f2(a1)))+~P107(f866(f866(f243(a1),f2(a1)),f866(f866(f41(a1),x73391),x73392)))
% 157.76/157.52 [7345]~P107(f866(f866(f244(a1),f2(a1)),x73451))+P107(f866(f866(f243(a1),x73451),x73452))+~P107(f866(f866(f244(a1),f2(a1)),f866(f866(f41(a1),x73452),x73451)))
% 157.76/157.52 [7346]~P107(f866(f866(f243(a1),f2(a1)),x73462))+P107(f866(f866(f243(a1),x73461),x73462))+~P107(f866(f866(f244(a1),f2(a1)),f866(f866(f41(a1),x73462),x73461)))
% 157.76/157.52 [7376]P107(f866(f866(f243(a1),f2(a1)),x73761))+~P107(f866(f866(f244(a1),f2(a1)),x73762))+~P107(f866(f866(f243(a1),f2(a1)),f866(f866(f41(a1),x73761),x73762)))
% 157.76/157.52 [7377]P107(f866(f866(f244(a1),f2(a1)),x73771))+~P107(f866(f866(f243(a1),f2(a1)),x73772))+~P107(f866(f866(f244(a1),f2(a1)),f866(f866(f41(a1),x73772),x73771)))
% 157.76/157.52 [7817]~P107(f866(f66(x78172),f250(f937(x78172,a925))))+~P107(f866(f66(x78171),f250(f937(x78171,a925))))+P107(f866(f66(f936(x78171,x78172)),f250(f937(f936(x78171,x78172),a925))))
% 157.76/157.52 [7818]~P107(f866(f66(x78182),f250(f937(x78182,a925))))+~P107(f866(f66(x78181),f250(f937(x78181,a925))))+P107(f866(f66(f938(x78181,x78182)),f250(f937(f938(x78181,x78182),a925))))
% 157.76/157.52 [7888]~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x78881))+~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x78882))+P107(f866(f866(f244(a930),x78881),f866(f866(f87(a930),x78882),x78881)))
% 157.76/157.52 [7889]~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x78891))+~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x78892))+P107(f866(f866(f244(a930),x78891),f866(f866(f87(a930),x78891),x78892)))
% 157.76/157.52 [7922]E(f866(f40(x79221),f250(f937(x79221,a925))),f866(a119,f2(a930)))+P107(f866(f66(x79222),f250(f937(x79222,a925))))+~P107(f866(f66(f937(x79222,x79221)),f250(f937(f937(x79222,x79221),a925))))
% 157.76/157.52 [8049]~P107(f866(f866(f243(a930),f866(a119,f2(a930))),x80491))+~P107(f866(f866(f243(a930),f866(a119,f2(a930))),x80492))+P107(f866(f866(f243(a930),f866(a119,f2(a930))),f866(f866(f87(a930),x80491),x80492)))
% 157.76/157.52 [8050]~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x80502))+~P107(f866(f866(f244(a930),f866(a119,f2(a930))),x80501))+P107(f866(f866(f244(a930),f866(a119,f2(a930))),f866(f866(f87(a930),x80501),x80502)))
% 157.76/157.52 [8720]E(x87201,f120(x87202))+~P107(f866(f144(x87202),x87201))+E(f184(x87202,f866(f866(f8(a925,a925,x87202),a329),f866(f866(f7(x87202,x87202,a925),a332),f151(x87202,x87201))),x87201),f121(x87202,x87201))
% 157.76/157.52 [8816]~P40(x88162)+~P40(x88161)+E(f866(f317(a930,a1,f107(a1)),f866(f866(f117(f937(a930,a925)),f866(f317(a1,a930,a111),x88161)),f866(f317(a1,a930,a111),x88162))),f866(f866(f117(f937(a1,a925)),x88161),x88162))
% 157.76/157.52 [8817]~P40(x88172)+~P40(x88171)+E(f866(f317(a930,a1,f107(a1)),f866(f866(f108(f937(a930,a925)),f866(f317(a1,a930,a111),x88171)),f866(f317(a1,a930,a111),x88172))),f866(f866(f108(f937(a1,a925)),x88171),x88172))
% 157.76/157.52 [9486]~P96(x94861)+~E(f866(f110(x94861),x94862),f84(x94861))+P28(x94861,f866(f110(x94861),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f85(a1),x94862))))
% 157.76/157.52 [9726]~P96(x97261)+E(f866(f110(x97261),x97262),f84(x97261))+~P28(x97261,f866(f110(x97261),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f85(a1),x97262))))
% 157.76/157.52 [10475]E(x104751,f2(a1))+E(x104752,f2(a1))+E(f866(f266(a1,a1,a1,a1,f32(a1),f866(f87(a1),f88(a1,x104752))),f866(f866(f866(f103(f936(a1,a1)),f866(f866(a332,f88(a1,x104751)),f88(a1,x104752))),f58(x104751,x104752)),f866(f866(f265(a1,a1,f936(a1,a1)),f866(f866(f18(a1,f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f937(f936(a1,a1),f936(a1,a1))),f937(f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),a1),f18(a1,f936(a1,a1),f936(a1,a1))),f866(f866(f8(f936(a1,a1),f937(a1,f937(f936(a1,a1),f936(a1,a1))),a1),f866(f7(a1,f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),f866(f866(f8(a925,f937(f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),a1),f103(f936(a1,a1))),f866(f866(f7(a1,a1,a925),a332),f2(a1))))),f866(f866(f7(a1,a1,f936(a1,a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f866(f866(f7(a1,f937(a1,a1),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f936(a1,a1)),f937(f937(a1,a1),f937(a1,f936(a1,a1))),a1),f8(a1,f936(a1,a1),a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f866(f866(f7(a1,a1,a1),f866(f866(f8(a1,f937(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f866(f23(a1),f866(f81(a1),x104752))))),f58(x104751,x104752)))),f51(x104751,x104752))
% 157.76/157.52 [10476]E(x104761,f2(a1))+E(x104762,f2(a1))+E(f866(f266(a1,a1,a1,a1,f32(a1),f866(f87(a1),f88(a1,x104762))),f866(f866(f866(f103(f936(a1,a1)),f866(f866(a334,f866(f866(a333,f866(f866(f244(a1),f2(a1)),x104762)),f866(f866(f243(a1),f2(a1)),x104761))),f866(f866(a333,f866(f866(f244(a1),x104762),f2(a1))),f866(f866(f244(a1),x104761),f2(a1))))),f58(x104761,x104762)),f866(f866(f265(a1,a1,f936(a1,a1)),f866(f866(f18(a1,f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f937(f936(a1,a1),f936(a1,a1))),f937(f937(a1,f936(a1,a1)),f937(a1,f936(a1,a1))),a1),f18(a1,f936(a1,a1),f936(a1,a1))),f866(f866(f8(f936(a1,a1),f937(a1,f937(f936(a1,a1),f936(a1,a1))),a1),f866(f7(a1,f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),f866(f866(f8(a925,f937(f936(a1,a1),f937(f936(a1,a1),f936(a1,a1))),a1),f103(f936(a1,a1))),f866(f866(f7(a1,a1,a925),a332),f2(a1))))),f866(f866(f7(a1,a1,f936(a1,a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f866(f866(f7(a1,f937(a1,a1),f937(a1,f936(a1,a1))),f866(f866(f8(f937(a1,f936(a1,a1)),f937(f937(a1,a1),f937(a1,f936(a1,a1))),a1),f8(a1,f936(a1,a1),a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f866(f866(f7(a1,a1,a1),f866(f866(f8(a1,f937(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f866(f23(a1),f866(f81(a1),x104762))))),f58(x104761,x104762)))),f51(x104761,x104762))
% 157.76/157.52 [5964]~P128(x59641)+~P96(x59641)+E(f866(f81(x59641),f866(f866(f252(x59641),f866(f110(x59641),a104)),x59642)),f84(x59641))
% 157.76/157.52 [6459]~P142(x64591)+~P107(f866(f866(f244(a1),x64592),f2(a1)))+E(f866(f85(x64591),f866(f107(x64591),f866(a111,f866(f85(a1),x64592)))),f866(f109(x64591),x64592))
% 157.76/157.52 [6664]P107(f866(f866(f243(a106),x66641),f84(a106)))+E(f866(f866(f86(a106),f84(a106)),f280(x66641,f866(f866(f41(a106),x66642),x66641))),f280(x66641,x66642))+P107(f866(f866(f244(a106),x66642),x66641))
% 157.76/157.52 [7264]~P95(x72641)+~P107(f866(f866(f336(x72641),x72642),f116(x72641)))+~E(f866(f866(f86(x72641),f866(f866(f86(x72641),f84(x72641)),x72642)),x72642),f2(x72641))
% 157.76/157.52 [7378]~P107(f866(f866(f243(a1),x73782),f2(a1)))+~P107(f866(f866(f244(a1),x73781),f2(a1)))+E(f866(f259(a1,a1),f866(a56,f52(f866(f85(a1),x73781),f866(f85(a1),x73782)))),f866(f866(f41(a1),x73781),x73782))
% 157.76/157.52 [7395]~P107(f866(f866(f243(a1),x73952),f2(a1)))+~P107(f866(f866(f244(a1),x73951),f2(a1)))+E(f866(f264(a1,a1),f866(a56,f52(f866(f85(a1),x73951),f866(f85(a1),x73952)))),f50(a1,x73951,x73952))
% 157.76/157.52 [7401]~P107(f866(f866(f244(a1),x74012),f2(a1)))+E(f866(f259(a1,a1),f866(a56,f55(f866(f85(a1),x74011),f866(f85(a1),x74012)))),f866(f866(f41(a1),x74011),x74012))+~P107(f866(f866(f244(a1),f2(a1)),x74011))
% 157.76/157.52 [7419]~P107(f866(f866(f244(a1),x74192),f2(a1)))+E(f866(f264(a1,a1),f866(a56,f55(f866(f85(a1),x74191),f866(f85(a1),x74192)))),f50(a1,x74191,x74192))+~P107(f866(f866(f244(a1),f2(a1)),x74191))
% 157.76/157.52 [7471]E(f866(f866(f41(a1),f866(f866(f252(a1),x74711),x74712)),x74711),f866(f866(f252(a1),x74711),f866(f866(f23(a930),x74712),f866(a119,f2(a930)))))+~P107(f866(f866(f244(a930),f2(a930)),x74712))+~P107(f866(f866(f244(a1),f2(a1)),x74711))
% 157.76/157.52 [7575]~P107(f866(f866(f244(a930),f2(a930)),x75751))+~P107(f866(f866(f244(a930),f2(a930)),x75752))+P107(f866(f866(f244(a930),f866(f866(f23(a930),x75751),x75752)),x75751))
% 157.76/157.52 [7576]~P107(f866(f866(f244(a930),f2(a930)),x75761))+~P107(f866(f866(f244(a930),f84(a930)),x75762))+P107(f866(f866(f244(a930),f866(f866(f41(a930),x75761),x75762)),x75761))
% 157.76/157.52 [7577]~P107(f866(f866(f244(a1),f2(a1)),x75771))+~P107(f866(f866(f244(a1),f84(a1)),x75772))+P107(f866(f866(f244(a1),f866(f866(f41(a1),x75771),x75772)),x75771))
% 157.76/157.52 [7713]E(x77131,f2(a930))+~E(x77132,f2(a1))+~P107(f866(f866(f244(a1),f2(a1)),f866(f866(f252(a1),f866(f81(a1),x77132)),x77131)))
% 157.76/157.52 [8126]~E(x81262,f120(f931(x81261)))+E(f866(f196(f931(f931(x81261))),f186(x81261,x81262)),f2(a930))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x81261),a930),f196(f931(x81261))),x81262)))
% 157.76/157.52 [8372]P107(f866(x83721,x83722))+~P107(f866(x83721,f866(a114,f544(x83721,x83722))))+~P107(f866(f866(f336(f937(f936(a930,a930),a925)),x83722),a105))
% 157.76/157.52 [8388]E(x83881,f120(f931(x83882)))+E(f866(f196(f931(x83882)),f866(f866(f171(f931(x83882)),x83881),f2(a930))),f866(f196(f931(f931(x83882))),f186(x83882,x83881)))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x83882),a930),f196(f931(x83882))),x83881)))
% 157.76/157.52 [8529]~P38(x85291,x85292)+~P39(x85291,x85292)+P38(x85291,f866(f866(f23(f937(f936(x85291,x85291),a925)),x85292),f314(x85291,f195(f937(f936(x85291,x85291),a925)))))
% 157.76/157.52 [9103]~P107(f866(f66(x91031),f866(f270(x91031),x91032)))+~P107(f866(f66(x91031),f250(f937(x91031,a925))))+P107(f866(f66(x91031),f866(f270(x91031),f866(f866(f8(a925,a925,x91031),a329),x91032))))
% 157.76/157.52 [9169]E(f866(f866(f260(a930,a930),f866(a119,f866(f866(f41(a930),f866(f866(f23(a930),x91691),x91692)),x91692))),f50(a930,f866(f866(f23(a930),x91691),x91692),x91692)),f91(f936(a930,a930),f53(x91691,x91692)))+~P107(f866(f866(f244(a930),f2(a930)),x91692))+~P107(f866(f866(f243(a930),x91692),x91691))
% 157.76/157.52 [9451]~P107(f866(f66(x94511),f866(f270(x94511),x94512)))+P107(f866(f66(x94511),f250(f937(x94511,a925))))+~P107(f866(f66(x94511),f866(f270(x94511),f866(f866(f8(a925,a925,x94511),a329),x94512))))
% 157.76/157.52 [10169]P27(x101691,x101692)+~P37(x101691,f866(f259(f937(f936(x101691,x101691),a925),f937(f936(x101691,x101691),a925)),x101692))+~P107(f866(f866(f243(f937(f936(x101691,x101691),a925)),f866(f866(f296(x101691,x101691,x101691),f866(f259(f937(f936(x101691,x101691),a925),f937(f936(x101691,x101691),a925)),x101692)),f866(f264(f937(f936(x101691,x101691),a925),f937(f936(x101691,x101691),a925)),x101692))),f866(f259(f937(f936(x101691,x101691),a925),f937(f936(x101691,x101691),a925)),x101692)))
% 157.76/157.52 [7501]~P107(f866(f866(f244(a930),f2(a930)),x75012))+P107(f866(f866(f244(a930),x75011),x75012))+E(f866(a119,f866(f866(f41(a930),f866(f866(f23(a930),x75011),x75012)),x75012)),f866(f866(f41(a930),x75011),x75012))
% 157.76/157.52 [7639]~P107(f866(f866(f244(a930),f2(a930)),x76392))+~P107(f866(f866(f243(a930),x76392),x76391))+E(f866(a119,f866(f866(f41(a930),f866(f866(f23(a930),x76391),x76392)),x76392)),f866(f866(f41(a930),x76391),x76392))
% 157.76/157.52 [8592]~P96(x85921)+~P95(x85921)+~P28(x85921,f866(f110(x85921),f866(f866(f23(a1),f866(f866(f86(a1),x85922),x85922)),a104)))
% 157.76/157.52 [9361]E(x93611,f2(a930))+E(f866(f866(f265(a930,a930,f936(a930,a930)),f866(f866(f8(a930,f937(a930,f936(a930,a930)),a930),f260(a930,a930)),a119)),f91(f936(a930,a930),f53(f866(f866(f23(a930),x93612),x93611),x93611))),f91(f936(a930,a930),f53(x93612,x93611)))+P107(f866(f866(f244(a930),x93612),x93611))
% 157.76/157.52 [9539]~P38(x95391,x95392)+~P52(x95391,x95392)+P107(f866(f866(f243(f937(f936(x95391,x95391),a925)),f866(f866(f296(x95391,x95391,x95391),f866(f294(x95391,x95391),x95392)),x95392)),x95392))
% 157.76/157.52 [9790]P107(f866(x97902,f646(x97902,x97901)))+P107(f866(x97901,f646(x97902,x97901)))+E(f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97901)),f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97902)))
% 157.76/157.52 [9794]~P107(f866(x97942,f646(x97942,x97941)))+~P107(f866(x97941,f646(x97942,x97941)))+E(f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97941)),f866(f270(a1),f866(f866(f18(a1,a925,a925),f866(f866(f8(a925,f937(a925,a925),a1),a333),f866(f243(a1),f2(a1)))),x97942)))
% 157.76/157.52 [7846]~P66(x78461)+~P96(x78461)+E(f866(f866(f297(x78461),x78462),f866(f110(x78461),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))),x78462)
% 157.76/157.52 [9485]~P96(x94851)+~E(f866(f110(x94851),x94852),f84(x94851))+P28(x94851,f866(f110(x94851),f866(f866(f86(a1),x94852),f866(f85(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.76/157.52 [9668]~P143(x96681)+~E(x96682,f84(x96681))+E(f866(f866(f252(x96681),x96682),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(x96681))
% 157.76/157.52 [9669]~P143(x96691)+~E(x96692,f2(x96691))+E(f866(f866(f252(x96691),x96692),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f2(x96691))
% 157.76/157.52 [9684]~P143(x96841)+~E(x96842,f866(f85(x96841),f84(x96841)))+E(f866(f866(f252(x96841),x96842),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(x96841))
% 157.76/157.52 [9727]~P96(x97271)+E(f866(f110(x97271),x97272),f84(x97271))+~P28(x97271,f866(f110(x97271),f866(f866(f86(a1),x97272),f866(f85(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.76/157.52 [10111]~P128(x101112)+E(x101111,f2(x101112))+P107(f866(f866(f244(x101112),f2(x101112)),f866(f866(f252(x101112),x101111),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.76/157.52 [10168]~P128(x101682)+~E(x101681,f2(x101682))+~P107(f866(f866(f244(x101682),f2(x101682)),f866(f866(f252(x101682),x101681),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.76/157.52 [10194]P107(f866(f866(f243(a1),x101941),f2(a1)))+P107(f866(f866(f244(a1),x101942),x101941))+E(f866(f48(x101941),f52(x101942,f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101941))),f52(x101942,x101941))
% 157.76/157.52 [10195]~P107(f866(f866(f244(a1),f2(a1)),x101951))+P107(f866(f866(f244(a1),x101952),x101951))+E(f866(f48(x101951),f52(x101952,f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101951))),f52(x101952,x101951))
% 157.76/157.52 [10196]P107(f866(f866(f243(a1),x101961),f2(a1)))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),x101962),x101961)))+E(f866(f48(x101961),f55(x101962,f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101961))),f55(x101962,x101961))
% 157.76/157.52 [10197]~P107(f866(f866(f244(a1),f2(a1)),x101971))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),x101972),x101971)))+E(f866(f48(x101971),f55(x101972,f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101971))),f55(x101972,x101971))
% 157.76/157.52 [10198]~P148(x101981)+~P107(f866(f866(f243(a1),f2(a1)),x101982))+E(f866(f107(x101981),f866(a111,f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x101982))),f866(f866(f86(x101981),f866(f107(x101981),f866(a111,x101982))),f866(f107(x101981),f866(a111,x101982))))
% 157.76/157.52 [5290]~P149(x52901,x52902,x52903)+~E(x52903,f2(a1))+P107(f866(x52901,x52902))
% 157.76/157.52 [5413]~P110(x54131)+~P13(x54131,x54133)+P13(x54131,f177(x54131,x54132,x54133))
% 157.76/157.52 [5414]~P110(x54141)+~P13(x54141,x54143)+P13(x54141,f184(x54141,x54142,x54143))
% 157.76/157.52 [4983]~P77(x49832)+~E(x49833,f866(f85(x49832),x49831))+E(x49831,f866(f85(x49832),x49833))
% 157.76/157.52 [4985]~P77(x49851)+~E(f866(f85(x49851),x49853),x49852)+E(f866(f85(x49851),x49852),x49853)
% 157.76/157.52 [5065]~P110(x50653)+E(x50651,x50652)+~E(f866(f290(x50653),x50651),f866(f290(x50653),x50652))
% 157.76/157.52 [5066]~P104(x50663)+E(x50661,x50662)+~E(f866(f107(x50663),x50661),f866(f107(x50663),x50662))
% 157.76/157.52 [5067]~P110(x50673)+E(x50671,x50672)+~E(f866(f311(x50673),x50671),f866(f311(x50673),x50672))
% 157.76/157.52 [5068]~P110(x50683)+E(x50681,x50682)+~E(f866(f308(x50683),x50681),f866(f308(x50683),x50682))
% 157.76/157.52 [5069]~P110(x50693)+E(x50691,x50692)+~E(f866(f291(x50693),x50691),f866(f291(x50693),x50692))
% 157.76/157.52 [5070]~P77(x50703)+E(x50701,x50702)+~E(f866(f85(x50703),x50701),f866(f85(x50703),x50702))
% 157.76/157.52 [5071]~P98(x50713)+E(x50711,x50712)+~E(f866(f85(x50713),x50711),f866(f85(x50713),x50712))
% 157.76/157.52 [5072]~P95(x50723)+E(x50721,x50722)+~E(f866(f109(x50723),x50721),f866(f109(x50723),x50722))
% 157.76/157.52 [5174]~P64(x51741)+~P107(f866(x51742,x51743))+P107(f866(f61(x51741),x51742))
% 157.76/157.52 [5210]~P64(x52103)+P107(f866(x52101,x52102))+~P107(f866(f62(x52103),x52101))
% 157.76/157.52 [5309]~P150(x53091,x53093,x53092)+~E(x53092,f2(a1))+P107(f866(x53091,f2(a1)))
% 157.76/157.52 [5348]~E(x53481,f2(a930))+E(f867(x53481,x53482,x53483),f195(f937(x53483,a925)))+~E(f866(f40(x53483),x53482),f866(a119,x53481))
% 157.76/157.52 [5499]~E(x54992,f2(a930))+E(f866(f259(a930,a930),x54991),f2(a930))+~P107(f866(f53(x54993,x54992),x54991))
% 157.76/157.52 [5542]P107(f866(x55421,x55422))+~E(x55423,f866(f107(a1),x55422))+~P107(f866(x55421,f866(a111,x55423)))
% 157.76/157.52 [6028]~E(x60283,f2(a930))+~P107(f866(x60281,x60282))+P107(f866(x60281,f50(a930,x60282,x60283)))
% 157.76/157.52 [6263]~P105(x62632)+~P105(x62631)+E(f138(x62631,x62632,f139(x62631,x62633),f139(x62632,x62633)),f139(f936(x62631,x62632),x62633))
% 157.76/157.52 [6441]~E(x64413,f2(a930))+P107(f866(x64411,x64412))+~P107(f866(x64411,f50(a930,x64412,x64413)))
% 157.76/157.52 [6934]E(x69341,f195(f937(x69342,a925)))+~P107(f866(f66(x69342),x69341))+P107(f866(f67(x69342,x69343,x69341),f861(x69343,x69341,x69342)))
% 157.76/157.52 [7122]E(x71221,f2(a930))+~P107(f866(x71222,f364(x71221,x71223,x71222)))+P107(f866(x71222,f50(a930,x71223,x71221)))
% 157.76/157.52 [7230]~P5(x72301)+~P107(f866(f866(f243(x72301),x72302),f593(x72303,x72302,x72301)))+P107(f866(f866(f243(x72301),x72302),f43(x72301,x72303)))
% 157.76/157.52 [7232]~P107(f866(x72321,x72322))+~P107(f866(x72321,f364(x72323,x72322,x72321)))+P107(f866(x72321,f50(a930,x72322,x72323)))
% 157.76/157.52 [7333]E(x73331,f120(x73332))+E(f866(f866(f158(x73332),f698(x73333,x73331,x73332)),f701(x73333,x73331,x73332)),x73331)+~P107(f866(f866(f336(f931(x73332)),x73331),f168(x73332,x73333)))
% 157.76/157.52 [7365]~P142(x73651)+~P107(f866(f866(f336(x73651),x73652),f116(x73651)))+P107(f866(f866(f336(x73651),f866(f866(f252(x73651),x73652),x73653)),f116(x73651)))
% 157.76/157.52 [7685]P37(x76851,x76852)+~P107(f866(f866(f336(x76851),x76853),f590(x76852,x76851)))+P107(f866(f866(f336(x76851),f645(x76852,x76851,x76853)),f590(x76852,x76851)))
% 157.76/157.52 [7949]E(x79491,f120(x79492))+~P107(f866(f866(f336(f931(x79492)),x79491),f168(x79492,x79493)))+P107(f866(f866(f336(f931(x79492)),f701(x79493,x79491,x79492)),f168(x79492,x79493)))
% 157.76/157.52 [8003]E(x80031,f2(a930))+E(f866(f866(f86(a930),f866(f866(f87(a930),x80031),f365(x80031,x80032,x80033))),f364(x80031,x80032,x80033)),x80032)+P107(f866(x80033,f50(a930,x80032,x80031)))
% 157.76/157.52 [8044]~P107(f866(x80443,x80442))+E(f866(f866(f86(a930),f866(f866(f87(a930),x80441),f365(x80441,x80442,x80443))),f364(x80441,x80442,x80443)),x80442)+P107(f866(x80443,f50(a930,x80442,x80441)))
% 157.76/157.52 [8181]P107(f866(f866(f244(a1),x81811),f355(x81812,x81813,x81811)))+P107(f866(f866(x81813,f866(f866(f41(a1),x81812),x81811)),f50(a1,x81812,x81811)))+~P107(f866(f866(f244(a1),x81811),f2(a1)))
% 157.76/157.52 [8443]P107(f866(f866(x84432,f866(f866(f41(a1),x84431),x84433)),f50(a1,x84431,x84433)))+~P107(f866(f866(f244(a1),x84433),f2(a1)))+P107(f866(f866(f243(a1),f355(x84431,x84432,x84433)),f2(a1)))
% 157.76/157.52 [8627]E(f866(f866(f86(a1),f866(f866(f87(a1),x86271),f358(x86272,x86273,x86271))),f355(x86272,x86273,x86271)),x86272)+P107(f866(f866(x86273,f866(f866(f41(a1),x86272),x86271)),f50(a1,x86272,x86271)))+~P107(f866(f866(f244(a1),x86271),f2(a1)))
% 157.76/157.52 [8864]~P107(f866(f866(x88641,f358(x88642,x88641,x88643)),f355(x88642,x88641,x88643)))+P107(f866(f866(x88641,f866(f866(f41(a1),x88642),x88643)),f50(a1,x88642,x88643)))+~P107(f866(f866(f244(a1),x88643),f2(a1)))
% 157.76/157.52 [9116]~P110(x91161)+~P13(x91161,x91163)+P13(x91161,f156(x91161,x91161,f5(x91161),x91162,x91163))
% 157.76/157.52 [9616]~P120(x96162)+E(x96161,f2(x96162))+~P107(f866(f866(f243(x96162),f866(f866(f86(x96162),f866(f866(f87(x96162),x96163),x96163)),f866(f866(f87(x96162),x96161),x96161))),f2(x96162)))
% 157.76/157.52 [9617]~P120(x96172)+E(x96171,f2(x96172))+~P107(f866(f866(f243(x96172),f866(f866(f86(x96172),f866(f866(f87(x96172),x96171),x96171)),f866(f866(f87(x96172),x96173),x96173))),f2(x96172)))
% 157.76/157.52 [10407]~P128(x104071)+~P107(f866(f866(f244(x104071),x104072),f2(x104071)))+P107(f866(f866(f244(x104071),f866(f866(f252(x104071),x104072),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x104073)))),f2(x104071)))
% 157.76/157.52 [10417]~P128(x104172)+E(x104171,f2(x104172))+~P107(f866(f866(f243(x104172),f866(f866(f86(x104172),f866(f866(f252(x104172),x104173),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x104172),x104171),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f2(x104172)))
% 157.76/157.52 [10418]~P128(x104182)+E(x104181,f2(x104182))+~P107(f866(f866(f243(x104182),f866(f866(f86(x104182),f866(f866(f252(x104182),x104181),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x104182),x104183),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f2(x104182)))
% 157.76/157.52 [5019]~E(x50192,x50193)+~P3(x50191)+E(f866(f866(f23(x50191),x50192),x50193),f2(x50191))
% 157.76/157.52 [5020]~E(x50202,x50203)+~P77(x50201)+E(f866(f866(f23(x50201),x50202),x50203),f2(x50201))
% 157.76/157.52 [5034]~P144(x50341)+~E(x50343,f2(x50341))+E(f866(f866(f86(x50341),x50342),x50343),x50342)
% 157.76/157.52 [5051]~P134(x50511)+~E(x50513,f2(x50511))+E(f866(f866(f87(x50511),x50512),x50513),f2(x50511))
% 157.76/157.52 [5052]~P134(x50521)+~E(x50522,f2(x50521))+E(f866(f866(f87(x50521),x50522),x50523),f2(x50521))
% 157.76/157.52 [5074]~E(x50743,f120(x50741))+~E(x50742,f120(x50741))+E(f866(f866(f141(x50741),x50742),x50743),f120(x50741))
% 157.76/157.52 [5164]~P144(x51642)+E(x51641,f2(x51642))+~E(f866(f866(f86(x51642),x51643),x51641),x51643)
% 157.76/157.52 [5165]~P77(x51651)+~E(x51652,f866(f85(x51651),x51653))+E(f866(f866(f86(x51651),x51652),x51653),f2(x51651))
% 157.76/157.52 [5172]E(x51721,f120(x51722))+E(x51723,f2(a930))+~E(f866(f866(f182(x51722),x51723),x51721),f120(x51722))
% 157.76/157.52 [5178]~P3(x51783)+E(x51781,x51782)+~E(f866(f866(f23(x51783),x51781),x51782),f2(x51783))
% 157.76/157.52 [5179]~P77(x51793)+E(x51791,x51792)+~E(f866(f866(f23(x51793),x51791),x51792),f2(x51793))
% 157.76/157.52 [5192]~P143(x51922)+E(x51921,f2(x51922))+~E(f866(f866(f252(x51922),x51921),x51923),f2(x51922))
% 157.76/157.52 [5193]~P85(x51932)+E(x51931,f195(x51932))+~E(f866(f866(f117(x51932),x51933),x51931),f195(x51932))
% 157.76/157.52 [5194]~P85(x51942)+E(x51941,f195(x51942))+~E(f866(f866(f117(x51942),x51941),x51943),f195(x51942))
% 157.76/157.52 [5195]~P84(x51952)+E(x51951,f250(x51952))+~E(f866(f866(f108(x51952),x51953),x51951),f250(x51952))
% 157.76/157.52 [5196]~P84(x51962)+E(x51961,f250(x51962))+~E(f866(f866(f108(x51962),x51961),x51963),f250(x51962))
% 157.76/157.52 [5264]~P77(x52642)+E(x52641,f866(f85(x52642),x52643))+~E(f866(f866(f86(x52642),x52641),x52643),f2(x52642))
% 157.76/157.52 [5265]~P77(x52651)+E(f866(f85(x52651),x52652),x52653)+~E(f866(f866(f86(x52651),x52652),x52653),f2(x52651))
% 157.76/157.52 [5267]~E(x52672,x52673)+~P108(x52671)+P107(f866(f866(f243(x52671),x52672),x52673))
% 157.76/157.52 [5269]~E(x52692,x52693)+~P111(x52691)+P107(f866(f866(f243(x52691),x52692),x52693))
% 157.76/157.52 [5365]~P123(x53651)+~E(x53652,f866(f85(x53651),x53653))+E(f866(f866(f87(x53651),x53652),x53652),f866(f866(f87(x53651),x53653),x53653))
% 157.76/157.52 [5374]~P110(x53741)+~P13(x53741,x53743)+P13(x53741,f866(f866(f182(x53741),x53742),x53743))
% 157.76/157.52 [5375]~P110(x53751)+~P13(x53751,x53753)+P13(x53751,f866(f866(f145(x53751),x53752),x53753))
% 157.76/157.52 [5411]E(x54111,x54112)+E(x54113,f2(a930))+~E(f866(f866(f87(a930),x54113),x54111),f866(f866(f87(a930),x54113),x54112))
% 157.76/157.52 [5412]E(x54121,x54122)+E(x54123,f2(a930))+~E(f866(f866(f87(a930),x54121),x54123),f866(f866(f87(a930),x54122),x54123))
% 157.76/157.52 [5492]~E(x54922,x54923)+~P111(x54921)+E(f310(x54921,x54922,x54923),f866(f866(f316(x54921),x54922),f195(f937(x54921,a925))))
% 157.76/157.52 [5540]~E(x55401,x55402)+~P110(x55403)+~P107(f866(f866(f244(x55403),x55401),x55402))
% 157.76/157.52 [5541]~E(x55411,x55412)+~P111(x55413)+~P107(f866(f866(f244(x55413),x55411),x55412))
% 157.76/157.52 [5553]~P111(x55531)+E(f866(f309(x55531,x55532),x55533),f195(f937(x55531,a925)))+P107(f866(f866(f244(x55531),x55532),x55533))
% 157.76/157.52 [5601]~P111(x56011)+E(f310(x56011,x56012,x56013),f195(f937(x56011,a925)))+P107(f866(f866(f243(x56011),x56012),x56013))
% 157.76/157.52 [5602]~P111(x56021)+E(f312(x56021,x56022,x56023),f195(f937(x56021,a925)))+P107(f866(f866(f244(x56021),x56022),x56023))
% 157.76/157.52 [5603]~P111(x56031)+E(f195(f937(x56031,a925)),f310(x56031,x56032,x56033))+P107(f866(f866(f243(x56031),x56032),x56033))
% 157.76/157.52 [5604]~P111(x56041)+E(f195(f937(x56041,a925)),f312(x56041,x56042,x56043))+P107(f866(f866(f244(x56041),x56042),x56043))
% 157.76/157.52 [5611]~P102(x56111)+~E(f866(f866(f117(x56111),x56112),x56113),x56113)+P107(f866(f866(f243(x56111),x56112),x56113))
% 157.76/157.52 [5612]~P103(x56121)+~E(f866(f866(f108(x56121),x56122),x56123),x56122)+P107(f866(f866(f243(x56121),x56122),x56123))
% 157.76/157.52 [5613]~P110(x56131)+~E(f866(f866(f241(x56131),x56132),x56133),x56132)+P107(f866(f866(f243(x56131),x56132),x56133))
% 157.76/157.52 [5614]~P110(x56141)+~E(f866(f866(f242(x56141),x56142),x56143),x56143)+P107(f866(f866(f243(x56141),x56142),x56143))
% 157.76/157.52 [5633]~P110(x56331)+P13(x56331,x56332)+~P13(x56331,f866(f866(f158(x56331),x56333),x56332))
% 157.76/157.52 [5634]~P110(x56341)+P13(x56341,x56342)+~P13(x56341,f866(f866(f141(x56341),x56343),x56342))
% 157.76/157.52 [5635]~P110(x56351)+P13(x56351,x56352)+~P13(x56351,f866(f866(f141(x56351),x56352),x56353))
% 157.76/157.52 [5700]~P110(x57001)+P107(f866(f866(f243(x57001),x57003),x57002))+P107(f866(f866(f243(x57001),x57002),x57003))
% 157.76/157.52 [5705]~P110(x57051)+P107(f866(f866(f244(x57051),x57053),x57052))+P107(f866(f866(f243(x57051),x57052),x57053))
% 157.76/157.52 [5743]~P102(x57431)+E(f866(f866(f117(x57431),x57432),x57433),x57432)+~P107(f866(f866(f243(x57431),x57433),x57432))
% 157.76/157.52 [5745]~P102(x57451)+E(f866(f866(f117(x57451),x57452),x57453),x57453)+~P107(f866(f866(f243(x57451),x57452),x57453))
% 157.76/157.52 [5746]~P103(x57461)+E(f866(f866(f108(x57461),x57462),x57463),x57463)+~P107(f866(f866(f243(x57461),x57463),x57462))
% 157.76/157.52 [5748]~P103(x57481)+E(f866(f866(f108(x57481),x57482),x57483),x57482)+~P107(f866(f866(f243(x57481),x57482),x57483))
% 157.76/157.52 [5749]~P110(x57491)+E(f866(f866(f241(x57491),x57492),x57493),x57493)+~P107(f866(f866(f243(x57491),x57493),x57492))
% 157.76/157.52 [5751]~P110(x57511)+E(f866(f866(f241(x57511),x57512),x57513),x57512)+~P107(f866(f866(f243(x57511),x57512),x57513))
% 157.76/157.52 [5752]~P110(x57521)+E(f866(f866(f242(x57521),x57522),x57523),x57522)+~P107(f866(f866(f243(x57521),x57523),x57522))
% 157.76/157.52 [5754]~P110(x57541)+E(f866(f866(f242(x57541),x57542),x57543),x57543)+~P107(f866(f866(f243(x57541),x57542),x57543))
% 157.76/157.52 [5761]~P125(x57612)+E(x57611,f2(x57612))+E(f866(f866(f297(x57612),f866(f85(x57612),x57613)),f866(f85(x57612),x57611)),f866(f866(f297(x57612),x57613),x57611))
% 157.76/157.52 [5816]~P111(x58161)+E(f866(f309(x58161,x58162),x58163),f195(f937(x58161,a925)))+~P107(f866(f866(f243(x58161),x58163),x58162))
% 157.76/157.52 [5851]~P111(x58511)+E(f313(x58511,x58512,x58513),f195(f937(x58511,a925)))+~P107(f866(f866(f243(x58511),x58513),x58512))
% 157.76/157.52 [5852]~P111(x58521)+E(f310(x58521,x58522,x58523),f195(f937(x58521,a925)))+~P107(f866(f866(f244(x58521),x58523),x58522))
% 157.76/157.52 [5853]~P111(x58531)+E(f312(x58531,x58532,x58533),f195(f937(x58531,a925)))+~P107(f866(f866(f243(x58531),x58533),x58532))
% 157.76/157.52 [5905]~E(f866(f866(f23(a930),x59051),x59053),x59052)+E(x59051,f866(f866(f86(a930),x59052),x59053))+~P107(f866(f866(f243(a930),x59053),x59051))
% 157.76/157.52 [5906]~E(x59061,f866(f866(f86(a930),x59063),x59062))+E(f866(f866(f23(a930),x59061),x59062),x59063)+~P107(f866(f866(f243(a930),x59062),x59061))
% 157.76/157.52 [5953]~P107(f866(x59531,x59533))+P107(f866(x59531,f407(x59531,x59532)))+~P107(f866(f866(f244(a930),x59533),x59532))
% 157.76/157.52 [5954]~P107(f866(x59541,x59543))+P107(f866(x59541,f414(x59541,x59542)))+~P107(f866(f866(f243(a930),x59543),x59542))
% 157.76/157.52 [5962]~P111(x59621)+~E(f866(f309(x59621,x59622),x59623),f195(f937(x59621,a925)))+~P107(f866(f866(f244(x59621),x59622),x59623))
% 157.76/157.52 [5967]~P108(x59671)+~P107(f866(f866(f244(x59671),x59672),x59673))+P107(f866(f866(f243(x59671),x59672),x59673))
% 157.76/157.52 [5969]~P111(x59691)+~P107(f866(f866(f244(x59691),x59692),x59693))+P107(f866(f866(f243(x59691),x59692),x59693))
% 157.76/157.52 [6078]~P111(x60781)+~E(f310(x60781,x60782,x60783),f195(f937(x60781,a925)))+~P107(f866(f866(f243(x60781),x60782),x60783))
% 157.76/157.52 [6079]~P111(x60791)+~E(f312(x60791,x60792,x60793),f195(f937(x60791,a925)))+~P107(f866(f866(f244(x60791),x60792),x60793))
% 157.76/157.52 [6080]~P111(x60801)+~E(f195(f937(x60801,a925)),f310(x60801,x60802,x60803))+~P107(f866(f866(f243(x60801),x60802),x60803))
% 157.76/157.52 [6081]~P111(x60811)+~E(f195(f937(x60811,a925)),f312(x60811,x60812,x60813))+~P107(f866(f866(f244(x60811),x60812),x60813))
% 157.76/157.52 [6091]P107(f866(x60911,x60912))+~P107(f866(x60911,f415(x60911,x60913)))+~P107(f866(f866(f244(a930),x60912),x60913))
% 157.76/157.52 [6092]P107(f866(x60921,x60922))+~P107(f866(x60921,f423(x60921,x60923)))+~P107(f866(f866(f243(a930),x60922),x60923))
% 157.76/157.52 [6102]~E(x61021,f866(a119,x61023))+P107(f866(f866(f244(a930),x61021),f866(a119,x61022)))+~P107(f866(f866(f244(a930),x61023),x61022))
% 157.76/157.52 [6121]E(x61211,x61212)+~E(f866(f866(f87(a930),x61213),x61211),f866(f866(f87(a930),x61213),x61212))+~P107(f866(f866(f244(a930),f2(a930)),x61213))
% 157.76/157.52 [6178]E(f866(x61781,f389(x61781,x61782,x61783)),f84(a930))+~E(f866(f866(f6(x61783,a930),x61781),x61782),f84(a930))+~P107(f866(f66(x61783),x61782))
% 157.76/157.52 [6194]~P5(x61941)+P107(f866(f866(f243(x61941),x61942),f42(x61941,x61943)))+~P107(f866(f866(f336(x61941),x61942),x61943))
% 157.76/157.52 [6217]~P108(x62171)+~P107(f866(f866(f244(x62171),x62173),x62172))+~P107(f866(f866(f243(x62171),x62172),x62173))
% 157.76/157.52 [6221]~P108(x62211)+~P107(f866(f866(f244(x62211),x62213),x62212))+~P107(f866(f866(f244(x62211),x62212),x62213))
% 157.76/157.52 [6224]~P110(x62241)+~P107(f866(f866(f244(x62241),x62243),x62242))+~P107(f866(f866(f243(x62241),x62242),x62243))
% 157.76/157.52 [6225]~P110(x62251)+~P107(f866(f866(f244(x62251),x62253),x62252))+~P107(f866(f866(f244(x62251),x62252),x62253))
% 157.76/157.52 [6226]~P111(x62261)+~P107(f866(f866(f244(x62261),x62263),x62262))+~P107(f866(f866(f244(x62261),x62262),x62263))
% 157.76/157.52 [6252]~E(f866(x62522,f912(x62522,x62523,x62521)),f84(a930))+E(f866(f866(f9(x62521,a930),x62522),x62523),f84(a930))+~P107(f866(f66(x62521),x62523))
% 157.76/157.52 [6253]~E(f866(x62532,f390(x62532,x62533,x62531)),f2(a930))+E(f866(f866(f6(x62531,a930),x62532),x62533),f2(a930))+~P107(f866(f66(x62531),x62533))
% 157.76/157.52 [6272]~P109(x62721)+~P107(f866(f866(f244(x62721),x62723),x62722))+P107(f866(f866(f336(x62721),x62722),f866(f311(x62721),x62723)))
% 157.76/157.52 [6273]~P109(x62731)+~P107(f866(f866(f243(x62731),x62733),x62732))+P107(f866(f866(f336(x62731),x62732),f866(f291(x62731),x62733)))
% 157.76/157.52 [6274]~P109(x62741)+~P107(f866(f866(f244(x62741),x62742),x62743))+P107(f866(f866(f336(x62741),x62742),f866(f290(x62741),x62743)))
% 157.76/157.52 [6275]~P109(x62751)+~P107(f866(f866(f243(x62751),x62752),x62753))+P107(f866(f866(f336(x62751),x62752),f866(f308(x62751),x62753)))
% 157.76/157.52 [6287]E(f866(x62871,f394(x62871,x62872,x62873)),f866(a119,f2(a930)))+~E(f866(f866(f6(x62873,a930),x62871),x62872),f866(a119,f2(a930)))+~P107(f866(f66(x62873),x62872))
% 157.76/157.52 [6368]~P5(x63681)+~P107(f866(f866(f336(x63681),x63683),x63682))+P107(f866(f866(f243(x63681),f43(x63681,x63682)),x63683))
% 157.76/157.52 [6387]~P107(f866(f866(f243(a930),x63871),x63873))+P107(f866(f866(f243(a930),x63871),x63872))+~P107(f866(f866(f243(a930),x63873),x63872))
% 157.76/157.52 [6388]~P107(f866(f866(f243(a1),x63881),x63883))+P107(f866(f866(f243(a1),x63881),x63882))+~P107(f866(f866(f243(a1),x63883),x63882))
% 157.76/157.52 [6408]~P109(x64081)+~P107(f866(f866(f336(x64081),x64083),f866(f291(x64081),x64082)))+P107(f866(f866(f243(x64081),x64082),x64083))
% 157.76/157.52 [6409]~P109(x64091)+~P107(f866(f866(f336(x64091),x64092),f866(f308(x64091),x64093)))+P107(f866(f866(f243(x64091),x64092),x64093))
% 157.76/157.52 [6410]~P109(x64101)+~P107(f866(f866(f336(x64101),x64103),f866(f311(x64101),x64102)))+P107(f866(f866(f244(x64101),x64102),x64103))
% 157.76/157.52 [6411]~P109(x64111)+~P107(f866(f866(f336(x64111),x64112),f866(f290(x64111),x64113)))+P107(f866(f866(f244(x64111),x64112),x64113))
% 157.76/157.52 [6484]~P107(f866(x64841,x64842))+P107(f866(x64841,f789(x64841)))+~P107(f866(f866(f336(x64843),x64842),f250(f937(x64843,a925))))
% 157.76/157.52 [6503]P57(a930,x65032,x65033)+E(x65031,f2(a930))+~P57(a930,f866(f866(f87(a930),x65031),x65032),f866(f866(f87(a930),x65031),x65033))
% 157.76/157.52 [6627]~P67(x66271)+P107(f866(f866(f244(x66271),f2(x66271)),f343(x66273,x66272,x66271)))+P107(f866(f866(f243(x66271),x66272),x66273))
% 157.76/157.52 [6628]~P68(x66281)+P107(f866(f866(f244(x66281),f2(x66281)),f778(x66283,x66282,x66281)))+P107(f866(f866(f243(x66281),x66282),x66283))
% 157.76/157.52 [6700]~P79(x67001)+~P107(f866(f866(f243(x67001),x67003),f866(f85(x67001),x67002)))+P107(f866(f866(f243(x67001),x67002),f866(f85(x67001),x67003)))
% 157.76/157.52 [6702]~P79(x67021)+~P107(f866(f866(f244(x67021),x67023),f866(f85(x67021),x67022)))+P107(f866(f866(f244(x67021),x67022),f866(f85(x67021),x67023)))
% 157.76/157.52 [6714]~P107(f866(f866(f244(a930),x67141),x67143))+~P107(f866(f866(f244(a930),x67143),x67142))+P107(f866(f866(f244(a930),f866(a119,x67141)),x67142))
% 157.76/157.52 [6740]~P113(x67401)+P107(f866(f866(f243(x67401),f866(f107(x67401),x67402)),f866(f107(x67401),x67403)))+~P107(f866(f866(f243(a930),x67402),x67403))
% 157.76/157.52 [6741]~P128(x67411)+P107(f866(f866(f243(x67411),f866(f109(x67411),x67412)),f866(f109(x67411),x67413)))+~P107(f866(f866(f243(a1),x67412),x67413))
% 157.76/157.52 [6743]~P128(x67431)+P107(f866(f866(f244(x67431),f866(f109(x67431),x67432)),f866(f109(x67431),x67433)))+~P107(f866(f866(f244(a1),x67432),x67433))
% 157.76/157.52 [6744]~P113(x67441)+P107(f866(f866(f244(x67441),f866(f107(x67441),x67442)),f866(f107(x67441),x67443)))+~P107(f866(f866(f244(a930),x67442),x67443))
% 157.76/157.52 [6750]~P110(x67501)+E(f866(f866(f117(f937(x67501,a925)),f866(f290(x67501),x67502)),f866(f309(x67501,x67502),x67503)),f866(f290(x67501),x67503))+~P107(f866(f866(f243(x67501),x67502),x67503))
% 157.76/157.52 [6781]~P79(x67811)+~P107(f866(f866(f243(x67811),x67813),x67812))+P107(f866(f866(f243(x67811),f866(f85(x67811),x67812)),f866(f85(x67811),x67813)))
% 157.76/157.52 [6783]~P98(x67831)+~P107(f866(f866(f243(x67831),x67833),x67832))+P107(f866(f866(f243(x67831),f866(f85(x67831),x67832)),f866(f85(x67831),x67833)))
% 157.76/157.52 [6784]~P79(x67841)+~P107(f866(f866(f244(x67841),x67843),x67842))+P107(f866(f866(f244(x67841),f866(f85(x67841),x67842)),f866(f85(x67841),x67843)))
% 157.76/157.52 [6820]~P110(x68201)+E(f866(f866(f117(f937(x68201,a925)),f866(f290(x68201),x68202)),f310(x68201,x68202,x68203)),f866(f308(x68201),x68203))+~P107(f866(f866(f243(x68201),x68202),x68203))
% 157.76/157.52 [6821]~P110(x68211)+E(f866(f866(f117(f937(x68211,a925)),f866(f308(x68211),x68212)),f313(x68211,x68212,x68213)),f866(f290(x68211),x68213))+~P107(f866(f866(f244(x68211),x68212),x68213))
% 157.76/157.52 [6822]~P110(x68221)+E(f866(f866(f117(f937(x68221,a925)),f866(f308(x68221),x68222)),f312(x68221,x68222,x68223)),f866(f308(x68221),x68223))+~P107(f866(f866(f243(x68221),x68222),x68223))
% 157.76/157.52 [6855]~P110(x68551)+E(f866(f866(f117(f937(x68551,a925)),f866(f309(x68551,x68552),x68553)),f866(f291(x68551),x68553)),f866(f291(x68551),x68552))+~P107(f866(f866(f243(x68551),x68552),x68553))
% 157.76/157.52 [7006]~P110(x70061)+E(f866(f866(f117(f937(x70061,a925)),f313(x70061,x70062,x70063)),f866(f291(x70061),x70063)),f866(f311(x70061),x70062))+~P107(f866(f866(f244(x70061),x70062),x70063))
% 157.76/157.52 [7007]~P110(x70071)+E(f866(f866(f117(f937(x70071,a925)),f310(x70071,x70072,x70073)),f866(f311(x70071),x70073)),f866(f291(x70071),x70072))+~P107(f866(f866(f243(x70071),x70072),x70073))
% 157.76/157.52 [7008]~P110(x70081)+E(f866(f866(f117(f937(x70081,a925)),f312(x70081,x70082,x70083)),f866(f311(x70081),x70083)),f866(f311(x70081),x70082))+~P107(f866(f866(f243(x70081),x70082),x70083))
% 157.76/157.52 [7027]P107(f866(x70271,x70272))+~P107(f866(f866(f243(a930),x70272),x70273))+P107(f866(f866(f336(a930),f423(x70271,x70273)),f310(a930,f2(a930),x70273)))
% 157.76/157.52 [7061]E(x70611,x70612)+~E(f866(f866(f171(x70613),x70611),f643(x70613,x70612,x70611)),f866(f866(f171(x70613),x70612),f643(x70613,x70612,x70611)))+~E(f866(f196(f931(x70613)),x70611),f866(f196(f931(x70613)),x70612))
% 157.76/157.52 [7067]~E(x70673,f866(f866(f41(a930),x70671),x70672))+~P107(f866(f866(f244(a930),f2(a930)),x70672))+P107(f866(f866(f244(a930),x70671),f866(f866(f87(a930),x70672),f866(a119,x70673))))
% 157.76/157.52 [7083]~P107(f866(x70831,x70833))+~P107(f866(f866(f243(a930),x70833),x70832))+P107(f866(f866(f336(a930),f414(x70831,x70832)),f310(a930,f2(a930),x70832)))
% 157.76/157.52 [7120]~P107(f866(x71201,x71203))+P107(f866(x71201,f424(x71201,x71202)))+~P107(f866(f866(f336(a930),x71203),f310(a930,f2(a930),x71202)))
% 157.76/157.52 [7139]~P113(x71393)+~P107(f866(f866(f243(x71393),f866(f107(x71393),x71391)),f866(f107(x71393),x71392)))+P107(f866(f866(f243(a930),x71391),x71392))
% 157.76/157.52 [7140]~P128(x71403)+~P107(f866(f866(f243(x71403),f866(f109(x71403),x71401)),f866(f109(x71403),x71402)))+P107(f866(f866(f243(a1),x71401),x71402))
% 157.76/157.52 [7142]~P113(x71423)+~P107(f866(f866(f244(x71423),f866(f107(x71423),x71421)),f866(f107(x71423),x71422)))+P107(f866(f866(f244(a930),x71421),x71422))
% 157.76/157.52 [7143]~P128(x71433)+~P107(f866(f866(f244(x71433),f866(f109(x71433),x71431)),f866(f109(x71433),x71432)))+P107(f866(f866(f244(a1),x71431),x71432))
% 157.76/157.52 [7144]~P57(a930,f866(f866(f252(a930),x71443),x71441),f866(f866(f252(a930),x71443),x71442))+P107(f866(f866(f243(a930),x71441),x71442))+~P107(f866(f866(f244(a930),f84(a930)),x71443))
% 157.76/157.52 [7160]~P113(x71601)+~P107(f866(f866(f244(x71601),f84(x71601)),x71602))+P107(f866(f866(f244(x71601),f84(x71601)),f866(f866(f252(x71601),x71602),f866(a119,x71603))))
% 157.76/157.52 [7162]~P79(x71621)+~P107(f866(f866(f243(x71621),f866(f85(x71621),x71623)),f866(f85(x71621),x71622)))+P107(f866(f866(f243(x71621),x71622),x71623))
% 157.76/157.52 [7163]~P98(x71631)+~P107(f866(f866(f243(x71631),f866(f85(x71631),x71633)),f866(f85(x71631),x71632)))+P107(f866(f866(f243(x71631),x71632),x71633))
% 157.76/157.52 [7164]~P79(x71641)+~P107(f866(f866(f244(x71641),f866(f85(x71641),x71643)),f866(f85(x71641),x71642)))+P107(f866(f866(f244(x71641),x71642),x71643))
% 157.76/157.52 [7188]P107(f866(x71881,x71882))+~P107(f866(x71881,f425(x71881,x71883)))+~P107(f866(f866(f336(a930),x71882),f310(a930,f2(a930),x71883)))
% 157.76/157.52 [7208]~P67(x72081)+P107(f866(f866(f244(x72081),f343(x72083,x72082,x72081)),f84(x72081)))+P107(f866(f866(f243(x72081),x72082),x72083))
% 157.76/157.52 [7227]~E(f50(a930,x72273,x72272),f50(a930,x72271,x72272))+E(f866(f866(f86(a930),x72271),f866(f866(f87(a930),x72272),f470(x72271,x72272,x72273))),x72273)+~P107(f866(f866(f243(a930),x72271),x72273))
% 157.76/157.52 [7281]E(f866(f866(f9(x72811,a930),x72812),x72813),f84(a930))+~P107(f866(f66(x72811),x72813))+P107(f866(f866(f336(x72811),f912(x72812,x72813,x72811)),x72813))
% 157.76/157.52 [7282]E(f866(f866(f6(x72821,a930),x72822),x72823),f2(a930))+~P107(f866(f66(x72821),x72823))+P107(f866(f866(f336(x72821),f390(x72822,x72823,x72821)),x72823))
% 157.76/157.52 [7304]~P110(x73041)+~P107(f866(f866(f243(x73041),x73042),x73043))+P107(f866(f866(f243(f937(x73041,a925)),f866(f290(x73041),x73042)),f866(f290(x73041),x73043)))
% 157.76/157.52 [7305]~P110(x73051)+~P107(f866(f866(f243(x73051),x73053),x73052))+P107(f866(f866(f243(f937(x73051,a925)),f866(f311(x73051),x73052)),f866(f311(x73051),x73053)))
% 157.76/157.52 [7306]~P111(x73061)+~P107(f866(f866(f243(x73061),x73062),x73063))+P107(f866(f866(f243(f937(x73061,a925)),f866(f308(x73061),x73062)),f866(f308(x73061),x73063)))
% 157.76/157.52 [7307]~P111(x73071)+~P107(f866(f866(f243(x73071),x73073),x73072))+P107(f866(f866(f243(f937(x73071,a925)),f866(f291(x73071),x73072)),f866(f291(x73071),x73073)))
% 157.76/157.52 [7308]~P110(x73081)+~P107(f866(f866(f244(x73081),x73082),x73083))+P107(f866(f866(f244(f937(x73081,a925)),f866(f290(x73081),x73082)),f866(f290(x73081),x73083)))
% 157.76/157.52 [7319]~P5(x73191)+P107(f866(f866(f243(x73191),x73192),f43(x73191,x73193)))+P107(f866(f866(f336(x73191),f593(x73193,x73192,x73191)),x73193))
% 157.76/157.52 [7325]~P79(x73251)+P107(f866(f866(f243(x73251),f866(f866(f23(x73251),x73252),x73253)),f2(x73251)))+~P107(f866(f866(f243(x73251),x73252),x73253))
% 157.76/157.52 [7326]~P79(x73261)+P107(f866(f866(f244(x73261),f866(f866(f23(x73261),x73262),x73263)),f2(x73261)))+~P107(f866(f866(f244(x73261),x73262),x73263))
% 157.76/157.52 [7368]P107(f866(x73681,x73682))+P107(f866(f866(f243(a930),f425(x73681,x73683)),x73683))+~P107(f866(f866(f336(a930),x73682),f310(a930,f2(a930),x73683)))
% 157.76/157.52 [7408]~E(f866(f866(f6(x74081,a930),x74082),x74083),f84(a930))+~P107(f866(f66(x74081),x74083))+P107(f866(f866(f336(x74081),f389(x74082,x74083,x74081)),x74083))
% 157.76/157.52 [7409]~P107(f866(x74091,x74093))+P107(f866(f866(f243(a930),f424(x74091,x74092)),x74092))+~P107(f866(f866(f336(a930),x74093),f310(a930,f2(a930),x74092)))
% 157.76/157.52 [7448]~P5(x74481)+P107(f866(f866(f336(x74481),f621(x74483,x74482,x74481)),x74482))+P107(f866(f866(f243(x74481),f42(x74481,x74482)),x74483))
% 157.76/157.52 [7482]~E(f866(f866(f6(x74821,a930),x74822),x74823),f866(a119,f2(a930)))+~P107(f866(f66(x74821),x74823))+P107(f866(f866(f336(x74821),f394(x74822,x74823,x74821)),x74823))
% 157.76/157.52 [7493]E(x74931,f2(a930))+P107(f866(x74932,f50(a930,x74933,x74931)))+P107(f866(f866(f244(a930),f364(x74931,x74933,x74932)),x74931))
% 157.76/157.52 [7604]~P107(f866(x76041,x76042))+P107(f866(x76041,f50(a930,x76042,x76043)))+P107(f866(f866(f244(a930),f364(x76043,x76042,x76041)),x76043))
% 157.76/157.52 [7717]E(x77171,f120(x77172))+~P107(f866(f866(f336(f931(x77172)),x77171),f168(x77172,x77173)))+P107(f866(f866(f336(x77172),f698(x77173,x77171,x77172)),x77173))
% 157.76/157.52 [7739]~P110(x77391)+E(f866(f866(f117(f937(x77391,a925)),f866(f866(f316(x77391),x77392),f195(f937(x77391,a925)))),f313(x77391,x77392,x77393)),f866(f309(x77391,x77392),x77393))+~P107(f866(f866(f244(x77391),x77392),x77393))
% 157.76/157.52 [7761]~P110(x77611)+E(f866(f866(f117(f937(x77611,a925)),f866(f866(f316(x77611),x77612),f195(f937(x77611,a925)))),f312(x77611,x77612,x77613)),f310(x77611,x77612,x77613))+~P107(f866(f866(f243(x77611),x77612),x77613))
% 157.76/157.52 [7868]~P110(x78681)+P107(f866(f866(f243(x78681),x78682),x78683))+~P107(f866(f866(f243(f937(x78681,a925)),f866(f311(x78681),x78683)),f866(f311(x78681),x78682)))
% 157.76/157.52 [7869]~P111(x78691)+P107(f866(f866(f243(x78691),x78692),x78693))+~P107(f866(f866(f243(f937(x78691,a925)),f866(f291(x78691),x78693)),f866(f291(x78691),x78692)))
% 157.76/157.52 [7870]~P110(x78701)+P107(f866(f866(f243(x78701),x78702),x78703))+~P107(f866(f866(f243(f937(x78701,a925)),f866(f290(x78701),x78702)),f866(f290(x78701),x78703)))
% 157.76/157.52 [7871]~P111(x78711)+P107(f866(f866(f243(x78711),x78712),x78713))+~P107(f866(f866(f243(f937(x78711,a925)),f866(f308(x78711),x78712)),f866(f308(x78711),x78713)))
% 157.76/157.52 [7872]~P110(x78721)+P107(f866(f866(f244(x78721),x78722),x78723))+~P107(f866(f866(f244(f937(x78721,a925)),f866(f290(x78721),x78722)),f866(f290(x78721),x78723)))
% 157.76/157.52 [7895]~P79(x78951)+~P107(f866(f866(f243(x78951),f866(f866(f23(x78951),x78952),x78953)),f2(x78951)))+P107(f866(f866(f243(x78951),x78952),x78953))
% 157.76/157.52 [7896]~P79(x78961)+~P107(f866(f866(f244(x78961),f866(f866(f23(x78961),x78962),x78963)),f2(x78961)))+P107(f866(f866(f244(x78961),x78962),x78963))
% 157.76/157.52 [8051]E(x80511,f2(a930))+~E(f866(f149(a930,a930,f86(a930),x80512),x80513),f2(a930))+~P107(f866(f866(f336(a930),x80511),f866(f179(a930),x80513)))
% 157.76/157.52 [8055]~P5(x80551)+~P107(f866(f866(f243(x80551),f621(x80553,x80552,x80551)),x80553))+P107(f866(f866(f243(x80551),f42(x80551,x80552)),x80553))
% 157.76/157.52 [8207]P107(f866(f866(f243(a1),f2(a1)),f356(x82071,x82072,x82073)))+P107(f866(f866(x82072,f866(f866(f41(a1),x82071),x82073)),f50(a1,x82071,x82073)))+~P107(f866(f866(f244(a1),f2(a1)),x82073))
% 157.76/157.52 [8295]E(x82951,x82952)+~E(f866(f196(f931(x82953)),x82951),f866(f196(f931(x82953)),x82952))+~P107(f866(f866(f265(x82953,x82953,a925),a332),f670(x82953,x82951,x82952)))
% 157.76/157.52 [8362]~P37(x83622,x83623)+E(x83621,f195(f937(x83622,a925)))+~P107(f866(f866(f243(f937(x83622,a925)),x83621),f866(f293(x83622,x83622,x83623),x83621)))
% 157.76/157.52 [8390]~P68(x83901)+~P107(f866(f866(f243(x83901),x83902),f866(f866(f86(x83901),x83903),f778(x83903,x83902,x83901))))+P107(f866(f866(f243(x83901),x83902),x83903))
% 157.76/157.52 [8425]P53(x84251,x84252,x84253)+P107(f866(f866(f336(x84251),f550(x84253,x84252,x84251)),x84252))+P107(f866(f866(f336(f936(x84251,x84251)),f551(x84253,x84252,x84251)),x84253))
% 157.76/157.52 [8446]P107(f866(f866(x84462,f866(f866(f41(a1),x84461),x84463)),f50(a1,x84461,x84463)))+~P107(f866(f866(f244(a1),f2(a1)),x84463))+P107(f866(f866(f244(a1),f356(x84461,x84462,x84463)),x84463))
% 157.76/157.52 [8470]E(f866(f317(a930,a930,f866(f866(f7(a930,a930,a930),f23(a930)),x84701)),f866(f309(a930,x84702),x84703)),f195(f937(a930,a925)))+P107(f866(f866(f244(a930),x84701),x84703))+P107(f866(f866(f244(a930),x84702),x84703))
% 157.76/157.52 [8581]E(f866(f317(a930,a930,f866(f866(f7(a930,a930,a930),f23(a930)),x85811)),f866(f309(a930,x85812),x85813)),f866(f866(f316(a930),f2(a930)),f195(f937(a930,a925))))+P107(f866(f866(f244(a930),x85811),x85813))+~P107(f866(f866(f244(a930),x85812),x85813))
% 157.76/157.52 [8595]~P110(x85951)+E(f156(x85951,x85951,f5(x85951),x85952,x85953),x85953)+~P107(f866(f866(f336(x85951),x85952),f866(f179(x85951),x85953)))
% 157.76/157.52 [8608]P25(x86081,x86081,x86082,x86083)+~P107(f866(f66(x86081),x86083))+~P107(f866(f866(f243(f937(x86081,a925)),x86083),f866(f317(x86081,x86081,x86082),x86083)))
% 157.76/157.52 [8634]E(f866(f866(f86(a1),f866(f866(f87(a1),x86341),f357(x86342,x86343,x86341))),f356(x86342,x86343,x86341)),x86342)+P107(f866(f866(x86343,f866(f866(f41(a1),x86342),x86341)),f50(a1,x86342,x86341)))+~P107(f866(f866(f244(a1),f2(a1)),x86341))
% 157.76/157.52 [8871]~P107(f866(f866(x88711,f357(x88712,x88711,x88713)),f356(x88712,x88711,x88713)))+P107(f866(f866(x88711,f866(f866(f41(a1),x88712),x88713)),f50(a1,x88712,x88713)))+~P107(f866(f866(f244(a1),f2(a1)),x88713))
% 157.76/157.52 [9758]~P107(f866(f66(x97581),x97582))+~P107(f866(f866(f336(x97581),x97583),x97582))+P107(f866(f866(f244(a930),f866(f40(x97581),f866(f866(f23(f937(x97581,a925)),x97582),f866(f866(f316(x97581),x97583),f195(f937(x97581,a925)))))),f866(f40(x97581),x97582)))
% 157.76/157.52 [10350]P53(x103501,x103502,x103503)+~P107(f866(f866(f265(x103501,x103501,a925),f866(f866(f7(x103501,f937(x103501,a925),f937(x103501,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x103501,a925),f937(x103501,a925)),x103501),f8(a925,a925,x103501)),f866(f866(f8(a925,f937(a925,a925),x103501),a333),f866(f866(f7(x103501,f937(x103501,a925),a925),f336(x103501)),x103502)))),f866(f866(f7(x103501,f937(x103501,a925),a925),f336(x103501)),x103502))),f551(x103503,x103502,x103501)))+P107(f866(f866(f336(x103501),f550(x103503,x103502,x103501)),x103502))
% 157.76/157.52 [5722]~P125(x57222)+E(x57221,f2(x57222))+E(f866(f866(f297(x57222),x57223),f866(f85(x57222),x57221)),f866(f85(x57222),f866(f866(f297(x57222),x57223),x57221)))
% 157.76/157.52 [5839]~P62(x58391)+~P57(x58391,x58392,x58393)+E(f866(f866(f87(x58391),x58392),f866(f866(f41(x58391),x58393),x58392)),x58393)
% 157.76/157.52 [5867]~E(x58673,f195(f937(x58671,a925)))+~E(x58672,f195(f937(x58671,a925)))+E(f866(f866(f117(f937(x58671,a925)),x58672),x58673),f195(f937(x58671,a925)))
% 157.76/157.52 [5925]~E(x59253,f2(a930))+~P107(f866(x59251,f2(a930)))+P107(f866(x59251,f866(f866(f41(a930),x59252),x59253)))
% 157.76/157.52 [6070]~P68(x60702)+E(x60701,f2(x60702))+E(f866(f866(f297(x60702),f866(f81(x60702),x60703)),f866(f81(x60702),x60701)),f866(f81(x60702),f866(f866(f297(x60702),x60703),x60701)))
% 157.76/157.52 [6242]~P107(f866(f66(x62421),x62423))+E(f866(f40(x62421),f866(f866(f316(x62421),x62422),x62423)),f866(a119,f866(f40(x62421),x62423)))+P107(f866(f866(f336(x62421),x62422),x62423))
% 157.76/157.52 [6317]~E(x63172,f2(a930))+P107(f866(x63171,f2(a930)))+~P107(f866(x63171,f866(f866(f41(a930),x63173),x63172)))
% 157.76/157.52 [6334]~P107(f866(f66(x63341),x63343))+E(f866(f40(x63341),f866(f866(f316(x63341),x63342),x63343)),f866(f40(x63341),x63343))+~P107(f866(f866(f336(x63341),x63342),x63343))
% 157.76/157.52 [6370]~P107(f866(f66(x63701),x63703))+E(f866(f40(x63701),f866(f866(f316(x63701),x63702),x63703)),f866(f866(f86(a930),f84(a930)),f866(f40(x63701),x63703)))+P107(f866(f866(f336(x63701),x63702),x63703))
% 157.76/157.52 [6485]E(f866(f866(f86(a930),x64851),f870(x64851,x64852,x64853)),x64852)+~P107(f866(x64853,f2(a930)))+P107(f866(x64853,f866(f866(f23(a930),x64852),x64851)))
% 157.76/157.52 [6486]E(f866(f866(f86(a930),x64861),f900(x64861,x64862,x64863)),x64862)+~P107(f866(x64863,f2(a930)))+P107(f866(x64863,f866(f866(f23(a930),x64862),x64861)))
% 157.76/157.52 [6533]~P5(x65331)+~P107(f866(f66(x65331),x65333))+E(f866(f866(f69(x65331,x65331,f117(x65331)),x65332),x65333),f866(f866(f117(x65331),x65332),f42(x65331,x65333)))
% 157.76/157.52 [6534]~P5(x65341)+~P107(f866(f66(x65341),x65343))+E(f866(f866(f69(x65341,x65341,f108(x65341)),x65342),x65343),f866(f866(f108(x65341),x65342),f43(x65341,x65343)))
% 157.76/157.52 [6540]~P96(x65401)+~E(f866(f110(x65401),x65402),f866(f110(x65401),x65403))+P28(x65401,f866(f110(x65401),f866(f866(f86(a1),x65402),f866(f85(a1),x65403))))
% 157.76/157.52 [6549]~P142(x65491)+E(f866(f866(f23(x65491),f866(f107(x65491),x65492)),f866(f107(x65491),x65493)),f866(f107(x65491),f866(f866(f23(a930),x65492),x65493)))+~P107(f866(f866(f243(a930),x65493),x65492))
% 157.76/157.52 [6638]E(f866(f866(f86(a930),x66381),f870(x66381,x66382,x66383)),x66382)+P107(f866(f866(f244(a930),x66382),x66381))+P107(f866(x66383,f866(f866(f23(a930),x66382),x66381)))
% 157.76/157.52 [6639]E(f866(f866(f86(a930),x66391),f900(x66391,x66392,x66393)),x66392)+P107(f866(f866(f244(a930),x66392),x66391))+P107(f866(x66393,f866(f866(f23(a930),x66392),x66391)))
% 157.76/157.52 [6656]~P128(x66561)+E(f866(f866(f87(x66561),f866(f81(x66561),x66562)),x66563),f866(f81(x66561),f866(f866(f87(x66561),x66562),x66563)))+~P107(f866(f866(f243(x66561),f2(x66561)),x66563))
% 157.76/157.52 [6657]~P67(x66571)+E(f866(f866(f297(x66571),f866(f81(x66571),x66572)),x66573),f866(f81(x66571),f866(f866(f297(x66571),x66572),x66573)))+~P107(f866(f866(f244(x66571),f2(x66571)),x66573))
% 157.76/157.52 [6665]~P83(x66651)+~P107(f866(f66(x66651),x66653))+E(f866(f866(f69(x66651,x66651,f117(x66651)),x66652),x66653),f13(x66651,f866(f866(f316(x66651),x66652),x66653)))
% 157.76/157.52 [6666]~P83(x66661)+~P107(f866(f66(x66661),x66663))+E(f866(f866(f69(x66661,x66661,f108(x66661)),x66662),x66663),f10(x66661,f866(f866(f316(x66661),x66662),x66663)))
% 157.76/157.52 [6667]~P110(x66671)+~P107(f866(f66(x66671),x66673))+E(f866(f866(f69(x66671,x66671,f242(x66671)),x66672),x66673),f14(x66671,f866(f866(f316(x66671),x66672),x66673)))
% 157.76/157.52 [6668]~P110(x66681)+~P107(f866(f66(x66681),x66683))+E(f866(f866(f69(x66681,x66681,f241(x66681)),x66682),x66683),f15(x66681,f866(f866(f316(x66681),x66682),x66683)))
% 157.76/157.52 [6716]E(x67161,f120(x67162))+~E(f186(x67162,x67163),f120(f931(x67162)))+~P107(f866(f866(f336(f931(x67162)),x67161),f866(f179(f931(x67162)),x67163)))
% 157.76/157.52 [6758]~P107(f866(f144(x67581),x67583))+P107(f866(f866(f336(x67581),x67582),f866(f179(x67581),x67583)))+P107(f866(f144(x67581),f866(f866(f158(x67581),x67582),x67583)))
% 157.76/157.52 [6770]~P99(x67701)+~P107(f866(f66(x67701),x67703))+E(f866(f68(x67701,f87(x67701)),f866(f866(f316(x67701),x67702),x67703)),f866(f866(f69(x67701,x67701,f87(x67701)),x67702),x67703))
% 157.76/157.52 [6794]~P110(x67941)+~P107(f866(f66(x67941),x67943))+E(f11(x67941,f241(x67941),f866(f866(f316(x67941),x67942),x67943)),f866(f866(f69(x67941,x67941,f241(x67941)),x67942),x67943))
% 157.76/157.52 [6795]~P110(x67951)+~P107(f866(f66(x67951),x67953))+E(f12(x67951,f242(x67951),f866(f866(f316(x67951),x67952),x67953)),f866(f866(f69(x67951,x67951,f242(x67951)),x67952),x67953))
% 157.76/157.52 [6797]P107(f866(x67971,f2(a930)))+~P107(f866(f866(f244(a930),x67972),x67973))+~P107(f866(x67971,f866(f866(f23(a930),x67972),x67973)))
% 157.76/157.52 [6818]~P89(x68181)+P107(f866(f866(f243(x68181),x68182),x68183))+~P107(f866(f866(f243(x68181),f866(f81(x68181),x68182)),x68183))
% 157.76/157.52 [6819]~P128(x68191)+P107(f866(f866(f244(x68191),x68192),x68193))+~P107(f866(f866(f244(x68191),f866(f81(x68191),x68192)),x68193))
% 157.76/157.52 [6836]E(x68361,f120(x68362))+E(f866(f148(x68362),f866(f866(f145(x68362),x68363),x68361)),f866(f866(f171(x68362),x68361),x68363))+~P107(f866(f866(f244(a930),x68363),f866(f196(f931(x68362)),x68361)))
% 157.76/157.52 [6886]~P107(f866(x68861,x68863))+P107(f866(x68861,f416(x68861,x68862)))+~P107(f866(f866(f336(a930),x68863),f866(f309(a930,f2(a930)),x68862)))
% 157.76/157.52 [6906]P107(f866(x69061,x69062))+~P107(f866(f866(f244(a930),x69062),x69063))+P107(f866(f866(f336(a930),f415(x69061,x69063)),f866(f309(a930,f2(a930)),x69063)))
% 157.76/157.52 [6921]~P113(x69211)+~P107(f866(f866(f243(x69211),f84(x69211)),x69212))+P107(f866(f866(f243(x69211),f84(x69211)),f866(f866(f252(x69211),x69212),x69213)))
% 157.76/157.52 [6923]~P113(x69231)+~P107(f866(f866(f243(x69231),f2(x69231)),x69232))+P107(f866(f866(f243(x69231),f2(x69231)),f866(f866(f252(x69231),x69232),x69233)))
% 157.76/157.52 [6925]~P113(x69251)+~P107(f866(f866(f244(x69251),f2(x69251)),x69252))+P107(f866(f866(f244(x69251),f2(x69251)),f866(f866(f252(x69251),x69252),x69253)))
% 157.76/157.52 [6951]~P107(f866(x69511,x69513))+~P107(f866(f866(f244(a930),x69513),x69512))+P107(f866(f866(f336(a930),f407(x69511,x69512)),f866(f309(a930,f2(a930)),x69512)))
% 157.76/157.52 [6959]P107(f866(f66(x69591),x69592))+~P107(f866(f66(x69591),x69593))+~P107(f866(f866(f243(f937(x69591,a925)),x69592),x69593))
% 157.76/157.52 [6966]P107(f866(x69661,x69662))+~P107(f866(x69661,f417(x69661,x69663)))+~P107(f866(f866(f336(a930),x69662),f866(f309(a930,f2(a930)),x69663)))
% 157.76/157.52 [6977]E(x69771,f2(a930))+P107(f866(x69772,f344(x69771,x69773,x69772)))+~P107(f866(x69772,f866(f866(f41(a930),x69773),x69771)))
% 157.76/157.52 [6984]~P120(x69842)+E(x69841,f2(x69842))+~E(f866(f866(f86(x69842),f866(f866(f87(x69842),x69843),x69843)),f866(f866(f87(x69842),x69841),x69841)),f2(x69842))
% 157.76/157.52 [6985]~P120(x69852)+E(x69851,f2(x69852))+~E(f866(f866(f86(x69852),f866(f866(f87(x69852),x69851),x69851)),f866(f866(f87(x69852),x69853),x69853)),f2(x69852))
% 157.76/157.52 [7028]E(x70281,f2(a930))+~P107(f866(x70282,f345(x70281,x70283,x70282)))+P107(f866(x70282,f866(f866(f41(a930),x70283),x70281)))
% 157.76/157.52 [7033]~P110(x70331)+~P13(x70331,x70333)+P13(x70331,f866(f866(f155(x70331,x70331,f5(x70331)),x70332),x70333))
% 157.76/157.52 [7076]P107(f866(x70761,f344(x70762,x70763,x70761)))+P107(f866(x70761,f2(a930)))+~P107(f866(x70761,f866(f866(f41(a930),x70763),x70762)))
% 157.76/157.52 [7082]~P96(x70821)+E(f866(f110(x70821),x70822),f866(f110(x70821),x70823))+~P28(x70821,f866(f110(x70821),f866(f866(f86(a1),x70822),f866(f85(a1),x70823))))
% 157.76/157.52 [7147]E(x71471,f2(a1))+E(x71472,f2(a1))+~P107(f866(f54(x71472,x71472),f866(f866(f260(a1,a1),x71473),x71471)))
% 157.76/157.52 [7148]E(x71481,f84(a1))+E(x71482,f2(a1))+~P107(f866(f54(x71482,x71482),f866(f866(f260(a1,a1),x71481),x71483)))
% 157.76/157.52 [7161]P107(f866(x71611,x71612))+P107(f866(f866(f244(a930),f417(x71611,x71613)),x71613))+~P107(f866(f866(f336(a930),x71612),f866(f309(a930,f2(a930)),x71613)))
% 157.76/157.52 [7184]~P107(f866(x71841,f870(x71843,x71842,x71841)))+~P107(f866(x71841,f2(a930)))+P107(f866(x71841,f866(f866(f23(a930),x71842),x71843)))
% 157.76/157.52 [7185]~P107(f866(x71851,f900(x71853,x71852,x71851)))+~P107(f866(x71851,f2(a930)))+P107(f866(x71851,f866(f866(f23(a930),x71852),x71853)))
% 157.76/157.52 [7186]~P107(f866(x71861,f345(x71863,x71862,x71861)))+~P107(f866(x71861,f2(a930)))+P107(f866(x71861,f866(f866(f41(a930),x71862),x71863)))
% 157.76/157.52 [7204]~P107(f866(x72041,x72043))+P107(f866(f866(f244(a930),f416(x72041,x72042)),x72042))+~P107(f866(f866(f336(a930),x72043),f866(f309(a930,f2(a930)),x72042)))
% 157.76/157.52 [7205]E(f866(f866(f23(a930),f866(f866(f23(a930),x72051),x72052)),f866(f866(f23(a930),x72053),x72052)),f866(f866(f23(a930),x72051),x72053))+~P107(f866(f866(f243(a930),x72052),x72051))+~P107(f866(f866(f243(a930),x72052),x72053))
% 157.76/157.52 [7240]~P79(x72401)+~P107(f866(f866(f243(x72401),f866(f85(x72401),x72403)),x72402))+P107(f866(f866(f243(x72401),f866(f85(x72401),x72402)),x72403))
% 157.76/157.52 [7242]~P89(x72421)+~P107(f866(f866(f243(x72421),f866(f81(x72421),x72422)),x72423))+P107(f866(f866(f243(x72421),f866(f85(x72421),x72422)),x72423))
% 157.76/157.52 [7244]~P79(x72441)+~P107(f866(f866(f244(x72441),f866(f85(x72441),x72443)),x72442))+P107(f866(f866(f244(x72441),f866(f85(x72441),x72442)),x72443))
% 157.76/157.52 [7245]~P128(x72451)+~P107(f866(f866(f244(x72451),f866(f81(x72451),x72452)),x72453))+P107(f866(f866(f244(x72451),f866(f85(x72451),x72452)),x72453))
% 157.76/157.52 [7276]~P107(f866(x72763,f870(x72762,x72761,x72763)))+P107(f866(f866(f244(a930),x72761),x72762))+P107(f866(x72763,f866(f866(f23(a930),x72761),x72762)))
% 157.76/157.52 [7277]~P107(f866(x72773,f900(x72772,x72771,x72773)))+P107(f866(f866(f244(a930),x72771),x72772))+P107(f866(x72773,f866(f866(f23(a930),x72771),x72772)))
% 157.76/157.52 [7329]~E(f628(x73293,x73292,x73291),f629(x73293,x73292,x73291))+E(f866(f866(f108(f937(x73291,a925)),x73292),f42(f937(x73291,a925),x73293)),f195(f937(x73291,a925)))+P107(f866(f866(f336(f937(x73291,a925)),x73292),x73293))
% 157.76/157.52 [7337]~P107(f866(f66(x73371),x73373))+P107(f866(f66(x73371),f43(f937(x73371,a925),x73372)))+~P107(f866(f866(f336(f937(x73371,a925)),x73373),x73372))
% 157.76/157.52 [7397]~P110(x73971)+E(f866(f866(f117(f937(x73971,a925)),f866(f309(x73971,x73972),x73973)),f866(f866(f316(x73971),x73973),f195(f937(x73971,a925)))),f310(x73971,x73972,x73973))+~P107(f866(f866(f243(x73971),x73972),x73973))
% 157.76/157.52 [7398]E(x73981,f2(a930))+P107(f866(f866(f244(a930),f350(x73981,x73983,x73982)),x73981))+P107(f866(x73982,f866(f866(f41(a930),x73983),x73981)))
% 157.76/157.52 [7427]P107(f866(f866(f244(a930),f866(f196(f931(x74271)),x74272)),f791(x74273,x74271)))+~P107(f866(f66(f931(x74271)),x74273))+~P107(f866(f866(f336(f931(x74271)),x74272),x74273))
% 157.76/157.52 [7433]E(x74331,x74332)+~P107(f866(f866(f243(f937(x74333,a925)),x74331),x74332))+P107(f866(f866(f244(f937(x74333,a925)),x74331),x74332))
% 157.76/157.52 [7445]E(x74451,x74452)+~E(f866(f196(f931(x74453)),x74451),f866(f196(f931(x74453)),x74452))+P107(f866(f866(f244(a930),f643(x74453,x74451,x74452)),f866(f196(f931(x74453)),x74452)))
% 157.76/157.52 [7494]P8(x74941,x74942,x74943)+~E(f866(f272(x74941,x74941),x74943),x74942)+~E(f866(f866(f296(x74941,x74941,x74941),f866(f294(x74941,x74941),x74943)),x74943),x74943)
% 157.76/157.52 [7574]~P107(f866(x75741,f2(a930)))+P107(f866(f866(f244(a930),f350(x75743,x75742,x75741)),x75743))+P107(f866(x75741,f866(f866(f41(a930),x75742),x75743)))
% 157.76/157.52 [7583]~P110(x75831)+E(f866(f866(f117(f937(x75831,a925)),f313(x75831,x75832,x75833)),f866(f866(f316(x75831),x75833),f195(f937(x75831,a925)))),f312(x75831,x75832,x75833))+~P107(f866(f866(f244(x75831),x75832),x75833))
% 157.76/157.52 [7674]~P107(f866(f66(x76741),x76743))+P107(f866(f866(f243(a930),f866(f40(x76741),x76742)),f866(f40(x76741),x76743)))+~P107(f866(f866(f243(f937(x76741,a925)),x76742),x76743))
% 157.76/157.52 [7675]~P107(f866(f66(x76751),x76753))+P107(f866(f866(f244(a930),f866(f40(x76751),x76752)),f866(f40(x76751),x76753)))+~P107(f866(f866(f244(f937(x76751,a925)),x76752),x76753))
% 157.76/157.52 [7805]E(x78051,x78052)+~P107(f866(f866(f243(f937(x78053,a925)),x78052),x78051))+~P107(f866(f866(f243(f937(x78053,a925)),x78051),x78052))
% 157.76/157.52 [7808]~P110(x78081)+P13(x78081,x78082)+~P13(x78081,f866(f866(f155(x78081,x78081,f5(x78081)),x78083),x78082))
% 157.76/157.52 [7877]~P107(f866(f866(f244(a930),x78773),x78772))+~P107(f866(f866(f244(a930),x78773),x78771))+P107(f866(f866(f244(a930),f866(f866(f23(a930),x78771),x78772)),f866(f866(f23(a930),x78771),x78773)))
% 157.76/157.52 [7878]~P107(f866(f866(f243(a930),x78782),x78781))+~P107(f866(f866(f244(a930),x78781),x78783))+P107(f866(f866(f244(a930),f866(f866(f23(a930),x78781),x78782)),f866(f866(f23(a930),x78783),x78782)))
% 157.76/157.52 [7893]~P107(f866(f866(f244(a1),x78932),f2(a1)))+~P107(f866(f866(f243(a1),x78933),x78931))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x78931),x78932)),f866(f866(f41(a1),x78933),x78932)))
% 157.76/157.52 [7910]~P107(f866(f866(f244(a930),f2(a930)),x79103))+~P107(f866(f866(f243(a930),x79103),x79102))+P107(f866(f866(f243(a930),f866(f866(f41(a930),x79101),x79102)),f866(f866(f41(a930),x79101),x79103)))
% 157.76/157.52 [7911]~P107(f866(f866(f244(a1),f2(a1)),x79112))+~P107(f866(f866(f243(a1),x79111),x79113))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x79111),x79112)),f866(f866(f41(a1),x79113),x79112)))
% 157.76/157.52 [7915]~P107(f866(f866(f244(a930),f2(a930)),x79152))+~P107(f866(f866(f244(a930),x79151),x79153))+P107(f866(f866(f244(a930),f866(f866(f87(a930),x79151),x79152)),f866(f866(f87(a930),x79153),x79152)))
% 157.76/157.52 [7916]~P107(f866(f866(f244(a930),f2(a930)),x79161))+~P107(f866(f866(f244(a930),x79162),x79163))+P107(f866(f866(f244(a930),f866(f866(f87(a930),x79161),x79162)),f866(f866(f87(a930),x79161),x79163)))
% 157.76/157.52 [7917]~P107(f866(f866(f244(a1),f2(a1)),x79171))+~P107(f866(f866(f244(a1),x79172),x79173))+P107(f866(f866(f244(a1),f866(f866(f87(a1),x79171),x79172)),f866(f866(f87(a1),x79171),x79173)))
% 157.76/157.52 [7964]E(x79641,f2(a930))+E(f866(f866(f86(a930),f866(f866(f87(a930),x79641),f345(x79641,x79642,x79643))),f350(x79641,x79642,x79643)),x79642)+P107(f866(x79643,f866(f866(f41(a930),x79642),x79641)))
% 157.76/157.52 [8025]E(f866(f866(f86(a930),f866(f866(f87(a930),x80251),f345(x80251,x80252,x80253))),f350(x80251,x80252,x80253)),x80252)+~P107(f866(x80253,f2(a930)))+P107(f866(x80253,f866(f866(f41(a930),x80252),x80251)))
% 157.76/157.52 [8042]~P107(f866(f66(x80421),x80423))+P107(f866(f866(f336(x80421),f916(x80422,x80423,x80421)),x80423))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f9(x80421,a930),x80422),x80423)))
% 157.76/157.52 [8043]~P107(f866(f66(x80431),x80433))+P107(f866(f866(f336(x80431),f360(x80432,x80433,x80431)),x80433))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f9(x80431,a930),x80432),x80433)))
% 157.76/157.52 [8330]E(x83301,f195(f937(x83302,a925)))+E(x83301,f866(f866(f316(x83302),x83303),f195(f937(x83302,a925))))+~P107(f866(f866(f243(f937(x83302,a925)),x83301),f866(f866(f316(x83302),x83303),f195(f937(x83302,a925)))))
% 157.76/157.52 [8364]~P107(f866(f866(f244(a930),f2(a930)),x83643))+P107(f866(f866(f243(a930),x83641),x83642))+~P107(f866(f866(f243(a930),f866(f866(f87(a930),x83643),x83641)),f866(f866(f87(a930),x83643),x83642)))
% 157.76/157.52 [8365]~P107(f866(f866(f244(a930),f2(a930)),x83653))+P107(f866(f866(f243(a930),x83651),x83652))+~P107(f866(f866(f243(a930),f866(f866(f87(a930),x83651),x83653)),f866(f866(f87(a930),x83652),x83653)))
% 157.76/157.52 [8367]~P107(f866(f866(f244(a930),f2(a930)),x83673))+P107(f866(f866(f244(a930),x83671),x83672))+~P107(f866(f866(f244(a930),f866(f866(f252(a930),x83673),x83671)),f866(f866(f252(a930),x83673),x83672)))
% 157.76/157.52 [8406]~E(f866(f866(f108(f937(x84061,a925)),f629(x84063,x84062,x84061)),f628(x84063,x84062,x84061)),f195(f937(x84061,a925)))+E(f866(f866(f108(f937(x84061,a925)),x84062),f42(f937(x84061,a925),x84063)),f195(f937(x84061,a925)))+P107(f866(f866(f336(f937(x84061,a925)),x84062),x84063))
% 157.76/157.52 [8420]E(x84201,f120(x84202))+~E(f866(f149(f931(x84202),f931(x84202),f141(x84202),f120(x84202)),x84203),f120(x84202))+~P107(f866(f866(f336(f931(x84202)),x84201),f866(f179(f931(x84202)),x84203)))
% 157.76/157.52 [8475]E(x84751,f195(f937(f937(x84752,a925),a925)))+P107(f866(f866(f336(f937(x84752,a925)),f633(x84753,x84751,x84752)),x84751))+P107(f866(f866(f243(f937(x84752,a925)),f43(f937(x84752,a925),x84751)),x84753))
% 157.76/157.52 [8481]~P71(x84811)+~P72(x84811)+E(f866(f866(f9(a1,x84811),f866(f866(f8(a930,x84811,a1),x84812),a111)),f866(f317(a930,a1,f107(a1)),x84813)),f866(f866(f9(a930,x84811),x84812),x84813))
% 157.76/157.52 [8482]~P71(x84821)+~P72(x84821)+E(f866(f866(f6(a1,x84821),f866(f866(f8(a930,x84821,a1),x84822),a111)),f866(f317(a930,a1,f107(a1)),x84823)),f866(f866(f6(a930,x84821),x84822),x84823))
% 157.76/157.52 [8525]~P107(f866(f66(x85251),x85253))+~P107(f866(f866(f244(a930),f2(a930)),f866(x85252,f916(x85252,x85253,x85251))))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f9(x85251,a930),x85252),x85253)))
% 157.76/157.52 [8526]~P107(f866(f66(x85261),x85263))+~P107(f866(f866(f244(a930),f2(a930)),f866(x85262,f360(x85262,x85263,x85261))))+P107(f866(f866(f244(a930),f2(a930)),f866(f866(f9(x85261,a930),x85262),x85263)))
% 157.76/157.52 [8562]~P66(x85622)+E(x85621,f84(x85622))+E(f866(f866(f297(x85622),f866(f866(f23(x85622),f866(f866(f252(x85622),x85621),x85623)),f84(x85622))),f866(f866(f23(x85622),x85621),f84(x85622))),f866(f866(f6(a930,x85622),f866(f252(x85622),x85621)),f866(f309(a930,f2(a930)),x85623)))
% 157.76/157.52 [8619]E(x86191,f2(a930))+~P107(f866(x86193,f866(f866(f41(a930),x86192),x86191)))+P107(f866(f866(f244(a930),x86192),f866(f866(f87(a930),x86191),f866(a119,f344(x86191,x86192,x86193)))))
% 157.76/157.52 [8637]P107(f866(x86371,f2(a930)))+~P107(f866(x86371,f866(f866(f41(a930),x86372),x86373)))+P107(f866(f866(f244(a930),x86372),f866(f866(f87(a930),x86373),f866(a119,f344(x86373,x86372,x86371)))))
% 157.76/157.52 [8675]E(x86751,f2(a930))+~P107(f866(x86753,f866(f866(f41(a930),x86752),x86751)))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x86751),f344(x86751,x86752,x86753))),x86752))
% 157.76/157.52 [8706]P107(f866(x87061,f2(a930)))+~P107(f866(x87061,f866(f866(f41(a930),x87063),x87062)))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x87062),f344(x87062,x87063,x87061))),x87063))
% 157.76/157.52 [8714]~P110(x87141)+E(f866(f866(f155(x87141,x87141,f5(x87141)),x87142),x87143),f156(x87141,x87141,f5(x87141),x87142,x87143))+P107(f866(f866(f336(x87141),x87142),f866(f179(x87141),x87143)))
% 157.76/157.52 [8750]~E(f866(x87503,f557(x87502,x87503,x87501)),f866(x87503,f560(x87502,x87503,x87501)))+~P61(x87501,f866(x87503,f558(x87502,x87503,x87501)))+P61(x87501,f866(f866(f44(x87502,f937(x87501,f937(x87501,a925))),f250(f937(x87502,a925))),x87503))
% 157.76/157.52 [8759]E(x87591,f195(f937(f937(x87592,a925),a925)))+~P107(f866(f866(f243(f937(x87592,a925)),f633(x87593,x87591,x87592)),x87593))+P107(f866(f866(f243(f937(x87592,a925)),f43(f937(x87592,a925),x87591)),x87593))
% 157.76/157.52 [8819]~P68(x88191)+~P107(f866(f866(f244(x88191),x88192),x88193))+P107(f866(f866(f244(x88191),x88192),f866(f866(f297(x88191),f866(f866(f86(x88191),x88192),x88193)),f866(f866(f86(x88191),f84(x88191)),f84(x88191)))))
% 157.76/157.52 [8877]~P107(f866(f866(x88771,f492(x88771,x88773,x88772)),f496(x88771,x88773,x88772)))+P107(f866(f866(x88771,x88772),x88773))+~P107(f866(f322(f936(a1,a1),a57),f866(f866(f260(a1,a1),x88772),x88773)))
% 157.76/157.52 [8878]~P107(f866(f866(x88781,f498(x88781,x88783,x88782)),f499(x88781,x88783,x88782)))+P107(f866(f866(x88781,x88782),x88783))+~P107(f866(f322(f936(a1,a1),a63),f866(f866(f260(a1,a1),x88782),x88783)))
% 157.76/157.52 [8879]~P107(f866(f866(x88791,f502(x88791,x88793,x88792)),f503(x88791,x88793,x88792)))+P107(f866(f866(x88791,x88792),x88793))+~P107(f866(f322(f936(a1,a1),a230),f866(f866(f260(a1,a1),x88792),x88793)))
% 157.76/157.52 [8880]~P107(f866(f866(x88801,f504(x88801,x88803,x88802)),f505(x88801,x88803,x88802)))+P107(f866(f866(x88801,x88802),x88803))+~P107(f866(f322(f936(a930,a930),a228),f866(f866(f260(a930,a930),x88802),x88803)))
% 157.76/157.52 [8881]~P107(f866(f866(x88811,f684(x88811,x88813,x88812)),f686(x88811,x88813,x88812)))+P107(f866(f866(x88811,x88812),x88813))+~P107(f866(f322(f936(a1,a1),a189),f866(f866(f260(a1,a1),x88812),x88813)))
% 157.76/157.52 [8882]~P107(f866(f866(x88821,f782(x88821,x88823,x88822)),f783(x88821,x88823,x88822)))+P107(f866(f866(x88821,x88822),x88823))+~P107(f866(f322(f936(a1,a1),a140),f866(f866(f260(a1,a1),x88822),x88823)))
% 157.76/157.52 [9159]P107(f866(f866(x91591,x91592),x91593))+P107(f866(f322(f936(a930,a930),a228),f866(f866(f260(a930,a930),f504(x91591,x91593,x91592)),f505(x91591,x91593,x91592))))+~P107(f866(f322(f936(a930,a930),a228),f866(f866(f260(a930,a930),x91592),x91593)))
% 157.76/157.52 [9160]P107(f866(f866(x91601,x91602),x91603))+P107(f866(f322(f936(a1,a1),a57),f866(f866(f260(a1,a1),f492(x91601,x91603,x91602)),f496(x91601,x91603,x91602))))+~P107(f866(f322(f936(a1,a1),a57),f866(f866(f260(a1,a1),x91602),x91603)))
% 157.76/157.52 [9161]P107(f866(f866(x91611,x91612),x91613))+P107(f866(f322(f936(a1,a1),a63),f866(f866(f260(a1,a1),f498(x91611,x91613,x91612)),f499(x91611,x91613,x91612))))+~P107(f866(f322(f936(a1,a1),a63),f866(f866(f260(a1,a1),x91612),x91613)))
% 157.76/157.52 [9162]P107(f866(f866(x91621,x91622),x91623))+P107(f866(f322(f936(a1,a1),a230),f866(f866(f260(a1,a1),f502(x91621,x91623,x91622)),f503(x91621,x91623,x91622))))+~P107(f866(f322(f936(a1,a1),a230),f866(f866(f260(a1,a1),x91622),x91623)))
% 157.76/157.52 [9163]P107(f866(f866(x91631,x91632),x91633))+P107(f866(f322(f936(a1,a1),a189),f866(f866(f260(a1,a1),f684(x91631,x91633,x91632)),f686(x91631,x91633,x91632))))+~P107(f866(f322(f936(a1,a1),a189),f866(f866(f260(a1,a1),x91632),x91633)))
% 157.76/157.52 [9164]P107(f866(f866(x91641,x91642),x91643))+P107(f866(f322(f936(a1,a1),a140),f866(f866(f260(a1,a1),f782(x91641,x91643,x91642)),f783(x91641,x91643,x91642))))+~P107(f866(f322(f936(a1,a1),a140),f866(f866(f260(a1,a1),x91642),x91643)))
% 157.76/157.52 [9498]~P107(f866(f66(x94981),x94983))+P107(f866(f866(f336(f936(f937(x94981,a925),f937(x94981,a925))),f866(f866(f260(f937(x94981,a925),f937(x94981,a925)),x94982),x94983)),f321(x94981)))+~P107(f866(f866(f244(f937(x94981,a925)),x94982),x94983))
% 157.76/157.52 [9507]P107(f866(f866(x95071,x95072),f874(x95073,x95071)))+~P24(a924,a940,f866(f866(f316(f929(a924)),f98(a924,x95073,a941,x95071)),f195(f937(f929(a924),a925))))+~P107(f866(f866(x95073,x95072),a865))
% 157.76/157.52 [9572]~P61(x95721,f866(x95723,f558(x95722,x95723,x95721)))+P61(x95721,f866(f866(f44(x95722,f937(x95721,f937(x95721,a925))),f250(f937(x95722,a925))),x95723))+~E(f866(f866(f108(f937(x95721,a925)),f257(x95721,x95721,f866(x95723,f557(x95722,x95723,x95721)))),f258(x95721,x95721,f866(x95723,f560(x95722,x95723,x95721)))),f195(f937(x95721,a925)))
% 157.76/157.52 [9771]P53(x97711,x97712,x97713)+P107(f866(f866(f336(f936(x97711,x97711)),f551(x97713,x97712,x97711)),x97713))+~P107(f866(f866(f336(f936(x97711,x97711)),f866(f866(f260(x97711,x97711),f550(x97713,x97712,x97711)),f550(x97713,x97712,x97711))),x97713))
% 157.76/157.52 [10353]P53(x103531,x103532,x103533)+~P107(f866(f866(f265(x103531,x103531,a925),f866(f866(f7(x103531,f937(x103531,a925),f937(x103531,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x103531,a925),f937(x103531,a925)),x103531),f8(a925,a925,x103531)),f866(f866(f8(a925,f937(a925,a925),x103531),a333),f866(f866(f7(x103531,f937(x103531,a925),a925),f336(x103531)),x103532)))),f866(f866(f7(x103531,f937(x103531,a925),a925),f336(x103531)),x103532))),f551(x103533,x103532,x103531)))+~P107(f866(f866(f336(f936(x103531,x103531)),f866(f866(f260(x103531,x103531),f550(x103533,x103532,x103531)),f550(x103533,x103532,x103531))),x103533))
% 157.76/157.52 [5907]~P62(x59072)+E(x59071,f2(x59072))+E(f866(f866(f41(x59072),f866(f866(f87(x59072),x59073),x59071)),x59071),x59073)
% 157.76/157.52 [5908]~P62(x59082)+E(x59081,f2(x59082))+E(f866(f866(f41(x59082),f866(f866(f87(x59082),x59081),x59083)),x59081),x59083)
% 157.76/157.52 [6257]~P62(x62571)+~P57(x62571,x62573,x62572)+E(f866(f866(f87(x62571),f866(f866(f41(x62571),x62572),x62573)),x62573),x62572)
% 157.76/157.52 [6715]~P72(x67151)+~E(f866(x67152,f2(a930)),f2(x67151))+E(f866(f866(f6(a930,x67151),x67152),f866(f309(a930,f866(a119,f2(a930))),x67153)),f866(f866(f6(a930,x67151),x67152),f866(f309(a930,f2(a930)),x67153)))
% 157.76/157.52 [6848]~P62(x68482)+E(x68481,f2(x68482))+E(f866(f866(f41(x68482),f866(f866(f86(x68482),x68483),x68481)),x68481),f866(f866(f86(x68482),f866(f866(f41(x68482),x68483),x68481)),f84(x68482)))
% 157.76/157.52 [6849]~P62(x68492)+E(x68491,f2(x68492))+E(f866(f866(f41(x68492),f866(f866(f86(x68492),x68491),x68493)),x68491),f866(f866(f86(x68492),f866(f866(f41(x68492),x68493),x68491)),f84(x68492)))
% 157.76/157.52 [7064]~P107(f866(x70643,f2(a1)))+P107(f866(f866(f243(a930),x70641),x70642))+P107(f866(x70643,f866(f107(a1),f866(f866(f23(a930),x70642),x70641))))
% 157.76/157.52 [7167]P107(f866(f866(f244(a930),x71672),x71671))+P107(f866(f866(f243(a930),x71671),x71672))+P107(f866(x71673,f866(f107(a1),f866(f866(f23(a930),x71672),x71671))))
% 157.76/157.52 [7238]E(f866(f866(f86(a930),f866(f110(a930),x72381)),f866(f866(f86(a930),f866(f110(a930),x72382)),x72383)),f866(f866(f86(a930),f866(f110(a930),x72381)),x72383))+P107(f866(a200,f866(f110(a1),x72381)))+~P107(f866(a200,f866(f110(a1),x72382)))
% 157.76/157.52 [7316]~E(x73162,f866(f866(f41(a930),x73163),x73161))+~P107(f866(f866(f244(a930),f2(a930)),x73161))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x73161),x73162)),x73163))
% 157.76/157.52 [7431]~P107(f866(f66(x74311),x74313))+~P107(f866(f66(x74311),x74312))+P107(f866(f66(x74311),f866(f866(f117(f937(x74311,a925)),x74312),x74313)))
% 157.76/157.52 [7479]~P38(x74791,x74793)+~P38(x74791,x74792)+P38(x74791,f866(f866(f108(f937(f936(x74791,x74791),a925)),x74792),x74793))
% 157.76/157.52 [7480]~P52(x74801,x74803)+~P52(x74801,x74802)+P52(x74801,f866(f866(f117(f937(f936(x74801,x74801),a925)),x74802),x74803))
% 157.76/157.52 [7481]~P52(x74811,x74813)+~P52(x74811,x74812)+P52(x74811,f866(f866(f108(f937(f936(x74811,x74811),a925)),x74812),x74813))
% 157.76/157.52 [7723]~P110(x77231)+~P107(f866(f66(x77231),x77232))+E(f146(x77231,f866(f866(f23(f937(x77231,a925)),x77232),f866(f866(f316(x77231),x77233),f195(f937(x77231,a925))))),f177(x77231,x77233,f146(x77231,x77232)))
% 157.76/157.52 [7784]P107(f866(x77841,f2(a1)))+~P107(f866(f866(f244(a930),x77842),x77843))+~P107(f866(x77841,f866(f107(a1),f866(f866(f23(a930),x77842),x77843))))
% 157.76/157.52 [7802]~P107(f866(f66(x78021),x78022))+E(f866(f40(x78021),f866(f866(f23(f937(x78021,a925)),x78022),f866(f866(f316(x78021),x78023),f195(f937(x78021,a925))))),f866(f40(x78021),x78022))+P107(f866(f866(f336(x78021),x78023),x78022))
% 157.76/157.52 [7932]~P113(x79321)+~P107(f866(f866(f244(x79321),f84(x79321)),x79322))+P107(f866(f866(f244(x79321),f84(x79321)),f866(f866(f87(x79321),x79322),f866(f866(f252(x79321),x79322),x79323))))
% 157.76/157.52 [7975]~P107(f866(f66(x79751),x79753))+E(f866(f866(f23(a930),f866(f40(x79751),x79752)),f866(f40(x79751),x79753)),f866(f40(x79751),f866(f866(f23(f937(x79751,a925)),x79752),x79753)))+~P107(f866(f866(f243(f937(x79751,a925)),x79753),x79752))
% 157.76/157.52 [8033]~P107(f866(f866(f243(a930),x80332),x80333))+~P107(f866(f866(f243(a930),x80331),f866(f866(f23(a930),x80333),x80332)))+P107(f866(f866(f243(a930),f866(f866(f86(a930),x80331),x80332)),x80333))
% 157.76/157.52 [8084]P107(f866(f66(x80841),x80842))+~P107(f866(f66(x80841),x80843))+~P107(f866(f66(x80841),f866(f866(f23(f937(x80841,a925)),x80842),x80843)))
% 157.76/157.52 [8090]~P107(f866(f66(x80901),x80902))+E(f866(f40(x80901),f866(f866(f23(f937(x80901,a925)),x80902),f866(f866(f316(x80901),x80903),f195(f937(x80901,a925))))),f866(f866(f23(a930),f866(f40(x80901),x80902)),f84(a930)))+~P107(f866(f866(f336(x80901),x80903),x80902))
% 157.76/157.52 [8165]P61(x81651,x81652)+~P61(x81651,x81653)+~P107(f866(f866(f243(f937(x81651,f937(x81651,a925))),x81652),x81653))
% 157.76/157.52 [8206]~P107(f866(f866(f243(a930),x82063),x82062))+P107(f866(f866(f243(a930),x82061),f866(f866(f23(a930),x82062),x82063)))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),x82061),x82063)),x82062))
% 157.76/157.52 [8224]P37(x82241,x82242)+~P37(x82241,x82243)+~P107(f866(f866(f243(f937(f936(x82241,x82241),a925)),x82242),x82243))
% 157.76/157.52 [8225]P59(x82251,x82252)+~P59(x82251,x82253)+~P107(f866(f866(f243(f937(f936(x82251,x82251),a925)),x82252),x82253))
% 157.76/157.52 [8226]P39(x82261,x82262)+~P39(x82261,x82263)+~P107(f866(f866(f243(f937(f936(x82261,x82261),a925)),x82262),x82263))
% 157.76/157.52 [8453]~P113(x84531)+~P107(f866(f866(f244(x84531),f84(x84531)),x84532))+P107(f866(f866(f244(x84531),f866(f866(f252(x84531),x84532),x84533)),f866(f866(f87(x84531),x84532),f866(f866(f252(x84531),x84532),x84533))))
% 157.76/157.52 [8544]~P107(f866(x85441,f2(a1)))+~P107(f866(x85441,f866(f866(f23(a1),f866(f107(a1),x85442)),f866(f107(a1),x85443))))+P107(f866(x85441,f866(f107(a1),f866(f866(f23(a930),x85442),x85443))))
% 157.76/157.52 [8559]~P107(f866(f866(f243(a930),x85593),x85592))+P107(f866(x85591,f866(f866(f23(a1),f866(f107(a1),x85592)),f866(f107(a1),x85593))))+~P107(f866(x85591,f866(f107(a1),f866(f866(f23(a930),x85592),x85593))))
% 157.76/157.52 [8578]P107(f866(f866(f244(a930),x85781),x85782))+~P107(f866(x85783,f866(f866(f23(a1),f866(f107(a1),x85781)),f866(f107(a1),x85782))))+P107(f866(x85783,f866(f107(a1),f866(f866(f23(a930),x85781),x85782))))
% 157.76/157.52 [8631]~P120(x86312)+E(x86311,f2(x86312))+P107(f866(f866(f244(x86312),f2(x86312)),f866(f866(f86(x86312),f866(f866(f87(x86312),x86313),x86313)),f866(f866(f87(x86312),x86311),x86311))))
% 157.76/157.52 [8632]~P120(x86322)+E(x86321,f2(x86322))+P107(f866(f866(f244(x86322),f2(x86322)),f866(f866(f86(x86322),f866(f866(f87(x86322),x86321),x86321)),f866(f866(f87(x86322),x86323),x86323))))
% 157.76/157.52 [8731]~P107(f866(f866(f244(a930),f2(a930)),x87311))+~P107(f866(f866(f244(a1),x87312),x87313))+P107(f866(f866(f244(a1),f866(f866(f87(a1),f866(f107(a1),x87311)),x87312)),f866(f866(f87(a1),f866(f107(a1),x87311)),x87313)))
% 157.76/157.52 [8788]E(f866(f866(f108(f937(x87881,a925)),x87882),f42(f937(x87881,a925),x87883)),f195(f937(x87881,a925)))+P107(f866(f866(f336(f937(x87881,a925)),x87882),x87883))+P107(f866(f866(f336(f937(x87881,a925)),f629(x87883,x87882,x87881)),f866(f866(f316(f937(x87881,a925)),x87882),x87883)))
% 157.76/157.52 [8789]E(f866(f866(f108(f937(x87891,a925)),x87892),f42(f937(x87891,a925),x87893)),f195(f937(x87891,a925)))+P107(f866(f866(f336(f937(x87891,a925)),x87892),x87893))+P107(f866(f866(f336(f937(x87891,a925)),f628(x87893,x87892,x87891)),f866(f866(f316(f937(x87891,a925)),x87892),x87893)))
% 157.76/157.52 [8818]E(x88181,x88182)+~E(f866(f196(f931(x88183)),x88181),f866(f196(f931(x88183)),x88182))+P107(f866(f866(f336(f936(x88183,x88183)),f670(x88183,x88181,x88182)),f866(f179(f936(x88183,x88183)),f866(f866(f188(x88183,x88183),x88182),x88181))))
% 157.76/157.52 [9068]E(f314(x90681,x90682),f314(x90681,x90683))+~P107(f866(f866(f243(f937(f936(x90681,x90681),a925)),x90683),f314(x90681,x90682)))+~P107(f866(f866(f243(f937(f936(x90681,x90681),a925)),x90682),x90683))
% 157.76/157.52 [9137]~P53(x91371,f250(f937(x91371,a925)),x91373)+P107(f866(f866(f243(f937(f936(f931(x91371),f931(x91371)),a925)),f164(x91371,x91372)),f165(x91371,x91373)))+~P107(f866(f866(f243(f937(f936(x91371,x91371),a925)),x91372),x91373))
% 157.76/157.52 [9337]P37(x93371,x93372)+~P107(f866(f866(f336(x93371),x93373),f590(x93372,x93371)))+P107(f866(f866(f336(f936(x93371,x93371)),f866(f866(f260(x93371,x93371),f645(x93372,x93371,x93373)),x93373)),x93372))
% 157.76/157.52 [9372]~P107(f866(f66(x93721),x93722))+P107(f866(f66(f937(x93721,a925)),f866(f866(f65(x93721),x93722),x93723)))+~P107(f866(f866(f243(f937(f936(x93721,x93721),a925)),x93723),f866(f866(f262(x93721,x93721),x93722),f866(f16(f937(x93721,a925),x93721),x93722))))
% 157.76/157.52 [9408]P53(x94081,x94082,x94083)+P107(f866(f866(f336(x94081),f545(x94083,x94082,x94081)),x94082))+~P107(f866(f866(f243(f937(f936(x94081,x94081),a925)),x94083),f866(f866(f262(x94081,x94081),x94082),f866(f16(f937(x94081,a925),x94081),x94082))))
% 157.76/157.52 [9409]P53(x94091,x94092,x94093)+P107(f866(f866(f336(x94091),f548(x94092,x94093,x94091)),x94092))+~P107(f866(f866(f243(f937(f936(x94091,x94091),a925)),x94093),f866(f866(f262(x94091,x94091),x94092),f866(f16(f937(x94091,a925),x94091),x94092))))
% 157.76/157.52 [9441]~P68(x94411)+~P107(f866(f866(f244(x94411),x94412),x94413))+P107(f866(f866(f244(x94411),f866(f866(f297(x94411),f866(f866(f86(x94411),x94412),x94413)),f866(f866(f86(x94411),f84(x94411)),f84(x94411)))),x94413))
% 157.76/157.52 [9470]~P67(x94701)+P107(f866(f866(f243(x94701),x94702),x94703))+~P107(f866(f866(f243(x94701),f866(f866(f87(x94701),f343(x94703,x94702,x94701)),x94702)),x94703))
% 157.76/157.52 [9607]E(f866(f196(f931(f931(x96071))),f866(f143(f931(x96071),f866(f866(f8(a930,a925,f931(x96071)),f866(f244(a930),x96072)),f196(f931(x96071)))),f186(x96071,x96073))),f866(f196(f931(x96071)),f866(f866(f171(f931(x96071)),x96073),x96072)))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x96071),a930),f196(f931(x96071))),x96073)))+~P107(f866(f866(f244(a930),x96072),f866(f196(f931(f931(x96071))),x96073)))
% 157.76/157.52 [9719]~P37(x97191,x97192)+P27(x97191,f866(f866(f260(f937(f936(x97191,x97191),a925),f937(f936(x97191,x97191),a925)),x97192),x97193))+~P107(f866(f866(f243(f937(f936(x97191,x97191),a925)),f866(f866(f296(x97191,x97191,x97191),x97192),x97193)),x97192))
% 157.76/157.52 [9724]E(f866(f866(f161(f931(x97241),x97241),f866(f866(f7(f931(x97241),a930,x97241),f171(x97241)),x97242)),f866(f143(f931(x97241),f866(f866(f8(a930,a925,f931(x97241)),f866(f244(a930),x97242)),f196(f931(x97241)))),f186(x97241,x97243))),f866(f866(f171(f931(x97241)),x97243),x97242))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x97241),a930),f196(f931(x97241))),x97243)))+~P107(f866(f866(f244(a930),x97242),f866(f196(f931(f931(x97241))),x97243)))
% 157.76/157.52 [9859]P53(x98591,x98592,x98593)+~P107(f866(f866(f336(f936(x98591,x98591)),f866(f866(f260(x98591,x98591),f545(x98593,x98592,x98591)),f545(x98593,x98592,x98591))),x98593))+~P107(f866(f866(f243(f937(f936(x98591,x98591),a925)),x98593),f866(f866(f262(x98591,x98591),x98592),f866(f16(f937(x98591,a925),x98591),x98592))))
% 157.76/157.52 [9860]P53(x98601,x98602,x98603)+~P107(f866(f866(f336(f936(x98601,x98601)),f866(f866(f260(x98601,x98601),f548(x98602,x98603,x98601)),f548(x98602,x98603,x98601))),x98603))+~P107(f866(f866(f243(f937(f936(x98601,x98601),a925)),x98603),f866(f866(f262(x98601,x98601),x98602),f866(f16(f937(x98601,a925),x98601),x98602))))
% 157.76/157.52 [10031]~P142(x100311)+~P127(x100311)+E(f866(f866(f297(x100311),f866(f109(x100311),f866(f866(f78(f936(a1,a1),a1,x100312,f259(a1,a1)),f221(x100312)),x100313))),f866(f109(x100311),f866(f866(f78(f936(a1,a1),a1,x100312,f264(a1,a1)),f221(x100312)),x100313))),f231(x100312,x100311,x100313))
% 157.76/157.52 [10226]~E(x102263,f2(a930))+~E(f866(f196(f931(x102261)),f866(f866(f171(f931(x102261)),x102262),f720(x102263,x102261,x102262))),x102263)+E(f866(f866(f161(a930,f931(x102261)),f866(f866(f7(a930,f931(a930),f931(x102261)),f866(f866(f8(f937(a930,x102261),f937(f931(a930),f931(x102261)),a930),f161(a930,x102261)),f866(f7(a930,a930,x102261),f866(f866(f8(f931(x102261),f937(a930,x102261),a930),f171(x102261)),f866(f171(f931(x102261)),x102262))))),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(f931(x102261))),x102262))))),f146(a930,f866(f309(a930,f2(a930)),x102263))),f186(x102261,x102262))
% 157.76/157.52 [10227]E(x102271,f120(f931(x102272)))+~E(f866(f196(f931(x102272)),f866(f866(f171(f931(x102272)),x102271),f720(x102273,x102272,x102271))),x102273)+E(f866(f866(f161(a930,f931(x102272)),f866(f866(f7(a930,f931(a930),f931(x102272)),f866(f866(f8(f937(a930,x102272),f937(f931(a930),f931(x102272)),a930),f161(a930,x102272)),f866(f7(a930,a930,x102272),f866(f866(f8(f931(x102272),f937(a930,x102272),a930),f171(x102272)),f866(f171(f931(x102272)),x102271))))),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(f931(x102272))),x102271))))),f146(a930,f866(f309(a930,f2(a930)),x102273))),f186(x102272,x102271))
% 157.76/157.52 [10228]~E(x102283,f2(a930))+E(f866(f866(f161(a930,f931(x102281)),f866(f866(f7(a930,f931(a930),f931(x102281)),f866(f866(f8(f937(a930,x102281),f937(f931(a930),f931(x102281)),a930),f161(a930,x102281)),f866(f7(a930,a930,x102281),f866(f866(f8(f931(x102281),f937(a930,x102281),a930),f171(x102281)),f866(f171(f931(x102281)),x102282))))),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(f931(x102281))),x102282))))),f146(a930,f866(f309(a930,f2(a930)),x102283))),f186(x102281,x102282))+P107(f866(f866(f244(a930),f720(x102283,x102281,x102282)),f866(f196(f931(f931(x102281))),x102282)))
% 157.76/157.52 [10229]E(x102291,f120(f931(x102292)))+E(f866(f866(f161(a930,f931(x102292)),f866(f866(f7(a930,f931(a930),f931(x102292)),f866(f866(f8(f937(a930,x102292),f937(f931(a930),f931(x102292)),a930),f161(a930,x102292)),f866(f7(a930,a930,x102292),f866(f866(f8(f931(x102292),f937(a930,x102292),a930),f171(x102292)),f866(f171(f931(x102292)),x102291))))),f146(a930,f866(f309(a930,f2(a930)),f866(f196(f931(f931(x102292))),x102291))))),f146(a930,f866(f309(a930,f2(a930)),x102293))),f186(x102292,x102291))+P107(f866(f866(f244(a930),f720(x102293,x102292,x102291)),f866(f196(f931(f931(x102292))),x102291)))
% 157.76/157.52 [7972]E(f866(f866(f86(a930),f866(f110(a930),x79721)),f866(f866(f86(a930),f866(f110(a930),x79722)),x79723)),f866(f866(f86(a930),f866(f110(a930),f866(f866(f86(a1),x79721),x79722))),x79723))+P107(f866(a200,f866(f110(a1),x79721)))+P107(f866(a200,f866(f110(a1),x79722)))
% 157.76/157.52 [8723]~P107(f866(f66(x87231),x87232))+~P107(f866(f866(f336(x87231),x87233),x87232))+E(f866(a119,f866(f40(x87231),f866(f866(f23(f937(x87231,a925)),x87232),f866(f866(f316(x87231),x87233),f195(f937(x87231,a925)))))),f866(f40(x87231),x87232))
% 157.76/157.52 [8740]~P107(f866(f66(x87401),x87402))+~P107(f866(f866(f336(x87401),x87403),x87402))+E(f866(f866(f86(a930),f84(a930)),f866(f40(x87401),f866(f866(f23(f937(x87401,a925)),x87402),f866(f866(f316(x87401),x87403),f195(f937(x87401,a925)))))),f866(f40(x87401),x87402))
% 157.76/157.52 [8827]~P110(x88271)+~P107(f866(f66(x88271),x88273))+E(f866(f866(f155(x88271,x88271,f5(x88271)),x88272),f146(x88271,f866(f866(f23(f937(x88271,a925)),x88273),f866(f866(f316(x88271),x88272),f195(f937(x88271,a925)))))),f146(x88271,f866(f866(f316(x88271),x88272),x88273)))
% 157.76/157.52 [8993]~P107(f866(f66(x89931),x89933))+~P107(f866(f66(x89931),x89932))+E(f866(f866(f86(a930),f866(f40(x89931),f866(f866(f117(f937(x89931,a925)),x89932),x89933))),f866(f40(x89931),f866(f866(f108(f937(x89931,a925)),x89932),x89933))),f866(f866(f86(a930),f866(f40(x89931),x89932)),f866(f40(x89931),x89933)))
% 157.76/157.52 [10174]~P25(x101741,f937(f937(x101741,a925),a925),f866(f866(f7(x101741,f937(f936(x101741,x101741),a925),f937(f937(x101741,a925),a925)),f866(f866(f8(f937(x101741,a925),f937(f937(f936(x101741,x101741),a925),f937(f937(x101741,a925),a925)),x101741),f65(x101741)),f866(f866(f7(x101741,f937(x101741,a925),f937(x101741,a925)),f316(x101741)),f195(f937(x101741,a925))))),x101743),x101742)+~P107(f866(f66(x101741),x101742))+E(f866(f40(f937(x101741,a925)),f866(f866(f65(x101741),x101742),x101743)),f866(f40(x101741),x101742))
% 157.76/157.52 [8238]~P96(x82381)+P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x82383)))+E(f866(f866(f252(x82381),x82382),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x82383),x82383)),a104))),f84(x82381))
% 157.76/157.52 [9704]~P96(x97041)+~P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),x97043)))+E(f866(f866(f252(x97041),x97042),f866(f110(a930),f866(f866(f23(a1),f866(f866(f86(a1),x97043),x97043)),a104))),f866(f866(f92(x97041,x97041),f866(f866(f252(x97041),x97042),f866(f110(a930),x97043))),f866(f866(f18(x97041,x97041,x97041),f866(f866(f8(x97041,f937(x97041,x97041),x97041),f87(x97041)),f866(f87(x97041),x97042))),f5(x97041))))
% 157.76/157.52 [10093]~P107(f866(f144(x100931),x100933))+~P107(f866(f866(f336(x100931),x100932),f866(f179(x100931),x100933)))+E(f866(f866(f145(x100931),f866(f196(f931(x100931)),f184(x100931,f866(f866(f8(a925,a925,x100931),a329),f866(f866(f7(x100931,x100931,a925),a332),x100932)),f866(f175(x100931),x100933)))),f866(f175(x100931),x100933)),f866(f866(f158(x100931),x100932),f866(f175(x100931),f184(x100931,f866(f866(f8(a925,a925,x100931),a329),f866(f866(f7(x100931,x100931,a925),a332),x100932)),x100933))))
% 157.76/157.52 [10154]P107(f866(f866(f243(f937(f936(x101541,x101541),a925)),f314(x101541,x101542)),x101543))+~P107(f866(f866(f243(f937(f936(x101541,x101541),a925)),f314(x101541,f195(f937(f936(x101541,x101541),a925)))),x101543))+~P107(f866(f866(f243(f937(f936(x101541,x101541),a925)),f866(f866(f296(x101541,x101541,x101541),f866(f866(f108(f937(f936(x101541,x101541),a925)),f314(x101541,x101542)),x101543)),x101542)),x101543))
% 157.76/157.52 [10011]~P107(f866(f66(x100111),f866(f270(x100111),x100113)))+~P107(f866(f66(x100111),f866(f270(x100111),x100112)))+P107(f866(f66(x100111),f866(f270(x100111),f866(f866(f18(x100111,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100111),a334),x100112)),x100113))))
% 157.76/157.52 [10288]P107(f866(f866(f243(f937(f936(x102881,x102881),a925)),f866(f866(f296(x102881,x102881,x102881),x102882),f314(x102881,x102882))),x102883))+~P107(f866(f866(f243(f937(f936(x102881,x102881),a925)),x102882),x102883))+~P107(f866(f866(f243(f937(f936(x102881,x102881),a925)),f866(f866(f296(x102881,x102881,x102881),f866(f866(f108(f937(f936(x102881,x102881),a925)),f866(f866(f296(x102881,x102881,x102881),x102882),f314(x102881,x102882))),x102883)),x102882)),x102883))
% 157.76/157.52 [10242]~P128(x102422)+E(x102421,f2(x102422))+~E(f866(f866(f86(x102422),f866(f866(f252(x102422),x102423),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x102422),x102421),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f2(x102422))
% 157.76/157.52 [10243]~P128(x102432)+E(x102431,f2(x102432))+~E(f866(f866(f86(x102432),f866(f866(f252(x102432),x102431),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x102432),x102433),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f2(x102432))
% 157.76/157.52 [10248]~P107(f866(f144(x102481),x102483))+~P107(f866(f866(f336(x102481),x102482),f866(f179(x102481),x102483)))+E(f866(f175(x102481),f866(f178(x102481),f866(f866(f145(x102481),f866(f196(f931(x102481)),f184(x102481,f866(f866(f8(a925,a925,x102481),a329),f866(f866(f7(x102481,x102481,a925),a332),x102482)),x102483))),x102483))),f184(x102481,f866(f866(f8(a925,a925,x102481),a329),f866(f866(f7(x102481,x102481,a925),a332),x102482)),f866(f175(x102481),x102483)))
% 157.76/157.52 [10335]~P128(x103352)+E(x103351,f2(x103352))+P107(f866(f866(f244(x103352),f2(x103352)),f866(f866(f86(x103352),f866(f866(f252(x103352),x103353),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103352),x103351),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))))
% 157.76/157.52 [10336]~P128(x103362)+E(x103361,f2(x103362))+P107(f866(f866(f244(x103362),f2(x103362)),f866(f866(f86(x103362),f866(f866(f252(x103362),x103361),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103362),x103363),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))))
% 157.76/157.52 [10391]~P128(x103911)+P107(f866(f866(f243(x103911),f2(x103911)),x103912))+~P107(f866(f866(f243(x103911),f2(x103911)),f866(f866(f252(x103911),x103912),f866(a119,f866(f866(f87(a930),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),x103913)))))
% 157.76/157.52 [5735]~P24(x57351,x57354,x57353)+P24(x57351,x57352,x57353)+~P24(x57351,x57352,x57354)
% 157.76/157.52 [5202]~E(x52022,f96(x52023,x52021))+P107(f866(x52021,x52022))+~P107(f866(x52021,x52024))
% 157.76/157.52 [5445]E(f73(x54453,x54452,x54454),x54452)+E(x54451,f746(x54452,x54453,x54454))+~P107(f866(x54454,x54451))
% 157.76/157.52 [6771]E(f73(x67711,x67712,x67713),f91(x67711,x67713))+~E(f787(x67712,x67711,x67713,x67714),x67714)+~P107(f866(x67713,x67714))
% 157.76/157.52 [6978]~P37(x69782,x69784)+~P37(x69781,x69783)+P37(f936(x69781,x69782),f326(x69781,x69782,x69783,x69784))
% 157.76/157.52 [6979]~P38(x69792,x69794)+~P38(x69791,x69793)+P38(f936(x69791,x69792),f326(x69791,x69792,x69793,x69794))
% 157.76/157.52 [5385]~P7(x53854,x53851)+~E(f866(x53851,x53852),f866(x53851,x53853))+P107(f866(f866(x53851,x53852),x53853))
% 157.76/157.52 [5550]~P7(x55504,x55501)+E(f866(x55501,x55502),f866(x55501,x55503))+~P107(f866(f866(x55501,x55502),x55503))
% 157.76/157.52 [5551]~P15(x55514,x55511)+E(f866(x55511,x55512),f866(x55511,x55513))+~P107(f866(f866(x55511,x55512),x55513))
% 157.76/157.52 [5642]~P18(x56423,x56424,x56421)+E(f866(x56421,x56422),f866(f68(x56423,x56424),x56422))+~P107(f866(f66(x56423),x56422))
% 157.76/157.52 [5643]~P9(x56433,x56434,x56431)+E(f866(x56431,x56432),f866(f68(x56433,x56434),x56432))+~P107(f866(f66(x56433),x56432))
% 157.76/157.52 [5768]~P7(x57684,x57681)+~P107(f866(f866(x57681,x57683),x57682))+P107(f866(f866(x57681,x57682),x57683))
% 157.76/157.52 [5769]~P51(x57694,x57691)+~P107(f866(f866(x57691,x57693),x57692))+P107(f866(f866(x57691,x57692),x57693))
% 157.76/157.52 [5770]~P15(x57704,x57701)+~P107(f866(f866(x57701,x57703),x57702))+P107(f866(f866(x57701,x57702),x57703))
% 157.76/157.52 [5771]~P15(x57713,x57711)+P107(f866(f866(x57711,x57712),x57712))+~P107(f866(f866(x57711,x57714),x57712))
% 157.76/157.52 [5772]~P15(x57723,x57721)+P107(f866(f866(x57721,x57722),x57722))+~P107(f866(f866(x57721,x57722),x57724))
% 157.76/157.52 [5849]E(x58491,x58492)+~E(f866(f259(x58493,x58494),x58491),f866(f259(x58493,x58494),x58492))+~E(f866(f264(x58493,x58494),x58491),f866(f264(x58493,x58494),x58492))
% 157.76/157.52 [5876]E(x58761,x58762)+~P107(f866(f53(x58763,x58764),x58762))+~P107(f866(f53(x58763,x58764),x58761))
% 157.76/157.52 [6069]~P72(x60692)+E(f240(x60691,x60692,x60693,x60694),f2(x60692))+P107(f866(f66(x60691),x60694))
% 157.76/157.52 [6119]~P7(x61193,x61192)+~P107(f866(x61191,x61194))+P107(f866(x61191,f827(x61191,x61192,x61193)))
% 157.76/157.52 [6212]~P107(f866(f322(x62121,x62122),x62124))+P107(f866(f322(x62121,x62122),x62123))+~P107(f866(f866(x62122,x62123),x62124))
% 157.76/157.52 [6644]P49(x66441,x66442,x66443,x66444)+P107(f866(f866(x66442,x66444),x66443))+~P107(f866(f866(x66442,x66443),x66444))
% 157.76/157.52 [7011]~P29(x70111,x70113,x70114)+P107(f866(x70111,x70112))+~P107(f866(f866(f336(a1),x70112),f310(a1,x70113,x70114)))
% 157.76/157.52 [7201]~P7(x72011,x72013)+~P107(f866(x72012,x72014))+P107(f866(f866(f336(x72011),f827(x72012,x72013,x72011)),f278(x72011,x72013)))
% 157.76/157.52 [8079]E(x80791,f2(a930))+~P107(f866(x80792,x80793))+P107(f866(x80792,f780(x80792,x80793,x80791,x80794)))
% 157.76/157.52 [8160]~P110(x81602)+~P107(f866(f144(x81601),x81604))+P107(f866(f144(x81601),f157(x81601,x81602,x81603,x81604)))
% 157.76/157.52 [8205]E(f73(x82051,x82052,x82053),f91(x82051,x82053))+~P107(f866(x82053,x82054))+P107(f866(x82053,f787(x82052,x82051,x82053,x82054)))
% 157.76/157.52 [8380]~P107(f866(f66(x83802),x83804))+~P107(f866(f66(x83801),x83803))+P107(f866(f66(f938(x83801,x83802)),f320(x83801,x83802,x83803,x83804)))
% 157.76/157.52 [8381]~P107(f866(f144(x83812),x83814))+~P107(f866(f144(x83811),x83813))+P107(f866(f144(f936(x83811,x83812)),f64(x83811,x83812,x83813,x83814)))
% 157.76/157.52 [8384]P107(f866(f866(f336(f931(x83841)),f866(f866(f141(x83841),x83842),x83843)),f168(x83841,x83844)))+~P107(f866(f866(f336(f931(x83841)),x83843),f168(x83841,x83844)))+~P107(f866(f866(f336(f931(x83841)),x83842),f168(x83841,x83844)))
% 157.76/157.52 [8661]E(x86611,f2(a930))+P107(f866(x86612,x86613))+~P107(f866(x86612,f781(x86612,x86613,x86611,x86614)))
% 157.76/157.52 [8698]~P110(x86983)+~P107(f866(f144(x86981),f157(x86981,x86983,x86984,x86982)))+P107(f866(f144(x86981),x86982))
% 157.76/157.52 [8982]~P107(f866(f866(f336(f936(x89821,x89821)),f866(f866(f260(x89821,x89821),x89822),x89824)),f314(x89821,x89823)))+P107(f866(f866(f336(x89821),x89822),f323(x89821,x89823)))+~P107(f866(f866(f336(x89821),x89824),f323(x89821,x89823)))
% 157.76/157.52 [5368]~P71(x53682)+E(f866(f866(f9(x53681,x53682),x53683),x53684),f84(x53682))+P107(f866(f66(x53681),x53684))
% 157.76/157.52 [5371]~P72(x53712)+E(f866(f866(f6(x53711,x53712),x53713),x53714),f2(x53712))+P107(f866(f66(x53711),x53714))
% 157.76/157.52 [5372]~P124(x53721)+P57(x53721,x53722,x53723)+~E(x53723,f866(f866(f87(x53721),x53722),x53724))
% 157.76/157.52 [5515]~P73(x55153)+E(x55151,x55152)+~E(f866(f866(f86(x55153),x55154),x55151),f866(f866(f86(x55153),x55154),x55152))
% 157.76/157.52 [5516]~P74(x55163)+E(x55161,x55162)+~E(f866(f866(f86(x55163),x55164),x55161),f866(f866(f86(x55163),x55164),x55162))
% 157.76/157.52 [5518]~P73(x55183)+E(x55181,x55182)+~E(f866(f866(f86(x55183),x55181),x55184),f866(f866(f86(x55183),x55182),x55184))
% 157.76/157.52 [5638]~P5(x56383)+E(x56381,f195(f937(x56382,a925)))+E(f866(f866(f44(x56382,x56383),x56381),f866(f16(x56383,x56382),x56384)),x56384)
% 157.76/157.52 [5639]~P5(x56393)+E(x56391,f195(f937(x56392,a925)))+E(f866(f866(f45(x56392,x56393),x56391),f866(f16(x56393,x56392),x56394)),x56394)
% 157.76/157.52 [5789]~E(x57894,f195(f937(x57891,a925)))+~E(x57894,f866(f866(f316(x57891),x57892),x57893))+P107(f866(f866(f336(x57891),x57892),x57893))
% 157.76/157.52 [5842]~P114(x58421)+~P57(x58421,x58422,x58424)+P57(x58421,x58422,f866(f866(f87(x58421),x58423),x58424))
% 157.76/157.52 [5843]~P114(x58431)+~P57(x58431,x58432,x58433)+P57(x58431,x58432,f866(f866(f87(x58431),x58433),x58434))
% 157.76/157.52 [5862]~P111(x58623)+E(x58621,x58622)+~E(f310(x58623,x58624,x58621),f866(f866(f316(x58623),x58622),f195(f937(x58623,a925))))
% 157.76/157.52 [5863]~P111(x58633)+E(x58631,x58632)+~E(f310(x58633,x58631,x58632),f866(f866(f316(x58633),x58634),f195(f937(x58633,a925))))
% 157.76/157.52 [5923]~P35(x59233,x59231,x59234)+P35(x59233,x59231,f866(f866(f158(x59233),x59232),x59234))+P107(f866(x59231,x59232))
% 157.76/157.52 [5934]~P123(x59341)+~E(x59343,f2(x59341))+P57(x59341,f866(f866(f87(x59341),x59342),x59343),f866(f866(f87(x59341),x59344),x59343))
% 157.76/157.52 [5935]~P123(x59351)+~E(x59352,f2(x59351))+P57(x59351,f866(f866(f87(x59351),x59352),x59353),f866(f866(f87(x59351),x59352),x59354))
% 157.76/157.52 [6027]~P31(x60271,x60272,x60274)+~P107(f866(x60272,x60273))+P31(x60271,x60272,f866(f866(f158(x60271),x60273),x60274))
% 157.76/157.52 [6096]~P114(x60961)+P57(x60961,x60962,x60963)+~P57(x60961,f866(f866(f87(x60961),x60964),x60962),x60963)
% 157.76/157.52 [6097]~P114(x60971)+P57(x60971,x60972,x60973)+~P57(x60971,f866(f866(f87(x60971),x60972),x60974),x60973)
% 157.76/157.52 [6168]P107(f866(x61681,x61682))+~P107(f866(f256(x61683,x61681),x61684))+~P107(f866(f866(f336(x61683),x61682),x61684))
% 157.76/157.52 [6177]~P31(x61771,x61772,x61774)+~P31(x61771,x61772,x61773)+P31(x61771,x61772,f866(f866(f141(x61771),x61773),x61774))
% 157.76/157.52 [6191]P33(x61911,x61912,x61913)+~P33(x61911,x61912,f866(f866(f158(x61911),x61914),x61913))+P107(f866(x61912,x61914))
% 157.76/157.52 [6192]P35(x61921,x61922,x61923)+~P35(x61921,x61922,f866(f866(f158(x61921),x61924),x61923))+P107(f866(x61922,x61924))
% 157.76/157.52 [6260]~P123(x62601)+~P57(x62601,x62603,x62604)+P57(x62601,f866(f866(f87(x62601),x62602),x62603),f866(f866(f87(x62601),x62602),x62604))
% 157.76/157.52 [6261]~P123(x62611)+~P57(x62611,x62612,x62614)+P57(x62611,f866(f866(f87(x62611),x62612),x62613),f866(f866(f87(x62611),x62614),x62613))
% 157.76/157.52 [6269]P33(x62691,x62692,x62693)+P33(x62691,x62692,x62694)+~P33(x62691,x62692,f866(f866(f141(x62691),x62694),x62693))
% 157.76/157.52 [6288]~P72(x62881)+E(f866(f866(f6(a930,x62881),x62882),f866(f309(a930,x62883),f866(a119,x62884))),f2(x62881))+~P107(f866(f866(f244(a930),x62884),x62883))
% 157.76/157.52 [6293]~P63(x62931)+~E(f50(x62931,x62932,x62933),f50(x62931,x62934,x62933))+E(f50(x62931,f866(f85(x62931),x62932),x62933),f50(x62931,f866(f85(x62931),x62934),x62933))
% 157.76/157.52 [6359]P107(f866(x63591,x63592))+~E(f866(f143(x63593,x63591),x63594),x63594)+~P107(f866(f866(f336(x63593),x63592),f866(f179(x63593),x63594)))
% 157.76/157.52 [6378]~E(f866(f866(f86(a930),x63783),x63782),f866(f866(f86(a930),x63781),x63784))+~P107(f866(f866(f244(a930),x63783),x63784))+P107(f866(f866(f244(a930),x63781),x63782))
% 157.76/157.52 [6384]P33(x63841,x63842,x63843)+~P107(f866(x63842,x63844))+~P107(f866(f866(f336(x63841),x63844),f866(f179(x63841),x63843)))
% 157.76/157.52 [6423]~P31(x64233,x64231,x64234)+P107(f866(x64231,x64232))+~P107(f866(f866(f336(x64233),x64232),f866(f179(x64233),x64234)))
% 157.76/157.52 [6425]~E(f866(f143(x64251,x64252),x64253),f120(x64251))+~P107(f866(x64252,x64254))+~P107(f866(f866(f336(x64251),x64254),f866(f179(x64251),x64253)))
% 157.76/157.52 [6426]~E(f184(x64263,x64261,x64264),x64264)+P107(f866(x64261,x64262))+~P107(f866(f866(f336(x64263),x64262),f866(f179(x64263),x64264)))
% 157.76/157.52 [6452]~E(x64524,f195(f937(x64522,a925)))+~E(x64523,f195(f937(x64521,a925)))+E(f320(x64521,x64522,x64523,x64524),f195(f937(f938(x64521,x64522),a925)))
% 157.76/157.52 [6600]P107(f866(x66001,x66002))+~P107(f866(f167(x66003,x66001),x66004))+~P107(f866(f866(f336(x66003),x66002),f866(f179(x66003),x66004)))
% 157.76/157.52 [6739]~P30(x67391,x67393,x67394)+P107(f866(x67391,x67392))+~P107(f866(f866(f336(a930),x67392),f866(f309(a930,x67393),x67394)))
% 157.76/157.52 [6876]~P72(x68761)+E(f866(f866(f6(a930,x68761),x68762),f310(a930,x68763,f866(a119,x68764))),f2(x68761))+~P107(f866(f866(f244(a930),f866(a119,x68764)),x68763))
% 157.76/157.52 [7014]~P110(x70141)+E(f866(f866(f23(f937(x70141,a925)),f866(f309(x70141,x70142),x70143)),f866(f309(x70141,x70142),x70144)),f866(f309(x70141,x70144),x70143))+~P107(f866(f866(f243(x70141),x70142),x70144))
% 157.76/157.52 [7086]~E(x70863,x70864)+E(x70861,f2(a930))+P107(f866(f866(f336(x70862),x70863),f866(f179(x70862),f176(x70862,x70861,x70864))))
% 157.76/157.52 [7362]~P107(f866(f866(f336(f931(x73621)),x73624),f168(x73621,x73623)))+P107(f866(f866(f336(x73621),x73622),x73623))+~P107(f866(f866(f336(x73621),x73622),f866(f179(x73621),x73624)))
% 157.76/157.52 [7369]~P37(x73691,x73692)+P107(f866(f866(f336(x73691),f631(x73692,x73691,x73693)),x73693))+~P107(f866(f866(f336(x73691),x73694),x73693))
% 157.76/157.52 [7424]~P71(x74241)+E(f866(f866(f866(f70(x74241,x74242,f87(x74241)),x74243),f84(x74241)),x74244),f866(f866(f9(x74242,x74241),x74243),x74244))+~P107(f866(f66(x74242),x74244))
% 157.76/157.52 [7426]~P72(x74261)+E(f866(f866(f866(f70(x74261,x74262,f86(x74261)),x74263),f2(x74261)),x74264),f866(f866(f6(x74262,x74261),x74263),x74264))+~P107(f866(f66(x74262),x74264))
% 157.76/157.52 [7454]P25(x74541,x74542,x74543,x74544)+~E(f866(f40(x74542),f866(f317(x74541,x74542,x74543),x74544)),f866(f40(x74541),x74544))+~P107(f866(f66(x74541),x74544))
% 157.76/157.52 [7645]~P72(x76451)+E(f866(f866(f86(x76451),f866(x76452,x76453)),f866(f866(f6(a930,x76451),x76452),f312(a930,x76453,x76454))),f866(f866(f6(a930,x76451),x76452),f310(a930,x76453,x76454)))+~P107(f866(f866(f243(a930),x76453),x76454))
% 157.76/157.52 [7655]~P71(x76551)+~P25(x76552,x76551,x76553,x76554)+E(f866(f866(f9(x76551,x76551),f32(x76551)),f866(f317(x76552,x76551,x76553),x76554)),f866(f866(f9(x76552,x76551),x76553),x76554))
% 157.76/157.52 [7656]~P72(x76561)+~P25(x76562,x76561,x76563,x76564)+E(f866(f866(f6(x76561,x76561),f32(x76561)),f866(f317(x76562,x76561,x76563),x76564)),f866(f866(f6(x76562,x76561),x76563),x76564))
% 157.76/157.52 [7705]E(f866(f40(f938(x77051,x77052)),f320(x77051,x77052,x77053,x77054)),f866(f866(f86(a930),f866(f40(x77051),x77053)),f866(f40(x77052),x77054)))+~P107(f866(f66(x77052),x77054))+~P107(f866(f66(x77051),x77053))
% 157.76/157.52 [7785]E(x77851,x77852)+P107(f866(f866(f336(x77853),x77851),f866(f179(x77853),f177(x77853,x77852,x77854))))+~P107(f866(f866(f336(x77853),x77851),f866(f179(x77853),x77854)))
% 157.76/157.52 [8012]~P72(x80121)+E(f866(f866(f86(x80121),f866(f866(f6(a930,x80121),x80122),f866(f309(a930,x80123),x80124))),f866(x80122,x80124)),f866(f866(f6(a930,x80121),x80122),f866(f309(a930,x80123),f866(a119,x80124))))+P107(f866(f866(f244(a930),x80124),x80123))
% 157.76/157.52 [8061]~P25(x80611,x80612,x80613,f250(f937(x80611,a925)))+~P107(f866(f66(x80612),x80614))+P107(f866(f66(x80611),f866(f318(x80611,x80612,x80613),x80614)))
% 157.76/157.52 [8175]P107(f866(f866(f336(f931(x81751)),f866(f866(f158(x81751),x81752),x81753)),f168(x81751,x81754)))+~P107(f866(f866(f336(f931(x81751)),x81753),f168(x81751,x81754)))+~P107(f866(f866(f336(x81751),x81752),x81754))
% 157.76/157.52 [8262]~E(f866(f317(x82623,x82621,x82624),f250(f937(x82623,a925))),f250(f937(x82621,a925)))+P107(f866(f66(x82621),x82622))+~P107(f866(f66(x82623),f866(f318(x82623,x82621,x82624),x82622)))
% 157.76/157.52 [8353]~P25(x83531,x83533,x83534,x83532)+P107(f866(f66(x83531),x83532))+~P107(f866(f66(x83533),f866(f317(x83531,x83533,x83534),x83532)))
% 157.76/157.52 [8374]~E(x83742,x83743)+P107(f866(f866(f336(f936(x83741,x83741)),f866(f866(f260(x83741,x83741),x83742),x83743)),f271(x83741,x83744)))+~P107(f866(f866(f336(x83741),x83742),x83744))
% 157.76/157.52 [8407]~P72(x84071)+E(f866(f866(f86(x84071),f866(f866(f6(a930,x84071),x84072),f310(a930,x84073,x84074))),f866(x84072,f866(a119,x84074))),f866(f866(f6(a930,x84071),x84072),f310(a930,x84073,f866(a119,x84074))))+P107(f866(f866(f244(a930),f866(a119,x84074)),x84073))
% 157.76/157.52 [8467]P107(f866(x84671,x84672))+~P107(f866(x84671,f866(f866(f171(x84673),x84674),f669(x84671,x84674,x84673))))+~P107(f866(f866(f336(x84673),x84672),f866(f179(x84673),x84674)))
% 157.76/157.52 [8607]~P107(f866(f866(f336(x86071),x86072),f323(x86071,x86074)))+P107(f866(f866(f336(f931(x86071)),f866(f866(f158(x86071),x86072),x86073)),f323(f931(x86071),f164(x86071,x86074))))+~P107(f866(f866(f336(f931(x86071)),x86073),f323(f931(x86071),f164(x86071,x86074))))
% 157.76/157.52 [8622]~P25(x86222,x86223,x86224,f634(x86224,x86223,x86222,x86221))+P25(x86222,x86223,x86224,f43(f937(x86222,a925),x86221))+E(x86221,f195(f937(f937(x86222,a925),a925)))
% 157.76/157.52 [8891]E(x88911,x88912)+~P107(f866(f866(f336(f936(x88913,x88913)),f866(f866(f260(x88913,x88913),x88911),x88912)),f314(x88913,x88914)))+P107(f866(f866(f336(x88913),x88911),f866(f272(x88913,x88913),x88914)))
% 157.76/157.52 [9175]E(x91751,f2(a930))+P107(f866(x91752,x91753))+P107(f866(f866(f336(x91754),f781(x91752,x91753,x91751,x91754)),f866(f179(x91754),f176(x91754,x91751,x91753))))
% 157.76/157.52 [9187]E(x91871,f2(a930))+~P107(f866(x91873,x91874))+P107(f866(f866(f336(x91872),f780(x91873,x91874,x91871,x91872)),f866(f179(x91872),f176(x91872,x91871,x91874))))
% 157.76/157.52 [9189]~P26(x91891,x91892,x91893,f250(f937(x91891,a925)),f250(f937(x91892,a925)))+~P107(f866(f66(x91892),x91894))+P107(f866(f66(x91891),f866(f318(x91891,x91892,x91893),x91894)))
% 157.76/157.52 [9192]P25(x91922,x91923,x91924,f43(f937(x91922,a925),x91921))+E(x91921,f195(f937(f937(x91922,a925),a925)))+P107(f866(f866(f336(f937(x91922,a925)),f634(x91924,x91923,x91922,x91921)),x91921))
% 157.76/157.52 [9307]~P26(x93073,x93071,x93074,f250(f937(x93073,a925)),f250(f937(x93071,a925)))+P107(f866(f66(x93071),x93072))+~P107(f866(f66(x93073),f866(f318(x93073,x93071,x93074),x93072)))
% 157.76/157.52 [9324]P107(f866(f66(x93241),x93242))+~P107(f866(f66(x93244),f866(f317(x93241,x93244,x93243),x93242)))+P107(f866(f866(f336(x93241),f897(x93243,x93244,x93242,x93241)),x93242))
% 157.76/157.52 [9419]~P5(x94192)+E(f866(f866(f69(x94191,x94192,f866(f866(f8(x94192,f937(x94192,x94192),x94191),f117(x94192)),x94193)),f195(x94192)),x94194),f866(f866(f44(x94191,x94192),x94194),x94193))+~P107(f866(f66(x94191),x94194))
% 157.76/157.52 [9420]~P5(x94202)+E(f866(f866(f69(x94201,x94202,f866(f866(f8(x94202,f937(x94202,x94202),x94201),f108(x94202)),x94203)),f250(x94202)),x94204),f866(f866(f45(x94201,x94202),x94204),x94203))+~P107(f866(f66(x94201),x94204))
% 157.76/157.52 [9501]P107(f866(x95011,x95012))+~P107(f866(x95011,f866(f866(f171(x95013),x95014),f706(x95012,x95011,x95014,x95013))))+~P107(f866(f866(f336(x95013),x95012),f866(f179(x95013),x95014)))
% 157.76/157.52 [9523]E(x95231,x95232)+~P107(f866(f866(f336(f936(x95233,x95233)),f866(f866(f260(x95233,x95233),x95231),x95232)),f314(x95233,x95234)))+P107(f866(f866(f336(f936(x95233,x95233)),f866(f866(f260(x95233,x95233),x95231),x95232)),f866(f866(f296(x95233,x95233,x95233),x95234),f314(x95233,x95234))))
% 157.76/157.52 [9573]~E(f866(f196(f931(x95731)),x95732),f866(f196(f931(x95731)),x95733))+~P107(f866(f866(f336(f936(f931(x95731),f931(x95731))),f866(f866(f260(f931(x95731),f931(x95731)),x95732),x95733)),f154(x95731,x95734)))+P107(f866(f866(f336(f936(f931(x95731),f931(x95731))),f866(f866(f260(f931(x95731),f931(x95731)),x95732),x95733)),f152(x95731,x95734)))
% 157.76/157.52 [9807]P31(x98071,f866(f866(f18(x98071,a925,a925),f866(f866(f8(a925,f937(a925,a925),x98071),a334),f866(f866(f8(a925,a925,x98071),a329),x98072))),f866(a332,x98073)),x98074)+~P107(f866(x98072,x98073))+~P35(x98071,x98072,f866(f866(f158(x98071),x98073),x98074))
% 157.76/157.52 [9974]~P31(x99741,f866(f866(f18(x99741,a925,a925),f866(f866(f8(a925,f937(a925,a925),x99741),a334),f866(f866(f8(a925,a925,x99741),a329),x99742))),f866(a332,x99743)),x99744)+~P107(f866(x99742,x99743))+P35(x99741,x99742,f866(f866(f158(x99741),x99743),x99744))
% 157.76/157.52 [9978]~P35(x99781,x99782,x99784)+~P31(x99781,f866(f866(f18(x99781,a925,a925),f866(f866(f8(a925,f937(a925,a925),x99781),a334),f866(f866(f8(a925,a925,x99781),a329),x99782))),f866(a332,x99783)),x99784)+P35(x99781,x99782,f866(f866(f158(x99781),x99783),x99784))
% 157.76/157.52 [10012]~P3(x100121)+E(f866(f866(f6(a930,x100121),f866(f866(f18(a930,x100121,x100121),f866(f866(f8(x100121,f937(x100121,x100121),a930),f23(x100121)),x100122)),f866(f866(f8(a930,x100121,a930),x100122),f866(f866(f7(a930,a930,a930),f86(a930)),f84(a930))))),f310(a930,x100123,x100124)),f2(x100121))+P107(f866(f866(f243(a930),x100123),x100124))
% 157.76/157.52 [10241]~P37(x102412,x102414)+~P25(x102412,x102411,x102413,f250(f937(x102412,a925)))+P37(x102411,f866(f317(f936(x102412,x102412),f936(x102411,x102411),f266(x102412,x102411,x102412,x102411,x102413,x102413)),x102414))
% 157.76/157.52 [10430]~E(f866(f196(f931(x104301)),x104303),f866(f196(f931(x104301)),x104302))+P107(f866(f866(f336(f936(f931(x104301),f931(x104301))),f866(f866(f260(f931(x104301),f931(x104301)),x104302),x104303)),f165(x104301,x104304)))+~P107(f866(f866(f265(x104301,x104301,a925),f866(f866(f7(x104301,f937(f936(x104301,x104301),a925),f937(x104301,a925)),f866(f866(f8(f937(x104301,f937(f937(f936(x104301,x104301),a925),a925)),f937(f937(f936(x104301,x104301),a925),f937(x104301,a925)),x104301),f7(x104301,f937(f936(x104301,x104301),a925),a925)),f866(f866(f8(f937(x104301,f936(x104301,x104301)),f937(x104301,f937(f937(f936(x104301,x104301),a925),a925)),x104301),f866(f8(f936(x104301,x104301),f937(f937(f936(x104301,x104301),a925),a925),x104301),f336(f936(x104301,x104301)))),f260(x104301,x104301)))),x104304)),f672(x104304,x104303,x104302,x104301)))
% 157.76/157.52 [6340]~P62(x63401)+~E(x63402,f2(x63401))+E(f866(f866(f41(x63401),f866(f866(f87(x63401),x63402),x63403)),f866(f866(f87(x63401),x63402),x63404)),f2(x63401))
% 157.76/157.52 [6381]E(x63811,f120(x63812))+E(x63813,f866(f866(f23(a930),f866(f196(f931(x63812)),x63811)),f84(a930)))+E(f151(x63812,f866(f866(f166(x63812,x63811),x63813),x63814)),f151(x63812,x63811))
% 157.76/157.52 [6414]E(x64141,x64142)+P107(f866(x64143,x64142))+~P107(f866(f866(f866(f316(x64144),x64141),x64143),x64142))
% 157.76/157.52 [6430]~P72(x64301)+~P107(f866(f144(x64302),x64304))+E(f866(f172(x64301),f866(f866(f161(x64302,x64301),x64303),x64304)),f866(f866(f6(x64302,x64301),x64303),f866(f179(x64302),x64304)))
% 157.76/157.52 [6445]~P71(x64452)+~P107(f866(f66(x64451),x64454))+E(f866(f866(f9(x64451,x64452),f866(f16(x64452,x64451),x64453)),x64454),f866(f866(f252(x64452),x64453),f866(f40(x64451),x64454)))
% 157.76/157.52 [6498]~P62(x64982)+E(x64981,f2(x64982))+E(f866(f866(f41(x64982),f866(f866(f87(x64982),x64983),x64981)),f866(f866(f87(x64982),x64984),x64981)),f866(f866(f41(x64982),x64983),x64984))
% 157.76/157.52 [6500]~P65(x65002)+E(x65001,f2(x65002))+E(f866(f866(f297(x65002),f866(f866(f87(x65002),x65003),x65001)),f866(f866(f87(x65002),x65004),x65001)),f866(f866(f297(x65002),x65003),x65004))
% 157.76/157.52 [6501]~P65(x65012)+E(x65011,f2(x65012))+E(f866(f866(f297(x65012),f866(f866(f87(x65012),x65011),x65013)),f866(f866(f87(x65012),x65011),x65014)),f866(f866(f297(x65012),x65013),x65014))
% 157.76/157.52 [6502]~P62(x65022)+E(x65021,f2(x65022))+E(f866(f866(f41(x65022),f866(f866(f87(x65022),x65021),x65023)),f866(f866(f87(x65022),x65021),x65024)),f866(f866(f41(x65022),x65023),x65024))
% 157.76/157.52 [6567]P107(f866(x65671,x65672))+~E(x65673,f866(f866(f86(a930),x65674),x65672))+~P107(f866(x65671,f866(f866(f23(a930),x65673),x65674)))
% 157.76/157.52 [6655]~P107(f866(x66552,x66553))+~P107(f866(f167(x66551,x66552),x66554))+P107(f866(f167(x66551,x66552),f866(f866(f158(x66551),x66553),x66554)))
% 157.76/157.52 [6698]E(x66981,f120(x66982))+~E(x66983,f866(f866(f23(a930),f866(f196(f931(x66982)),x66981)),f84(a930)))+E(f151(x66982,f866(f866(f166(x66982,x66981),x66983),x66984)),x66984)
% 157.76/157.52 [6721]~P102(x67211)+~P107(f866(f866(f243(x67211),x67212),x67214))+P107(f866(f866(f243(x67211),x67212),f866(f866(f117(x67211),x67213),x67214)))
% 157.76/157.52 [6722]~P102(x67221)+~P107(f866(f866(f243(x67221),x67222),x67223))+P107(f866(f866(f243(x67221),x67222),f866(f866(f117(x67221),x67223),x67224)))
% 157.76/157.52 [6724]~P110(x67241)+~P107(f866(f866(f243(x67241),x67242),x67244))+P107(f866(f866(f243(x67241),x67242),f866(f866(f242(x67241),x67243),x67244)))
% 157.76/157.52 [6726]~P110(x67261)+~P107(f866(f866(f243(x67261),x67262),x67263))+P107(f866(f866(f243(x67261),x67262),f866(f866(f242(x67261),x67263),x67264)))
% 157.76/157.52 [6727]~P102(x67271)+~P107(f866(f866(f244(x67271),x67272),x67274))+P107(f866(f866(f244(x67271),x67272),f866(f866(f117(x67271),x67273),x67274)))
% 157.76/157.52 [6728]~P102(x67281)+~P107(f866(f866(f244(x67281),x67282),x67283))+P107(f866(f866(f244(x67281),x67282),f866(f866(f117(x67281),x67283),x67284)))
% 157.76/157.52 [6730]~P110(x67301)+~P107(f866(f866(f244(x67301),x67302),x67304))+P107(f866(f866(f244(x67301),x67302),f866(f866(f242(x67301),x67303),x67304)))
% 157.76/157.52 [6732]~P110(x67321)+~P107(f866(f866(f244(x67321),x67322),x67323))+P107(f866(f866(f244(x67321),x67322),f866(f866(f242(x67321),x67323),x67324)))
% 157.76/157.52 [6823]~E(f866(f866(f171(x68231),x68232),x68233),x68234)+E(f866(f866(f166(x68231,x68232),x68233),x68234),x68232)+~P107(f866(f866(f244(a930),x68233),f866(f196(f931(x68231)),x68232)))
% 157.76/157.52 [6862]P107(f866(x68621,x68622))+~P107(f866(x68623,x68622))+~P107(f866(f866(f243(f937(x68624,a925)),x68623),x68621))
% 157.76/157.52 [6893]~E(f866(f866(f166(x68931,x68932),x68933),x68934),x68932)+E(f866(f866(f171(x68931),x68932),x68933),x68934)+~P107(f866(f866(f244(a930),x68933),f866(f196(f931(x68931)),x68932)))
% 157.76/157.52 [6907]~P107(f866(f167(x69071,x69072),x69074))+~P107(f866(f167(x69071,x69072),x69073))+P107(f866(f167(x69071,x69072),f866(f866(f141(x69071),x69073),x69074)))
% 157.76/157.52 [7010]E(x70101,f195(f937(x70102,a925)))+E(x70103,f195(f937(x70104,a925)))+~E(f866(f866(f262(x70104,x70102),x70103),f866(f16(f937(x70102,a925),x70104),x70101)),f195(f937(f936(x70104,x70102),a925)))
% 157.76/157.52 [7030]E(x70301,x70302)+P107(f866(f866(f336(x70303),x70301),x70304))+~P107(f866(f866(f336(x70303),x70301),f866(f866(f316(x70303),x70302),x70304)))
% 157.76/157.52 [7047]~P110(x70471)+P107(f866(f866(f243(x70471),x70472),x70473))+~P107(f866(f866(f243(x70471),x70472),f866(f866(f241(x70471),x70474),x70473)))
% 157.76/157.52 [7049]~P110(x70491)+P107(f866(f866(f243(x70491),x70492),x70493))+~P107(f866(f866(f243(x70491),x70492),f866(f866(f241(x70491),x70493),x70494)))
% 157.76/157.52 [7051]~P103(x70511)+P107(f866(f866(f243(x70511),x70512),x70513))+~P107(f866(f866(f243(x70511),x70512),f866(f866(f108(x70511),x70514),x70513)))
% 157.76/157.52 [7053]~P103(x70531)+P107(f866(f866(f243(x70531),x70532),x70533))+~P107(f866(f866(f243(x70531),x70532),f866(f866(f108(x70531),x70533),x70534)))
% 157.76/157.52 [7054]~P110(x70541)+P107(f866(f866(f244(x70541),x70542),x70543))+~P107(f866(f866(f244(x70541),x70542),f866(f866(f241(x70541),x70544),x70543)))
% 157.76/157.52 [7055]~P110(x70551)+P107(f866(f866(f244(x70551),x70552),x70553))+~P107(f866(f866(f244(x70551),x70552),f866(f866(f241(x70551),x70553),x70554)))
% 157.76/157.52 [7077]~E(f866(f866(f171(x70771),x70773),x70774),x70772)+P107(f866(f866(f336(x70771),x70772),f866(f179(x70771),x70773)))+~P107(f866(f866(f244(a930),x70774),f866(f196(f931(x70771)),x70773)))
% 157.76/157.52 [7087]~P110(x70871)+~P13(x70871,f866(f866(f158(x70871),x70872),f866(f866(f158(x70871),x70873),x70874)))+P107(f866(f866(f243(x70871),x70872),x70873))
% 157.76/157.52 [7228]~P31(x72282,x72281,x72283)+P107(f866(x72281,f866(f866(f171(x72282),x72283),x72284)))+~P107(f866(f866(f244(a930),x72284),f866(f196(f931(x72282)),x72283)))
% 157.76/157.52 [7246]E(x72461,f2(a1))+E(f866(f866(f41(a1),x72462),x72461),x72463)+~P107(f866(f54(x72462,x72461),f866(f866(f260(a1,a1),x72463),x72464)))
% 157.76/157.52 [7267]E(f50(a1,x72672,x72671),x72673)+E(x72671,f2(a1))+~P107(f866(f54(x72672,x72671),f866(f866(f260(a1,a1),x72674),x72673)))
% 157.76/157.52 [7386]P107(f866(f866(f336(x73861),x73862),x73863))+~P107(f866(f866(f336(x73861),x73862),x73864))+~P107(f866(f866(f244(f937(x73861,a925)),x73864),x73863))
% 157.76/157.52 [7387]P107(f866(f866(f336(x73871),x73872),x73873))+~P107(f866(f866(f336(x73871),x73872),x73874))+~P107(f866(f866(f243(f937(x73871,a925)),x73874),x73873))
% 157.76/157.52 [7498]P33(x74981,x74982,x74983)+~P107(f866(x74982,f866(f866(f171(x74981),x74983),x74984)))+~P107(f866(f866(f244(a930),x74984),f866(f196(f931(x74981)),x74983)))
% 157.76/157.52 [7612]~P109(x76122)+~P107(f866(f866(f244(f937(x76121,x76122)),x76123),x76124))+P107(f866(f866(f243(f937(x76121,x76122)),x76123),x76124))
% 157.76/157.52 [7694]~P24(x76941,x76942,x76944)+P24(x76941,x76942,f866(f866(f316(f929(x76941)),x76943),x76944))+~P24(x76941,x76942,f866(f866(f316(f929(x76941)),x76943),f195(f937(f929(x76941),a925))))
% 157.76/157.52 [7736]~P107(f866(f866(f336(x77361),x77362),x77364))+P107(f866(f866(f336(x77361),x77362),f42(f937(x77361,a925),x77363)))+~P107(f866(f866(f336(f937(x77361,a925)),x77364),x77363))
% 157.76/157.52 [7764]~P87(x77641)+~P107(f866(f866(f243(x77641),x77643),x77644))+P107(f866(f866(f243(x77641),f866(f866(f86(x77641),x77642),x77643)),f866(f866(f86(x77641),x77642),x77644)))
% 157.76/157.52 [7765]~P88(x77651)+~P107(f866(f866(f243(x77651),x77653),x77654))+P107(f866(f866(f243(x77651),f866(f866(f86(x77651),x77652),x77653)),f866(f866(f86(x77651),x77652),x77654)))
% 157.76/157.52 [7766]~P87(x77661)+~P107(f866(f866(f243(x77661),x77662),x77664))+P107(f866(f866(f243(x77661),f866(f866(f86(x77661),x77662),x77663)),f866(f866(f86(x77661),x77664),x77663)))
% 157.76/157.52 [7767]~P88(x77671)+~P107(f866(f866(f243(x77671),x77672),x77674))+P107(f866(f866(f243(x77671),f866(f866(f86(x77671),x77672),x77673)),f866(f866(f86(x77671),x77674),x77673)))
% 157.76/157.52 [7768]~P87(x77681)+~P107(f866(f866(f244(x77681),x77683),x77684))+P107(f866(f866(f244(x77681),f866(f866(f86(x77681),x77682),x77683)),f866(f866(f86(x77681),x77682),x77684)))
% 157.76/157.52 [7769]~P90(x77691)+~P107(f866(f866(f244(x77691),x77693),x77694))+P107(f866(f866(f244(x77691),f866(f866(f86(x77691),x77692),x77693)),f866(f866(f86(x77691),x77692),x77694)))
% 157.76/157.52 [7770]~P87(x77701)+~P107(f866(f866(f244(x77701),x77702),x77704))+P107(f866(f866(f244(x77701),f866(f866(f86(x77701),x77702),x77703)),f866(f866(f86(x77701),x77704),x77703)))
% 157.76/157.52 [7771]~P90(x77711)+~P107(f866(f866(f244(x77711),x77712),x77714))+P107(f866(f866(f244(x77711),f866(f866(f86(x77711),x77712),x77713)),f866(f866(f86(x77711),x77714),x77713)))
% 157.76/157.52 [7778]~P136(x77781)+~P97(x77781)+E(f866(f866(f23(x77781),f866(f866(f87(x77781),x77782),f866(f110(x77781),x77783))),f866(f866(f87(x77781),x77784),f866(f110(x77781),x77783))),f866(f866(f87(x77781),f866(f866(f23(x77781),x77782),x77784)),f866(f110(x77781),x77783)))
% 157.76/157.52 [7779]~P145(x77791)+~P97(x77791)+E(f866(f866(f86(x77791),f866(f866(f87(x77791),x77792),f866(f110(x77791),x77793))),f866(f866(f87(x77791),x77794),f866(f110(x77791),x77793))),f866(f866(f87(x77791),f866(f866(f86(x77791),x77792),x77794)),f866(f110(x77791),x77793)))
% 157.76/157.52 [7816]~P72(x78161)+E(f866(f866(f86(x78161),f866(x78162,x78163)),f866(f866(f6(a930,x78161),x78162),f310(a930,f866(a119,x78163),x78164))),f866(f866(f6(a930,x78161),x78162),f310(a930,x78163,x78164)))+~P107(f866(f866(f243(a930),x78163),x78164))
% 157.76/157.52 [7828]~P25(x78282,x78281,x78283,f866(f179(x78282),x78284))+~P107(f866(f144(x78282),x78284))+P107(f866(f144(x78281),f866(f866(f161(x78282,x78281),x78283),x78284)))
% 157.76/157.52 [7875]~P107(f866(f866(f243(a930),x78752),x78754))+~P107(f866(f866(f243(a930),x78751),x78753))+P107(f866(f866(f243(a930),f866(f866(f87(a930),x78751),x78752)),f866(f866(f87(a930),x78753),x78754)))
% 157.76/157.52 [7876]~P107(f866(f866(f243(a930),x78762),x78764))+~P107(f866(f866(f243(a930),x78761),x78763))+P107(f866(f866(f243(a930),f866(f866(f86(a930),x78761),x78762)),f866(f866(f86(a930),x78763),x78764)))
% 157.76/157.52 [7879]~P107(f866(f866(f244(a930),x78792),x78794))+~P107(f866(f866(f244(a930),x78791),x78793))+P107(f866(f866(f244(a930),f866(f866(f86(a930),x78791),x78792)),f866(f866(f86(a930),x78793),x78794)))
% 157.76/157.52 [7880]~P107(f866(f866(f243(a1),x78802),x78804))+~P107(f866(f866(f244(a1),x78801),x78803))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x78801),x78802)),f866(f866(f86(a1),x78803),x78804)))
% 157.76/157.52 [7927]P107(f866(f866(f336(x79271),x79272),x79273))+~P107(f866(f866(f336(x79271),x79272),f43(f937(x79271,a925),x79274)))+~P107(f866(f866(f336(f937(x79271,a925)),x79273),x79274))
% 157.76/157.52 [7943]~P107(f866(x79431,f667(x79431,x79433,x79432)))+P107(f866(x79431,f866(f866(f171(x79432),x79433),x79434)))+~P107(f866(f866(f244(a930),x79434),f866(f196(f931(x79432)),x79433)))
% 157.76/157.52 [7948]P107(f866(x79481,x79482))+~P107(f866(f866(f336(x79484),x79482),f866(f179(x79484),x79483)))+P107(f866(f866(f244(a930),f669(x79481,x79483,x79484)),f866(f196(f931(x79484)),x79483)))
% 157.76/157.52 [7997]~P109(x79971)+~P107(f866(f866(f244(f937(x79972,x79971)),x79974),x79973))+~P107(f866(f866(f243(f937(x79972,x79971)),x79973),x79974))
% 157.76/157.52 [8040]~P107(f866(x80404,x80402))+~P107(f866(f866(f336(x80401),x80402),x80403))+P107(f866(f866(f336(x80401),x80402),f866(f866(f108(f937(x80401,a925)),x80403),f866(f270(x80401),x80404))))
% 157.76/157.52 [8182]~P107(f866(f866(f336(x81821),x81823),x81824))+~P107(f866(f866(f244(f937(x81821,a925)),x81822),x81824))+P107(f866(f866(f244(f937(x81821,a925)),x81822),f866(f866(f316(x81821),x81823),x81824)))
% 157.76/157.52 [8184]E(f866(f866(f108(f937(x81841,a925)),x81842),x81843),f195(f937(x81841,a925)))+~E(f866(f866(f108(f937(x81841,a925)),f42(f937(x81841,a925),x81844)),x81843),f195(f937(x81841,a925)))+~P107(f866(f866(f336(f937(x81841,a925)),x81842),x81844))
% 157.76/157.52 [8258]P107(f866(f866(f336(x82581),x82582),x82583))+~P107(f866(f866(f243(f937(x82581,a925)),x82583),f866(f866(f316(x82581),x82582),x82584)))+P107(f866(f866(f243(f937(x82581,a925)),x82583),x82584))
% 157.76/157.52 [8275]P107(f866(f866(f336(x82752),f667(x82751,x82753,x82752)),f866(f179(x82752),x82753)))+P107(f866(x82751,f866(f866(f171(x82752),x82753),x82754)))+~P107(f866(f866(f244(a930),x82754),f866(f196(f931(x82752)),x82753)))
% 157.76/157.52 [8283]~P107(f866(f866(f243(f937(x82831,a925)),x82832),x82834))+P107(f866(f866(f243(f937(x82831,a925)),x82832),x82833))+~P107(f866(f866(f243(f937(x82831,a925)),x82834),x82833))
% 157.76/157.52 [8284]~P107(f866(f866(f244(f937(x82841,a925)),x82842),x82844))+~P107(f866(f866(f243(f937(x82841,a925)),x82844),x82843))+P107(f866(f866(f244(f937(x82841,a925)),x82842),x82843))
% 157.76/157.52 [8285]~P107(f866(f866(f243(f937(x82851,a925)),x82852),x82854))+~P107(f866(f866(f244(f937(x82851,a925)),x82854),x82853))+P107(f866(f866(f244(f937(x82851,a925)),x82852),x82853))
% 157.76/157.52 [8286]~P107(f866(f866(f244(f937(x82861,a925)),x82862),x82864))+P107(f866(f866(f244(f937(x82861,a925)),x82862),x82863))+~P107(f866(f866(f244(f937(x82861,a925)),x82864),x82863))
% 157.76/157.52 [8329]~P107(f866(f866(f336(x83291),x83294),x83293))+~P107(f866(f866(f244(f937(x83291,a925)),x83292),f866(f866(f316(x83291),x83294),x83293)))+P107(f866(f866(f244(f937(x83291,a925)),x83292),x83293))
% 157.76/157.52 [8340]~P87(x83401)+P107(f866(f866(f243(x83401),x83402),x83403))+~P107(f866(f866(f243(x83401),f866(f866(f86(x83401),x83404),x83402)),f866(f866(f86(x83401),x83404),x83403)))
% 157.76/157.52 [8342]~P87(x83421)+P107(f866(f866(f243(x83421),x83422),x83423))+~P107(f866(f866(f243(x83421),f866(f866(f86(x83421),x83422),x83424)),f866(f866(f86(x83421),x83423),x83424)))
% 157.76/157.52 [8344]~P87(x83441)+P107(f866(f866(f244(x83441),x83442),x83443))+~P107(f866(f866(f244(x83441),f866(f866(f86(x83441),x83444),x83442)),f866(f866(f86(x83441),x83444),x83443)))
% 157.76/157.52 [8346]~P87(x83461)+P107(f866(f866(f244(x83461),x83462),x83463))+~P107(f866(f866(f244(x83461),f866(f866(f86(x83461),x83462),x83464)),f866(f866(f86(x83461),x83463),x83464)))
% 157.76/157.52 [8391]P107(f866(x83911,x83912))+~E(f866(f866(f145(x83913),f866(f196(f931(x83913)),f184(x83913,x83911,x83914))),x83914),f120(x83913))+~P107(f866(f866(f336(x83913),x83912),f866(f179(x83913),x83914)))
% 157.76/157.52 [8509]P107(f866(x85091,x85092))+~P107(f866(f866(f336(x85093),x85092),f866(f179(x85093),x85094)))+P107(f866(f866(f244(a930),f866(f196(f931(x85093)),f866(f143(x85093,x85091),x85094))),f866(f196(f931(x85093)),x85094)))
% 157.76/157.52 [8998]~P107(f866(x89981,f761(x89981,x89983,x89982,x89984)))+P107(f866(x89981,f866(f866(f171(x89982),x89983),x89984)))+~P107(f866(f866(f244(a930),x89984),f866(f196(f931(x89982)),x89983)))
% 157.76/157.52 [9022]~P25(x90224,x90223,x90221,f250(f937(x90224,a925)))+E(f866(x90221,f671(x90222,x90221,x90223,x90224)),x90222)+~P107(f866(f866(f336(x90223),x90222),f866(f317(x90224,x90223,x90221),f250(f937(x90224,a925)))))
% 157.76/157.52 [9090]E(f184(x90901,x90902,x90903),f866(f866(f182(x90901),x90904),x90903))+P107(f866(f866(f244(a930),f731(x90902,x90903,x90901,x90904)),x90904))+P107(f866(f866(f244(a930),x90904),f866(f196(f931(x90901)),x90903)))
% 157.76/157.52 [9093]E(f184(x90931,x90932,x90933),f866(f866(f182(x90931),x90934),x90933))+P107(f866(f866(f244(a930),f731(x90932,x90933,x90931,x90934)),x90934))+P107(f866(x90932,f866(f866(f171(x90931),x90933),x90934)))
% 157.76/157.52 [9130]P107(f866(x91301,x91302))+~P107(f866(f866(f336(x91304),x91302),f866(f179(x91304),x91303)))+P107(f866(f866(f244(a930),f706(x91302,x91301,x91303,x91304)),f866(f196(f931(x91304)),x91303)))
% 157.76/157.52 [9132]E(f184(x91321,x91322,x91323),f866(f866(f182(x91321),x91324),x91323))+P107(f866(f866(f244(a930),x91324),f866(f196(f931(x91321)),x91323)))+P107(f866(f866(f244(a930),f731(x91322,x91323,x91321,x91324)),f866(f196(f931(x91321)),x91323)))
% 157.76/157.52 [9139]E(f184(x91391,x91392,x91393),f866(f866(f182(x91391),x91394),x91393))+P107(f866(x91392,f866(f866(f171(x91391),x91393),x91394)))+P107(f866(f866(f244(a930),f731(x91392,x91393,x91391,x91394)),f866(f196(f931(x91391)),x91393)))
% 157.76/157.52 [9166]~P113(x91664)+P107(f866(f866(f336(x91661),f652(x91662,x91663,x91661,x91664)),x91663))+P107(f866(f866(f244(x91664),f2(x91664)),f866(f866(f9(x91661,x91664),x91662),x91663)))
% 157.76/157.52 [9167]~P113(x91674)+P107(f866(f866(f336(x91671),f656(x91672,x91673,x91671,x91674)),x91673))+P107(f866(f866(f243(x91674),f2(x91674)),f866(f866(f9(x91671,x91674),x91672),x91673)))
% 157.76/157.52 [9194]~P107(f866(f66(x91941),x91944))+P107(f866(f866(f336(x91941),f532(x91942,x91943,x91944,x91941)),x91944))+P107(f866(f66(f936(x91941,x91943)),f866(f866(f262(x91941,x91943),x91944),x91942)))
% 157.76/157.52 [9226]P107(f866(f866(f336(x92262),f761(x92261,x92263,x92262,x92264)),f866(f179(x92262),x92263)))+P107(f866(x92261,f866(f866(f171(x92262),x92263),x92264)))+~P107(f866(f866(f244(a930),x92264),f866(f196(f931(x92262)),x92263)))
% 157.76/157.52 [9356]P107(f866(f866(f243(a930),x93564),f866(f196(f931(x93562)),f184(x93562,x93563,x93561))))+P107(f866(f866(f244(a930),f732(x93561,x93562,x93563,x93564)),x93564))+~P107(f866(f866(f243(a930),x93564),f866(f196(f931(x93562)),x93561)))
% 157.76/157.52 [9505]E(f184(x95051,x95052,x95053),f866(f866(f182(x95051),x95054),x95053))+~P107(f866(x95052,f866(f866(f171(x95051),x95053),f731(x95052,x95053,x95051,x95054))))+P107(f866(f866(f244(a930),x95054),f866(f196(f931(x95051)),x95053)))
% 157.76/157.52 [9513]E(f184(x95131,x95132,x95133),f866(f866(f182(x95131),x95134),x95133))+~P107(f866(x95132,f866(f866(f171(x95131),x95133),f731(x95132,x95133,x95131,x95134))))+P107(f866(x95132,f866(f866(f171(x95131),x95133),x95134)))
% 157.76/157.52 [9517]~P107(f866(f66(x95171),x95173))+~P107(f866(f66(x95172),f866(x95174,f532(x95174,x95172,x95173,x95171))))+P107(f866(f66(f936(x95171,x95172)),f866(f866(f262(x95171,x95172),x95173),x95174)))
% 157.76/157.52 [9525]~P113(x95251)+~P107(f866(f866(f243(x95251),f2(x95251)),f866(x95253,f656(x95253,x95254,x95252,x95251))))+P107(f866(f866(f243(x95251),f2(x95251)),f866(f866(f9(x95252,x95251),x95253),x95254)))
% 157.76/157.52 [9526]~P113(x95261)+~P107(f866(f866(f244(x95261),f2(x95261)),f866(x95263,f652(x95263,x95264,x95262,x95261))))+P107(f866(f866(f244(x95261),f2(x95261)),f866(f866(f9(x95262,x95261),x95263),x95264)))
% 157.76/157.52 [9534]~E(f866(f196(f931(x95344)),x95342),f866(f196(f931(x95344)),x95343))+P107(f866(f866(f336(f936(f931(x95344),f931(x95344))),f866(f866(f260(f931(x95344),f931(x95344)),x95343),x95342)),f165(x95344,x95341)))+P107(f866(f866(f244(a930),f662(x95341,x95342,x95343,x95344)),f866(f196(f931(x95344)),x95343)))
% 157.76/157.52 [9586]~P107(f866(x95863,f866(f866(f171(x95862),x95864),f732(x95864,x95862,x95863,x95861))))+P107(f866(f866(f243(a930),x95861),f866(f196(f931(x95862)),f184(x95862,x95863,x95864))))+~P107(f866(f866(f243(a930),x95861),f866(f196(f931(x95862)),x95864)))
% 157.76/157.52 [9665]E(f866(f866(f182(x96651),f668(x96652,x96653,x96654,x96651)),x96653),f866(f866(f182(x96651),f668(x96652,x96653,x96654,x96651)),x96654))+~P107(f866(f866(f336(f936(f931(x96651),f931(x96651))),f866(f866(f260(f931(x96651),f931(x96651)),x96654),x96653)),f154(x96651,x96652)))+P107(f866(f866(f244(a930),f866(f196(f931(x96651)),x96654)),f866(f196(f931(x96651)),x96653)))
% 157.76/157.52 [9721]~P107(f866(f866(f244(a930),f2(a930)),x97213))+~P107(f866(f866(f244(a930),x97214),x97211))+P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),x97211),f50(a930,x97212,x97213))),x97214)),f866(f866(f87(a930),x97211),x97213)))
% 157.76/157.52 [9913]~P109(x99132)+~P107(f866(f866(f243(x99132),f866(x99133,f923(x99134,x99133,x99131,x99132))),f866(x99134,f923(x99134,x99133,x99131,x99132))))+P107(f866(f866(f243(f937(x99131,x99132)),x99133),x99134))
% 157.76/157.52 [10017]~P3(x100171)+E(f866(f866(f6(a930,x100171),f866(f866(f18(a930,x100171,x100171),f866(f866(f8(x100171,f937(x100171,x100171),a930),f23(x100171)),x100172)),f866(f866(f8(a930,x100171,a930),x100172),f866(f866(f7(a930,a930,a930),f86(a930)),f84(a930))))),f310(a930,x100173,x100174)),f866(f866(f23(x100171),f866(x100172,x100173)),f866(x100172,f866(f866(f86(a930),x100174),f84(a930)))))+~P107(f866(f866(f243(a930),x100173),x100174))
% 157.76/157.52 [10092]~P37(x100923,f866(f866(f296(x100923,x100923,x100923),x100922),f314(x100923,x100922)))+~P107(f866(f866(f336(f936(x100923,x100923)),f866(f866(f260(x100923,x100923),f866(x100921,f866(a119,f844(x100922,x100921,x100923)))),f866(x100921,f844(x100922,x100921,x100923)))),f314(x100923,x100922)))+E(f866(x100921,f866(f866(f86(a930),f843(x100922,x100921,x100923)),x100924)),f866(x100921,f843(x100922,x100921,x100923)))
% 157.76/157.52 [6768]~P62(x67681)+~P57(x67681,x67684,x67683)+E(f866(f866(f41(x67681),f866(f866(f87(x67681),x67682),x67683)),x67684),f866(f866(f87(x67681),x67682),f866(f866(f41(x67681),x67683),x67684)))
% 157.76/157.52 [7065]~P62(x70651)+~P57(x70651,x70654,x70652)+E(f866(f866(f41(x70651),f866(f866(f87(x70651),x70652),x70653)),x70654),f866(f866(f87(x70651),f866(f866(f41(x70651),x70652),x70654)),x70653))
% 157.76/157.52 [7081]E(f866(f866(f141(x70811),x70812),x70813),x70814)+~E(x70813,f866(f866(f145(x70811),f866(f196(f931(x70811)),x70812)),x70814))+~E(f866(f866(f182(x70811),f866(f196(f931(x70811)),x70812)),x70814),x70812)
% 157.76/157.52 [7135]~P66(x71352)+E(x71351,f2(x71352))+E(f866(f866(f297(x71352),f866(f866(f252(x71352),x71353),x71354)),f866(f866(f252(x71352),x71351),x71354)),f866(f866(f252(x71352),f866(f866(f297(x71352),x71353),x71351)),x71354))
% 157.76/157.52 [7283]~P103(x72831)+~P107(f866(f866(f243(x72831),x72833),x72834))+P107(f866(f866(f243(x72831),f866(f866(f108(x72831),x72832),x72833)),x72834))
% 157.76/157.52 [7284]~P103(x72841)+~P107(f866(f866(f243(x72841),x72842),x72844))+P107(f866(f866(f243(x72841),f866(f866(f108(x72841),x72842),x72843)),x72844))
% 157.76/157.52 [7286]~P110(x72861)+~P107(f866(f866(f243(x72861),x72863),x72864))+P107(f866(f866(f243(x72861),f866(f866(f241(x72861),x72862),x72863)),x72864))
% 157.76/157.52 [7288]~P110(x72881)+~P107(f866(f866(f243(x72881),x72882),x72884))+P107(f866(f866(f243(x72881),f866(f866(f241(x72881),x72882),x72883)),x72884))
% 157.76/157.52 [7289]~P103(x72891)+~P107(f866(f866(f244(x72891),x72893),x72894))+P107(f866(f866(f244(x72891),f866(f866(f108(x72891),x72892),x72893)),x72894))
% 157.76/157.52 [7290]~P103(x72901)+~P107(f866(f866(f244(x72901),x72902),x72904))+P107(f866(f866(f244(x72901),f866(f866(f108(x72901),x72902),x72903)),x72904))
% 157.76/157.52 [7292]~P110(x72921)+~P107(f866(f866(f244(x72921),x72923),x72924))+P107(f866(f866(f244(x72921),f866(f866(f241(x72921),x72922),x72923)),x72924))
% 157.76/157.52 [7294]~P110(x72941)+~P107(f866(f866(f244(x72941),x72942),x72944))+P107(f866(f866(f244(x72941),f866(f866(f241(x72941),x72942),x72943)),x72944))
% 157.76/157.52 [7317]~P107(f866(x73173,x73174))+~P107(f866(x73172,x73174))+P107(f866(f866(f866(f108(f937(x73171,a925)),x73172),x73173),x73174))
% 157.76/157.52 [7441]P24(x74411,x74412,x74413)+~P24(x74411,x74412,x74414)+~P107(f866(f866(f243(f937(f929(x74411),a925)),x74413),x74414))
% 157.76/157.52 [7806]~P72(x78061)+E(f866(f866(f86(x78061),f866(x78062,x78063)),f866(f866(f6(a930,x78061),x78062),f866(f309(a930,f866(a119,x78063)),x78064))),f866(f866(f6(a930,x78061),x78062),f866(f309(a930,x78063),x78064)))+~P107(f866(f866(f244(a930),x78063),x78064))
% 157.76/157.52 [7824]E(x78241,x78242)+P107(f866(f866(f179(x78243),x78244),x78242))+~P107(f866(f866(f179(x78243),f866(f866(f158(x78243),x78241),x78244)),x78242))
% 157.76/157.52 [7836]~P110(x78361)+P107(f866(f866(f243(x78361),x78362),x78363))+~P107(f866(f866(f243(x78361),f866(f866(f242(x78361),x78364),x78362)),x78363))
% 157.76/157.52 [7838]~P110(x78381)+P107(f866(f866(f243(x78381),x78382),x78383))+~P107(f866(f866(f243(x78381),f866(f866(f242(x78381),x78382),x78384)),x78383))
% 157.76/157.52 [7840]~P102(x78401)+P107(f866(f866(f243(x78401),x78402),x78403))+~P107(f866(f866(f243(x78401),f866(f866(f117(x78401),x78404),x78402)),x78403))
% 157.76/157.52 [7842]~P102(x78421)+P107(f866(f866(f243(x78421),x78422),x78423))+~P107(f866(f866(f243(x78421),f866(f866(f117(x78421),x78422),x78424)),x78423))
% 157.76/157.52 [7843]~P110(x78431)+P107(f866(f866(f244(x78431),x78432),x78433))+~P107(f866(f866(f244(x78431),f866(f866(f242(x78431),x78434),x78432)),x78433))
% 157.76/157.52 [7844]~P110(x78441)+P107(f866(f866(f244(x78441),x78442),x78443))+~P107(f866(f866(f244(x78441),f866(f866(f242(x78441),x78442),x78444)),x78443))
% 157.76/157.52 [7919]~P107(f866(f866(f336(x79191),x79192),x79194))+P107(f866(f866(f336(x79191),x79192),x79193))+P107(f866(f866(f336(x79191),x79192),f866(f866(f23(f937(x79191,a925)),x79194),x79193)))
% 157.76/157.52 [8004]P107(f866(x80041,x80042))+P107(f866(x80043,x80042))+~P107(f866(f866(f866(f117(f937(x80044,a925)),x80043),x80041),x80042))
% 157.76/157.52 [8015]~P107(f866(f866(f336(x80151),x80152),x80154))+~P107(f866(f866(f336(x80151),x80152),x80153))+P107(f866(f866(f336(x80151),x80152),f866(f866(f108(f937(x80151,a925)),x80153),x80154)))
% 157.76/157.52 [8062]~P102(x80621)+~P107(f866(f66(x80621),x80624))+E(f866(f866(f69(x80621,x80621,f117(x80621)),x80622),f866(f866(f316(x80621),x80623),x80624)),f866(f866(f117(x80621),x80623),f866(f866(f69(x80621,x80621,f117(x80621)),x80622),x80624)))
% 157.76/157.52 [8063]~P103(x80631)+~P107(f866(f66(x80631),x80634))+E(f866(f866(f69(x80631,x80631,f108(x80631)),x80632),f866(f866(f316(x80631),x80633),x80634)),f866(f866(f108(x80631),x80633),f866(f866(f69(x80631,x80631,f108(x80631)),x80632),x80634)))
% 157.76/157.52 [8064]~P110(x80641)+~P107(f866(f66(x80641),x80644))+E(f866(f866(f69(x80641,x80641,f241(x80641)),x80642),f866(f866(f316(x80641),x80643),x80644)),f866(f866(f241(x80641),x80643),f866(f866(f69(x80641,x80641,f241(x80641)),x80642),x80644)))
% 157.76/157.52 [8065]~P110(x80651)+~P107(f866(f66(x80651),x80654))+E(f866(f866(f69(x80651,x80651,f242(x80651)),x80652),f866(f866(f316(x80651),x80653),x80654)),f866(f866(f242(x80651),x80653),f866(f866(f69(x80651,x80651,f242(x80651)),x80652),x80654)))
% 157.76/157.52 [8066]~P136(x80661)+~P97(x80661)+E(f866(f866(f23(x80661),f866(f866(f87(x80661),f866(f110(x80661),x80662)),x80663)),f866(f866(f87(x80661),f866(f110(x80661),x80662)),x80664)),f866(f866(f87(x80661),f866(f110(x80661),x80662)),f866(f866(f23(x80661),x80663),x80664)))
% 157.76/157.52 [8067]~P145(x80671)+~P97(x80671)+E(f866(f866(f86(x80671),f866(f866(f87(x80671),f866(f110(x80671),x80672)),x80673)),f866(f866(f87(x80671),f866(f110(x80671),x80672)),x80674)),f866(f866(f87(x80671),f866(f110(x80671),x80672)),f866(f866(f86(x80671),x80673),x80674)))
% 157.76/157.52 [8180]E(x81801,x81802)+P107(f866(f866(f336(x81803),x81801),f866(f179(x81803),x81804)))+~P107(f866(f866(f336(x81803),x81801),f866(f179(x81803),f866(f866(f158(x81803),x81802),x81804))))
% 157.76/157.52 [8351]P55(x83511,x83512,x83513)+~P55(x83511,x83512,x83514)+~P107(f866(f866(f243(f937(f936(x83511,x83512),a925)),x83513),x83514))
% 157.76/157.52 [8393]P107(f866(f866(f336(x83931),x83932),x83933))+P107(f866(f866(f336(x83931),x83932),x83934))+~P107(f866(f866(f336(x83931),x83932),f866(f866(f117(f937(x83931,a925)),x83934),x83933)))
% 157.76/157.52 [8403]~P53(x84031,x84034,x84033)+~P107(f866(f866(f336(x84031),x84032),x84034))+P107(f866(f866(f336(f936(x84031,x84031)),f866(f866(f260(x84031,x84031),x84032),x84032)),x84033))
% 157.76/157.52 [8415]~P107(f866(f66(x84152),x84154))+~P107(f866(f66(x84151),x84153))+P107(f866(f66(f936(x84151,x84152)),f866(f866(f262(x84151,x84152),x84153),f866(f16(f937(x84152,a925),x84151),x84154))))
% 157.76/157.52 [8416]~P107(f866(f866(f336(x84161),x84162),x84164))+~P107(f866(f866(f243(f937(x84161,a925)),x84163),x84164))+P107(f866(f866(f243(f937(x84161,a925)),f866(f866(f316(x84161),x84162),x84163)),x84164))
% 157.76/157.52 [8423]~P71(x84232)+~P148(x84232)+E(f866(f866(f9(x84231,x84232),f866(f866(f8(a930,x84232,x84231),f107(x84232)),x84233)),x84234),f866(f107(x84232),f866(f866(f9(x84231,a930),x84233),x84234)))
% 157.76/157.52 [8424]~P71(x84242)+~P142(x84242)+E(f866(f866(f9(x84241,x84242),f866(f866(f8(a1,x84242,x84241),f109(x84242)),x84243)),x84244),f866(f109(x84242),f866(f866(f9(x84241,a1),x84243),x84244)))
% 157.76/157.52 [8448]E(f866(f866(f23(f937(x84481,a925)),x84482),f866(f866(f23(f937(x84481,a925)),x84483),x84484)),x84484)+~P107(f866(f866(f243(f937(x84481,a925)),x84482),x84483))+~P107(f866(f866(f243(f937(x84481,a925)),x84484),x84482))
% 157.76/157.52 [8545]~P107(f866(f66(x85451),x85454))+E(f866(f866(f23(a930),f866(f866(f6(x85451,a930),x85452),x85453)),f866(f866(f6(x85451,a930),x85452),x85454)),f866(f866(f6(x85451,a930),x85452),f866(f866(f23(f937(x85451,a925)),x85453),x85454)))+~P107(f866(f866(f243(f937(x85451,a925)),x85454),x85453))
% 157.76/157.52 [8695]~P8(x86951,x86954,x86953)+~P107(f866(f866(f336(x86951),x86952),x86954))+P107(f866(f866(f336(x86951),x86952),f866(f293(x86951,x86951,x86953),f866(f866(f316(x86951),x86952),f195(f937(x86951,a925))))))
% 157.76/157.52 [8757]~P107(f866(f866(f243(f937(x87571,a925)),x87572),x87573))+~P107(f866(f866(f243(f937(x87571,a925)),x87572),x87574))+P107(f866(f866(f243(f937(x87571,a925)),x87572),f866(f866(f108(f937(x87571,a925)),x87573),x87574)))
% 157.76/157.52 [8859]E(x88591,f195(f937(x88592,a925)))+P107(f866(f66(x88593),x88594))+~P107(f866(f66(f936(x88593,x88592)),f866(f866(f262(x88593,x88592),x88594),f866(f16(f937(x88592,a925),x88593),x88591))))
% 157.76/157.52 [8860]E(x88601,f195(f937(x88602,a925)))+P107(f866(f66(x88603),x88604))+~P107(f866(f66(f936(x88602,x88603)),f866(f866(f262(x88602,x88603),x88601),f866(f16(f937(x88603,a925),x88602),x88604))))
% 157.76/157.52 [8933]P107(f866(f866(f336(x89331),x89332),f323(x89331,x89333)))+~P107(f866(f866(f336(x89331),x89334),f323(x89331,x89333)))+~P107(f866(f866(f336(f936(x89331,x89331)),f866(f866(f260(x89331,x89331),x89332),x89334)),x89333))
% 157.76/157.52 [8990]~P37(x89901,x89904)+P107(f866(f866(f336(f936(x89901,x89901)),f866(f866(f260(x89901,x89901),x89903),x89902)),f314(x89901,x89904)))+P37(x89901,f866(f866(f316(f936(x89901,x89901)),f866(f866(f260(x89901,x89901),x89902),x89903)),x89904))
% 157.76/157.52 [8991]~P59(x89911,x89914)+P107(f866(f866(f336(f936(x89911,x89911)),f866(f866(f260(x89911,x89911),x89913),x89912)),f314(x89911,x89914)))+P59(x89911,f866(f866(f316(f936(x89911,x89911)),f866(f866(f260(x89911,x89911),x89912),x89913)),x89914))
% 157.76/157.52 [9073]~E(x90732,x90733)+~P107(f866(f866(f336(x90731),x90732),f866(f179(x90731),x90734)))+P107(f866(f866(f336(f936(x90731,x90731)),f866(f866(f260(x90731,x90731),x90732),x90733)),f866(f179(f936(x90731,x90731)),f866(f866(f188(x90731,x90731),x90734),x90734))))
% 157.76/157.52 [9165]~E(x91653,x91654)+P107(f866(f866(f265(x91651,x91651,a925),a332),x91652))+~P107(f866(f866(f336(f936(x91651,x91651)),x91652),f866(f179(f936(x91651,x91651)),f866(f866(f188(x91651,x91651),x91653),x91654))))
% 157.76/157.52 [9211]P107(f866(f866(f336(f936(f931(x92111),f931(x92111))),f866(f866(f260(f931(x92111),f931(x92111)),x92112),x92113)),f154(x92111,x92114)))+~E(f866(f866(f182(x92111),f866(f196(f931(x92111)),x92112)),x92113),x92112)+~P107(f866(f866(f244(a930),f866(f196(f931(x92111)),x92112)),f866(f196(f931(x92111)),x92113)))
% 157.76/157.52 [9214]~P52(x92141,x92144)+~P107(f866(f866(f336(f936(x92141,x92141)),f866(f866(f260(x92141,x92141),x92143),x92142)),x92144))+P107(f866(f866(f336(f936(x92141,x92141)),f866(f866(f260(x92141,x92141),x92142),x92143)),x92144))
% 157.76/157.52 [9305]~P107(f866(f66(x93051),x93054))+P107(f866(f866(f336(x93051),f792(x93052,x93053,x93054,x93051)),x93054))+P107(f866(f66(x93053),f866(f866(f44(x93051,f937(x93053,a925)),x93054),x93052)))
% 157.76/157.52 [9306]~P107(f866(f66(x93061),x93064))+P107(f866(f866(f336(x93061),f361(x93062,x93063,x93064,x93061)),x93064))+P107(f866(f66(x93063),f866(f866(f44(x93061,f937(x93063,a925)),x93064),x93062)))
% 157.76/157.52 [9392]P107(f866(f866(f336(f936(x93921,x93921)),x93922),f866(f866(f296(x93921,x93921,x93921),x93923),f314(x93921,x93923))))+~P107(f866(f866(f244(a930),f2(a930)),x93924))+~P107(f866(f866(f336(f936(x93921,x93921)),x93922),f866(f866(f190(f936(x93921,x93921),a925),x93924),x93923)))
% 157.76/157.52 [9400]~P37(x94001,x94002)+~P107(f866(f866(f336(f936(x94001,x94001)),f866(f866(f260(x94001,x94001),x94004),x94003)),x94002))+~P107(f866(f866(f336(f936(x94001,x94001)),f866(f866(f260(x94001,x94001),x94003),x94004)),x94002))
% 157.76/157.52 [9524]~P107(f866(f66(x95241),x95244))+E(f866(f866(f6(x95241,a930),f866(f866(f8(f937(x95242,a925),a930,x95241),f40(x95242)),x95243)),x95244),f866(f40(f936(x95241,x95242)),f866(f866(f262(x95241,x95242),x95244),x95243)))+P107(f866(f866(f336(x95241),f533(x95243,x95242,x95244,x95241)),x95244))
% 157.76/157.52 [9528]~P107(f866(f144(x95281),x95282))+P107(f866(f144(x95281),f866(f866(f166(x95281,x95282),x95283),x95284)))+P107(f866(f866(f336(x95281),x95284),f866(f866(f23(f937(x95281,a925)),f866(f179(x95281),x95282)),f866(f866(f316(x95281),f866(f866(f171(x95281),x95282),x95283)),f195(f937(x95281,a925))))))
% 157.76/157.52 [9545]~P107(f866(f66(x95452),x95453))+~P107(f866(f66(x95451),f866(x95454,f792(x95454,x95451,x95453,x95452))))+P107(f866(f66(x95451),f866(f866(f44(x95452,f937(x95451,a925)),x95453),x95454)))
% 157.76/157.52 [9546]~P107(f866(f66(x95462),x95463))+~P107(f866(f66(x95461),f866(x95464,f361(x95464,x95461,x95463,x95462))))+P107(f866(f66(x95461),f866(f866(f44(x95462,f937(x95461,a925)),x95463),x95464)))
% 157.76/157.52 [9624]~P107(f866(f866(f336(f936(x96241,x96241)),x96242),f866(f866(f296(x96241,x96241,x96241),x96244),f314(x96241,x96244))))+P107(f866(f866(f336(f936(x96241,x96241)),x96242),f866(f866(f296(x96241,x96241,x96241),x96243),f314(x96241,x96243))))+~P107(f866(f866(f243(f937(f936(x96241,x96241),a925)),x96244),x96243))
% 157.76/157.52 [9632]E(f866(f866(f182(x96321),f668(x96324,x96323,x96322,x96321)),x96323),f866(f866(f182(x96321),f668(x96324,x96323,x96322,x96321)),x96322))+~P107(f866(f866(f336(f936(f931(x96321),f931(x96321))),f866(f866(f260(f931(x96321),f931(x96321)),x96322),x96323)),f154(x96321,x96324)))+E(f866(f866(f182(x96321),f866(f196(f931(x96321)),x96322)),x96323),x96322)
% 157.76/157.52 [9648]~P107(f866(f66(x96481),x96484))+E(f866(f866(f6(x96481,a930),f866(f866(f8(f937(x96482,a925),a930,x96481),f40(x96482)),x96483)),x96484),f866(f40(f936(x96481,x96482)),f866(f866(f262(x96481,x96482),x96484),x96483)))+~P107(f866(f66(x96482),f866(x96483,f533(x96483,x96482,x96484,x96481))))
% 157.76/157.52 [9652]~E(f866(f196(f931(x96521)),x96523),f866(f196(f931(x96521)),x96522))+P107(f866(f866(f336(f936(f931(x96521),f931(x96521))),f866(f866(f260(f931(x96521),f931(x96521)),x96522),x96523)),f165(x96521,x96524)))+P107(f866(f866(f336(f936(x96521,x96521)),f672(x96524,x96523,x96522,x96521)),f866(f179(f936(x96521,x96521)),f866(f866(f188(x96521,x96521),x96522),x96523))))
% 157.76/157.52 [9732]~P107(f866(f866(f336(f936(f931(x97321),f931(x97321))),f866(f866(f260(f931(x97321),f931(x97321)),x97322),x97323)),f154(x97321,x97324)))+E(f866(f866(f182(x97321),f866(f196(f931(x97321)),x97322)),x97323),x97322)+P107(f866(f866(f244(a930),f668(x97324,x97323,x97322,x97321)),f866(f866(f241(a930),f866(f196(f931(x97321)),x97322)),f866(f196(f931(x97321)),x97323))))
% 157.76/157.52 [9756]~P107(f866(f866(f336(f936(f931(x97561),f931(x97561))),f866(f866(f260(f931(x97561),f931(x97561)),x97562),x97563)),f154(x97561,x97564)))+P107(f866(f866(f244(a930),f866(f196(f931(x97561)),x97562)),f866(f196(f931(x97561)),x97563)))+P107(f866(f866(f244(a930),f668(x97564,x97563,x97562,x97561)),f866(f866(f241(a930),f866(f196(f931(x97561)),x97562)),f866(f196(f931(x97561)),x97563))))
% 157.76/157.52 [10160]~P107(f866(f866(f336(f936(f931(x101601),f931(x101601))),f866(f866(f260(f931(x101601),f931(x101601)),x101602),x101603)),f154(x101601,x101604)))+E(f866(f866(f182(x101601),f866(f196(f931(x101601)),x101602)),x101603),x101602)+P107(f866(f866(f336(f936(x101601,x101601)),f866(f866(f260(x101601,x101601),f866(f866(f171(x101601),x101602),f668(x101604,x101603,x101602,x101601))),f866(f866(f171(x101601),x101603),f668(x101604,x101603,x101602,x101601)))),x101604))
% 157.76/157.52 [10161]~P107(f866(f866(f336(f936(f931(x101611),f931(x101611))),f866(f866(f260(f931(x101611),f931(x101611)),x101612),x101613)),f154(x101611,x101614)))+P107(f866(f866(f244(a930),f866(f196(f931(x101611)),x101612)),f866(f196(f931(x101611)),x101613)))+P107(f866(f866(f336(f936(x101611,x101611)),f866(f866(f260(x101611,x101611),f866(f866(f171(x101611),x101612),f668(x101614,x101613,x101612,x101611))),f866(f866(f171(x101611),x101613),f668(x101614,x101613,x101612,x101611)))),x101614))
% 157.76/157.52 [10219]~E(f866(f196(f931(x102191)),x102192),f866(f196(f931(x102191)),x102193))+P107(f866(f866(f336(f936(f931(x102191),f931(x102191))),f866(f866(f260(f931(x102191),f931(x102191)),x102192),x102193)),f165(x102191,x102194)))+~P107(f866(f866(f336(f936(x102191,x102191)),f866(f866(f260(x102191,x102191),f866(f866(f171(x102191),x102192),f662(x102194,x102193,x102192,x102191))),f866(f866(f171(x102191),x102193),f662(x102194,x102193,x102192,x102191)))),x102194))
% 157.76/157.52 [10364]~P72(x103641)+~P107(f866(f66(x103642),x103644))+E(f866(f172(x103641),f866(f866(f161(x103642,x103641),x103643),f96(f931(x103642),f866(f866(f18(f931(x103642),a925,a925),f866(f866(f8(a925,f937(a925,a925),f931(x103642)),a333),f866(f866(f7(f931(x103642),f937(x103642,a925),a925),f866(f866(f8(f937(x103642,a925),f937(f937(x103642,a925),a925),f931(x103642)),a332),f179(x103642))),x103644))),f144(x103642))))),f240(x103642,x103641,x103643,x103644))
% 157.76/157.52 [7657]~P65(x76572)+E(x76571,f2(x76572))+E(f866(f866(f297(x76572),f866(f866(f86(x76572),x76573),f866(f866(f87(x76572),x76574),x76571))),x76571),f866(f866(f86(x76572),x76574),f866(f866(f297(x76572),x76573),x76571)))
% 157.76/157.52 [7658]~P62(x76582)+E(x76581,f2(x76582))+E(f866(f866(f41(x76582),f866(f866(f86(x76582),x76583),f866(f866(f87(x76582),x76584),x76581))),x76581),f866(f866(f86(x76582),x76584),f866(f866(f41(x76582),x76583),x76581)))
% 157.76/157.52 [7659]~P62(x76592)+E(x76591,f2(x76592))+E(f866(f866(f41(x76592),f866(f866(f86(x76592),x76593),f866(f866(f87(x76592),x76591),x76594))),x76591),f866(f866(f86(x76592),x76594),f866(f866(f41(x76592),x76593),x76591)))
% 157.76/157.52 [7883]~P66(x78832)+E(x78831,f2(x78832))+E(f866(f866(f297(x78832),f866(f866(f23(x78832),x78833),f866(f866(f87(x78832),x78831),x78834))),x78831),f866(f866(f23(x78832),f866(f866(f297(x78832),x78833),x78831)),x78834))
% 157.76/157.52 [7884]~P65(x78842)+E(x78841,f2(x78842))+E(f866(f866(f297(x78842),f866(f866(f86(x78842),x78843),f866(f866(f87(x78842),x78844),x78841))),x78841),f866(f866(f86(x78842),f866(f866(f297(x78842),x78843),x78841)),x78844))
% 157.76/157.52 [7885]~P66(x78852)+E(x78851,f2(x78852))+E(f866(f866(f297(x78852),f866(f866(f86(x78852),x78853),f866(f866(f87(x78852),x78851),x78854))),x78851),f866(f866(f86(x78852),f866(f866(f297(x78852),x78853),x78851)),x78854))
% 157.76/157.52 [8576]~P107(f866(f167(x85761,x85763),x85764))+~P107(f866(f167(x85761,x85762),x85764))+P107(f866(f167(x85761,f866(f866(f108(f937(x85761,a925)),x85762),x85763)),x85764))
% 157.76/157.52 [8948]~E(f866(f866(f296(x89481,x89481,x89481),x89482),x89484),f195(f937(f936(x89481,x89481),a925)))+~E(f866(f866(f296(x89481,x89481,x89481),x89482),x89483),f195(f937(f936(x89481,x89481),a925)))+E(f866(f866(f296(x89481,x89481,x89481),x89482),f866(f866(f117(f937(f936(x89481,x89481),a925)),x89483),x89484)),f195(f937(f936(x89481,x89481),a925)))
% 157.76/157.52 [9074]~P107(f866(f866(f243(f937(x90741,a925)),x90743),x90744))+~P107(f866(f866(f243(f937(x90741,a925)),x90742),x90744))+P107(f866(f866(f243(f937(x90741,a925)),f866(f866(f117(f937(x90741,a925)),x90742),x90743)),x90744))
% 157.76/157.52 [9452]~P107(f866(f66(x94521),x94524))+~P107(f866(f66(x94521),x94523))+E(f866(f866(f23(a930),f866(f866(f86(a930),f866(f866(f6(x94521,a930),x94522),x94523)),f866(f866(f6(x94521,a930),x94522),x94524))),f866(f866(f6(x94521,a930),x94522),f866(f866(f108(f937(x94521,a925)),x94523),x94524))),f866(f866(f6(x94521,a930),x94522),f866(f866(f117(f937(x94521,a925)),x94523),x94524)))
% 157.76/157.52 [9542]~P107(f866(f866(f336(x95421),x95423),x95422))+~P107(f866(f866(f243(f937(x95421,a925)),x95422),f866(f866(f316(x95421),x95423),x95424)))+P107(f866(f866(f243(f937(x95421,a925)),f866(f866(f23(f937(x95421,a925)),x95422),f866(f866(f316(x95421),x95423),f195(f937(x95421,a925))))),x95424))
% 157.76/157.52 [9708]~P107(f866(f866(f336(x97081),x97083),x97082))+P107(f866(f866(f243(f937(x97081,a925)),x97082),f866(f866(f316(x97081),x97083),x97084)))+~P107(f866(f866(f243(f937(x97081,a925)),f866(f866(f23(f937(x97081,a925)),x97082),f866(f866(f316(x97081),x97083),f195(f937(x97081,a925))))),x97084))
% 157.76/157.52 [9796]~P107(f866(f866(f243(a930),x97961),x97963))+~P107(f866(f866(f244(a930),x97962),x97964))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x97961),x97962)),f866(f866(f260(a930,a930),x97963),x97964))),a38))
% 157.76/157.52 [9797]~P107(f866(f866(f243(a930),x97972),x97974))+~P107(f866(f866(f243(a930),x97971),x97973))+P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),f866(f866(f260(a930,a930),x97971),x97972)),f866(f866(f260(a930,a930),x97973),x97974))),a76))
% 157.76/157.52 [10090]~P107(f866(f866(f336(f931(x100901)),x100904),f168(x100901,x100903)))+~P107(f866(f866(f336(f931(x100901)),x100904),f168(x100901,x100902)))+P107(f866(f167(x100901,f866(f866(f108(f937(x100901,a925)),f866(f866(f7(x100901,f937(x100901,a925),a925),f336(x100901)),x100902)),f866(f866(f7(x100901,f937(x100901,a925),a925),f336(x100901)),x100903))),x100904))
% 157.76/157.52 [10185]~P25(x101851,f937(f937(x101851,a925),a925),f866(f866(f7(x101851,f937(f936(x101851,x101851),a925),f937(f937(x101851,a925),a925)),f866(f866(f8(f937(x101851,a925),f937(f937(f936(x101851,x101851),a925),f937(f937(x101851,a925),a925)),x101851),f65(x101851)),f866(f866(f7(x101851,f937(x101851,a925),f937(x101851,a925)),f316(x101851)),f195(f937(x101851,a925))))),x101853),x101852)+~P107(f866(f866(f336(x101851),x101854),x101852))+E(f866(f866(f23(f937(f937(x101851,a925),a925)),f866(f866(f65(x101851),x101852),x101853)),f866(f866(f65(x101851),f866(f866(f316(x101851),x101854),f195(f937(x101851,a925)))),x101853)),f866(f866(f65(x101851),f866(f866(f23(f937(x101851,a925)),x101852),f866(f866(f316(x101851),x101854),f195(f937(x101851,a925))))),x101853))
% 157.76/157.52 [10318]~P53(x103181,x103182,x103184)+~P107(f866(f866(f336(f936(x103181,x103181)),x103183),x103184))+P107(f866(f866(f265(x103181,x103181,a925),f866(f866(f7(x103181,f937(x103181,a925),f937(x103181,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x103181,a925),f937(x103181,a925)),x103181),f8(a925,a925,x103181)),f866(f866(f8(a925,f937(a925,a925),x103181),a333),f866(f866(f7(x103181,f937(x103181,a925),a925),f336(x103181)),x103182)))),f866(f866(f7(x103181,f937(x103181,a925),a925),f336(x103181)),x103182))),x103183))
% 157.76/157.52 [10332]P107(f866(f66(x103321),x103322))+~P107(f866(f66(x103323),f866(f317(x103321,x103323,x103324),x103322)))+~P107(f866(f66(x103321),f866(f270(x103321),f866(f866(f18(x103321,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103321),a333),f866(f866(f7(x103321,f937(x103321,a925),a925),f336(x103321)),x103322))),f866(f866(f7(x103321,x103323,a925),f866(f866(f8(x103323,f937(x103323,a925),x103321),a332),x103324)),f866(x103324,f897(x103324,x103323,x103322,x103321)))))))
% 157.76/157.52 [8335]~P66(x83352)+E(x83351,f2(x83352))+E(f866(f866(f297(x83352),f866(f866(f23(x83352),f866(f866(f87(x83352),x83351),x83353)),x83354)),x83351),f866(f866(f23(x83352),x83353),f866(f866(f297(x83352),x83354),x83351)))
% 157.76/157.52 [8336]~P66(x83362)+E(x83361,f2(x83362))+E(f866(f866(f297(x83362),f866(f866(f86(x83362),f866(f866(f87(x83362),x83361),x83363)),x83364)),x83361),f866(f866(f86(x83362),x83363),f866(f866(f297(x83362),x83364),x83361)))
% 157.76/157.52 [9240]~E(f866(f866(f296(x92401,x92401,x92401),x92403),x92404),f195(f937(f936(x92401,x92401),a925)))+~E(f866(f866(f296(x92401,x92401,x92401),x92402),x92404),f195(f937(f936(x92401,x92401),a925)))+E(f866(f866(f296(x92401,x92401,x92401),f866(f866(f117(f937(f936(x92401,x92401),a925)),x92402),x92403)),x92404),f195(f937(f936(x92401,x92401),a925)))
% 157.76/157.52 [10007]~P107(f866(f167(x100071,x100073),x100074))+~P107(f866(f167(x100071,x100072),x100074))+P107(f866(f167(x100071,f866(f866(f18(x100071,a925,a925),f866(f866(f8(a925,f937(a925,a925),x100071),a333),x100072)),x100073)),x100074))
% 157.76/157.52 [10254]P107(f866(x102541,f922(x102542,x102543,x102541,x102544)))+~P107(f866(f66(x102544),f866(f270(x102544),x102541)))+P107(f866(f66(x102543),f866(f270(x102543),f866(f866(f8(f937(x102544,a925),a925,x102543),f93(x102544)),f866(f866(f8(f937(x102544,a925),f937(x102544,a925),x102543),f866(f18(x102544,a925,a925),f866(f866(f8(a925,f937(a925,a925),x102544),a333),x102541))),x102542)))))
% 157.76/157.52 [10272]~P107(f866(f66(x102722),f866(f270(x102722),x102723)))+~P107(f866(f66(x102721),f866(f270(x102721),f866(f866(f7(x102721,x102722,a925),x102724),f922(x102724,x102721,x102723,x102722)))))+P107(f866(f66(x102721),f866(f270(x102721),f866(f866(f8(f937(x102722,a925),a925,x102721),f93(x102722)),f866(f866(f8(f937(x102722,a925),f937(x102722,a925),x102721),f866(f18(x102722,a925,a925),f866(f866(f8(a925,f937(a925,a925),x102722),a333),x102723))),x102724)))))
% 157.76/157.52 [10343]~P107(f866(f66(x103431),x103434))+P107(f866(f866(f336(x103431),f805(x103432,x103433,x103434,x103431)),x103434))+P107(f866(f66(x103433),f866(f270(x103433),f866(f866(f8(f937(x103431,a925),a925,x103433),f93(x103431)),f866(f866(f8(f937(x103431,a925),f937(x103431,a925),x103433),f866(f18(x103431,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103431),a333),f866(f866(f7(x103431,f937(x103431,a925),a925),f336(x103431)),x103434)))),x103432)))))
% 157.76/157.52 [10349]~P107(f866(f66(x103492),x103493))+~P107(f866(f66(x103491),f866(f270(x103491),f866(f866(f7(x103491,x103492,a925),x103494),f805(x103494,x103491,x103493,x103492)))))+P107(f866(f66(x103491),f866(f270(x103491),f866(f866(f8(f937(x103492,a925),a925,x103491),f93(x103492)),f866(f866(f8(f937(x103492,a925),f937(x103492,a925),x103491),f866(f18(x103492,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103492),a333),f866(f866(f7(x103492,f937(x103492,a925),a925),f336(x103492)),x103493)))),x103494)))))
% 157.76/157.52 [5278]~E(x52782,x52784)+E(f176(x52781,x52782,x52783),f176(x52781,x52784,x52785))+~E(x52782,f2(a930))
% 157.76/157.52 [5532]E(x55321,x55322)+~E(f176(x55324,x55323,x55321),f176(x55324,x55325,x55322))+E(x55323,f2(a930))
% 157.76/157.52 [6802]E(x68021,x68022)+~E(f866(x68023,x68021),f866(x68023,x68022))+~P25(x68024,x68025,x68023,f250(f937(x68024,a925)))
% 157.76/157.52 [7689]E(x76891,x76892)+~P25(x76893,x76894,x76895,f250(f937(x76893,a925)))+~E(f866(f317(x76893,x76894,x76895),x76891),f866(f317(x76893,x76894,x76895),x76892))
% 157.76/157.52 [7936]P25(x79362,x79363,f485(x79364,x79363,x79362,x79361),x79361)+~E(f866(f317(x79363,x79362,x79365),x79364),x79361)+E(x79361,f195(f937(x79362,a925)))
% 157.76/157.52 [8459]~P107(f866(f866(x84593,x84592),x84595))+~P107(f866(f866(x84593,x84594),x84592))+P107(f866(f866(f336(x84591),x84592),f306(x84591,x84593,x84594,x84595)))
% 157.76/157.52 [8460]~P107(f866(f866(x84603,x84602),x84605))+~P107(f866(f866(x84603,x84604),x84602))+P107(f866(f866(f336(x84601),x84602),f303(x84601,x84603,x84604,x84605)))
% 157.76/157.52 [8765]~P25(x87651,x87652,x87653,x87654)+P26(x87651,x87652,x87653,x87654,x87655)+~E(f866(f317(x87651,x87652,x87653),x87654),x87655)
% 157.76/157.52 [8898]~P26(x88981,x88983,x88984,x88982,x88985)+~P107(f866(f66(x88983),x88985))+P107(f866(f66(x88981),x88982))
% 157.76/157.52 [8899]~P26(x88993,x88991,x88994,x88995,x88992)+~P107(f866(f66(x88993),x88995))+P107(f866(f66(x88991),x88992))
% 157.76/157.52 [9031]~P25(x90311,x90313,x90315,f250(f937(x90311,a925)))+~P25(x90313,x90312,x90314,f250(f937(x90313,a925)))+P25(x90311,x90312,f866(f78(x90313,x90312,x90311,x90314),x90315),f250(f937(x90311,a925)))
% 157.76/157.52 [9601]P107(f866(f866(f336(f936(x96011,x96011)),f866(f866(f260(x96011,x96011),x96012),x96013)),f314(x96011,x96014)))+~P107(f866(f866(f336(f936(x96011,x96011)),f866(f866(f260(x96011,x96011),x96012),x96015)),f314(x96011,x96014)))+~P107(f866(f866(f336(f936(x96011,x96011)),f866(f866(f260(x96011,x96011),x96015),x96013)),f314(x96011,x96014)))
% 157.76/157.52 [9639]~P110(x96392)+~P107(f866(f144(x96391),x96395))+P107(f866(f144(x96391),f156(x96391,x96392,x96393,x96394,x96395)))
% 157.76/157.52 [5606]~E(x56062,f120(x56061))+E(f866(f866(f141(x56061),x56062),x56063),f866(f866(f158(x56061),x56064),x56065))+~E(x56063,f866(f866(f158(x56061),x56064),x56065))
% 157.76/157.52 [5607]~E(x56072,f120(x56071))+E(f866(f866(f141(x56071),x56072),x56073),f866(f866(f158(x56071),x56074),x56075))+~E(f866(f866(f158(x56071),x56074),x56075),x56073)
% 157.76/157.52 [6756]~E(f866(f196(f931(x67561)),x67565),f866(f196(f931(x67562)),x67564))+E(f866(f866(f161(f936(x67561,x67562),x67562),f264(x67561,x67562)),x67563),x67564)+~E(f866(f866(f188(x67561,x67562),x67565),x67564),x67563)
% 157.76/157.52 [6757]~E(f866(f196(f931(x67571)),x67574),f866(f196(f931(x67572)),x67575))+E(f866(f866(f161(f936(x67571,x67572),x67571),f259(x67571,x67572)),x67573),x67574)+~E(f866(f866(f188(x67571,x67572),x67574),x67575),x67573)
% 157.76/157.52 [7229]~P110(x72291)+~P13(x72291,f866(f866(f161(x72292,x72291),x72293),x72295))+P13(x72291,f866(f866(f161(x72292,x72291),x72293),f866(f143(x72292,x72294),x72295)))
% 157.76/157.52 [7271]~P107(f866(x72713,x72715))+~P107(f866(f866(x72712,x72714),x72715))+P107(f866(f866(f99(x72711,x72712,x72713),x72714),x72715))
% 157.76/157.52 [7370]~P110(x73701)+P13(x73701,f866(f866(f161(x73702,x73701),x73703),f177(x73702,x73704,x73705)))+~P13(x73701,f866(f866(f161(x73702,x73701),x73703),x73705))
% 157.76/157.52 [7393]~P55(x73933,x73932,x73935)+~P55(x73931,x73933,x73934)+P55(x73931,x73932,f866(f866(f296(x73931,x73933,x73932),x73934),x73935))
% 157.76/157.52 [7487]E(x74871,x74872)+~P25(x74873,x74874,x74875,f250(f937(x74873,a925)))+~E(f866(f866(f161(x74873,x74874),x74875),x74871),f866(f866(f161(x74873,x74874),x74875),x74872))
% 157.76/157.52 [7643]~P107(f866(f866(f243(a930),x76431),f866(x76433,x76435)))+P107(f866(f866(f243(a930),x76431),f162(x76432,x76433,x76434)))+~P107(f866(f866(f336(x76432),x76435),f866(f179(x76432),x76434)))
% 157.76/157.52 [7644]~P107(f866(f866(f244(a930),x76441),f866(x76443,x76445)))+P107(f866(f866(f244(a930),x76441),f162(x76442,x76443,x76444)))+~P107(f866(f866(f336(x76442),x76445),f866(f179(x76442),x76444)))
% 157.76/157.52 [8034]P107(f866(x80341,x80342))+~P107(f866(x80341,x80343))+~P107(f866(f866(f336(x80344),x80342),f866(f179(x80344),f176(x80344,x80345,x80343))))
% 157.76/157.52 [8035]P107(f866(x80351,x80352))+~P107(f866(x80351,x80353))+~P107(f866(f866(f336(x80354),x80353),f866(f179(x80354),f176(x80354,x80355,x80352))))
% 157.76/157.52 [8039]~P111(x80391)+P107(f866(f866(f243(f937(x80391,a925)),f310(x80391,x80392,x80393)),f310(x80391,x80394,x80395)))+P107(f866(f866(f243(x80391),x80392),x80393))
% 157.76/157.52 [8060]~P5(x80601)+P107(f866(f866(f243(x80601),f866(f866(f45(x80602,x80601),x80603),x80604)),f866(x80604,x80605)))+~P107(f866(f866(f336(x80602),x80605),x80603))
% 157.76/157.52 [8127]~P25(x81271,x81272,x81274,x81273)+E(f866(f83(x81271,x81272,x81273,x81274),f866(x81274,x81275)),x81275)+~P107(f866(f866(f336(x81271),x81275),x81273))
% 157.76/157.52 [8128]~P25(x81281,x81282,x81284,x81283)+E(f866(f97(x81281,x81282,x81283,x81284),f866(x81284,x81285)),x81285)+~P107(f866(f866(f336(x81281),x81285),x81283))
% 157.76/157.52 [8324]~P107(f866(x83241,x83245))+P107(f866(x83241,f648(x83241,x83242,x83243,x83244)))+~P107(f866(f866(f336(x83244),x83245),x83243))
% 157.76/157.52 [8325]~P107(f866(x83251,x83255))+P107(f866(x83251,f648(x83251,x83252,x83253,x83254)))+~P107(f866(f866(f336(x83254),x83255),x83252))
% 157.76/157.52 [8413]P107(f866(f66(x84131),x84132))+~P107(f866(f66(x84133),x84134))+~P107(f866(f866(f243(f937(x84131,a925)),x84132),f866(f317(x84133,x84131,x84135),x84134)))
% 157.76/157.52 [8580]E(x85801,x85802)+~P25(x85803,x85804,x85805,f866(f866(f117(f937(x85803,a925)),f866(f179(x85803),x85801)),f866(f179(x85803),x85802)))+~E(f866(f866(f161(x85803,x85804),x85805),x85801),f866(f866(f161(x85803,x85804),x85805),x85802))
% 157.76/157.52 [8633]~P111(x86331)+~P107(f866(f866(f244(f937(x86331,a925)),f310(x86331,x86334,x86335)),f310(x86331,x86332,x86333)))+P107(f866(f866(f243(x86331),x86332),x86333))
% 157.76/157.52 [8694]~P25(x86941,x86944,x86945,f250(f937(x86941,a925)))+~P107(f866(f866(f336(x86944),f866(x86945,x86942)),f866(f317(x86941,x86944,x86945),x86943)))+P107(f866(f866(f336(x86941),x86942),x86943))
% 157.76/157.52 [8771]P107(f866(x87711,x87712))+~P107(f866(x87711,f596(x87711,x87713,x87714,x87715)))+~P107(f866(f866(f336(x87715),x87712),x87714))
% 157.76/157.52 [8772]P107(f866(x87721,x87722))+~P107(f866(x87721,f596(x87721,x87723,x87724,x87725)))+~P107(f866(f866(f336(x87725),x87722),x87723))
% 157.76/157.52 [9071]~P25(x90712,x90713,x90711,x90714)+E(f866(x90711,f866(f83(x90712,x90713,x90714,x90711),x90715)),x90715)+~P107(f866(f866(f336(x90713),x90715),f866(f317(x90712,x90713,x90711),x90714)))
% 157.76/157.52 [9180]E(x91801,f120(x91802))+E(f866(f866(f158(x91802),x91803),f688(x91804,x91803,x91805,x91801,x91802)),x91801)+~E(f866(f866(f141(x91802),x91801),x91805),f866(f866(f158(x91802),x91803),x91804))
% 157.76/157.52 [9181]E(x91811,f120(x91812))+E(f866(f866(f158(x91812),x91813),f689(x91814,x91811,x91815,x91813,x91812)),x91811)+~E(f866(f866(f141(x91812),x91811),x91814),f866(f866(f158(x91812),x91813),x91815))
% 157.76/157.52 [9199]E(f866(f866(f158(x91992),x91993),f688(x91994,x91993,x91991,x91995,x91992)),x91995)+~E(f866(f866(f141(x91992),x91995),x91991),f866(f866(f158(x91992),x91993),x91994))+E(x91991,f866(f866(f158(x91992),x91993),x91994))
% 157.76/157.52 [9200]E(f866(f866(f158(x92001),x92002),f689(x92004,x92005,x92003,x92002,x92001)),x92005)+~E(f866(f866(f141(x92001),x92005),x92004),f866(f866(f158(x92001),x92002),x92003))+E(f866(f866(f158(x92001),x92002),x92003),x92004)
% 157.76/157.52 [9276]~E(f866(f317(x92763,x92762,x92764),f250(f937(x92763,a925))),f250(f937(x92762,a925)))+~E(f866(f317(x92761,x92763,x92765),f250(f937(x92761,a925))),f250(f937(x92763,a925)))+E(f866(f317(x92761,x92762,f866(f78(x92763,x92762,x92761,x92764),x92765)),f250(f937(x92761,a925))),f250(f937(x92762,a925)))
% 157.76/157.52 [9645]E(x96451,f120(x96452))+~E(f866(f866(f141(x96452),x96451),x96453),f866(f866(f158(x96452),x96455),x96454))+E(f866(f866(f141(x96452),f689(x96453,x96451,x96454,x96455,x96452)),x96453),x96454)
% 157.76/157.52 [9646]E(x96461,f120(x96462))+~E(f866(f866(f141(x96462),x96461),x96465),f866(f866(f158(x96462),x96464),x96463))+E(f866(f866(f141(x96462),f688(x96463,x96464,x96465,x96461,x96462)),x96465),x96463)
% 157.76/157.52 [9653]E(f866(f866(f141(x96532),f688(x96534,x96533,x96531,x96535,x96532)),x96531),x96534)+~E(f866(f866(f141(x96532),x96535),x96531),f866(f866(f158(x96532),x96533),x96534))+E(x96531,f866(f866(f158(x96532),x96533),x96534))
% 157.76/157.52 [9654]~E(f866(f866(f141(x96541),x96545),x96544),f866(f866(f158(x96541),x96542),x96543))+E(f866(f866(f141(x96541),f689(x96544,x96545,x96543,x96542,x96541)),x96544),x96543)+E(f866(f866(f158(x96541),x96542),x96543),x96544)
% 157.76/157.52 [9655]E(f866(f866(f141(x96551),x96555),f692(x96553,x96552,x96554,x96555,x96551)),x96552)+E(f866(f866(f141(x96551),x96552),f691(x96553,x96552,x96554,x96555,x96551)),x96555)+~E(f866(f866(f141(x96551),x96555),x96554),f866(f866(f141(x96551),x96552),x96553))
% 157.76/157.52 [9691]~P110(x96911)+P13(x96911,f866(f866(f161(x96912,x96911),x96913),f156(x96912,x96911,x96913,x96914,x96915)))+~P13(x96911,f866(f866(f161(x96912,x96911),x96913),x96915))
% 157.76/157.52 [9705]~P60(x97055,x97051,x97054,x97053)+P107(f866(f866(x97051,x97052),f521(x97053,x97054,x97051,x97055,x97052)))+~P107(f866(f866(f336(x97055),x97052),x97054))
% 157.76/157.52 [9706]~P60(x97065,x97061,x97064,x97063)+P107(f866(f866(x97061,x97062),f810(x97063,x97064,x97061,x97065,x97062)))+~P107(f866(f866(f336(x97065),x97062),x97064))
% 157.76/157.52 [9808]~P107(f866(f866(f336(f936(x98081,x98081)),f866(f866(f260(x98081,x98081),x98085),x98083)),f314(x98081,x98084)))+P107(f866(f866(f336(f936(x98081,x98081)),f866(f866(f260(x98081,x98081),x98082),x98083)),f866(f866(f296(x98081,x98081,x98081),x98084),f314(x98081,x98084))))+~P107(f866(f866(f336(f936(x98081,x98081)),f866(f866(f260(x98081,x98081),x98082),x98085)),f866(f866(f296(x98081,x98081,x98081),x98084),f314(x98081,x98084))))
% 157.76/157.52 [9809]~P107(f866(f866(f336(f936(x98091,x98091)),f866(f866(f260(x98091,x98091),x98092),x98095)),f314(x98091,x98094)))+P107(f866(f866(f336(f936(x98091,x98091)),f866(f866(f260(x98091,x98091),x98092),x98093)),f866(f866(f296(x98091,x98091,x98091),x98094),f314(x98091,x98094))))+~P107(f866(f866(f336(f936(x98091,x98091)),f866(f866(f260(x98091,x98091),x98095),x98093)),f866(f866(f296(x98091,x98091,x98091),x98094),f314(x98091,x98094))))
% 157.76/157.52 [9811]P107(f866(f866(f336(f936(f931(x98111),f931(x98111))),f866(f866(f260(f931(x98111),f931(x98111)),x98112),x98113)),f165(x98111,f314(x98111,x98114))))+~P107(f866(f866(f336(f936(f931(x98111),f931(x98111))),f866(f866(f260(f931(x98111),f931(x98111)),x98112),x98115)),f165(x98111,f314(x98111,x98114))))+~P107(f866(f866(f336(f936(f931(x98111),f931(x98111))),f866(f866(f260(f931(x98111),f931(x98111)),x98115),x98113)),f165(x98111,f314(x98111,x98114))))
% 157.76/157.52 [9815]E(f866(f866(f141(x98151),x98152),f691(x98153,x98152,x98154,x98155,x98151)),x98155)+E(f866(f866(f141(x98151),f692(x98153,x98152,x98154,x98155,x98151)),x98153),x98154)+~E(f866(f866(f141(x98151),x98152),x98153),f866(f866(f141(x98151),x98155),x98154))
% 157.76/157.52 [9816]E(f866(f866(f141(x98161),x98162),f692(x98163,x98164,x98165,x98162,x98161)),x98164)+E(f866(f866(f141(x98161),f691(x98163,x98164,x98165,x98162,x98161)),x98165),x98163)+~E(f866(f866(f141(x98161),x98162),x98165),f866(f866(f141(x98161),x98164),x98163))
% 157.76/157.52 [9870]P107(f866(f866(f336(f936(x98701,x98701)),f866(f866(f260(x98701,x98701),x98702),x98703)),f866(f866(f296(x98701,x98701,x98701),x98704),f314(x98701,x98704))))+~P107(f866(f866(f336(f936(x98701,x98701)),f866(f866(f260(x98701,x98701),x98702),x98705)),f866(f866(f296(x98701,x98701,x98701),x98704),f314(x98701,x98704))))+~P107(f866(f866(f336(f936(x98701,x98701)),f866(f866(f260(x98701,x98701),x98705),x98703)),f866(f866(f296(x98701,x98701,x98701),x98704),f314(x98701,x98704))))
% 157.76/157.52 [9897]P34(x98971,x98972,x98973,x98974,x98975)+~E(f866(f196(f931(x98971)),x98974),f866(f196(f931(x98972)),x98975))+~P107(f866(f866(f265(x98971,x98972,a925),x98973),f707(x98975,x98974,x98973,x98972,x98971)))
% 157.76/157.52 [9898]P34(x98981,x98982,x98983,x98984,x98985)+~E(f866(f196(f931(x98981)),x98984),f866(f196(f931(x98982)),x98985))+~P107(f866(f866(f265(x98981,x98982,a925),x98983),f708(x98983,x98985,x98984,x98982,x98981)))
% 157.76/157.52 [9904]E(f866(f866(f141(x99041),f691(x99042,x99043,x99044,x99045,x99041)),x99044),x99042)+~E(f866(f866(f141(x99041),x99043),x99042),f866(f866(f141(x99041),x99045),x99044))+E(f866(f866(f141(x99041),f692(x99042,x99043,x99044,x99045,x99041)),x99042),x99044)
% 157.76/157.52 [9919]~P110(x99192)+E(f866(f866(f155(x99191,x99192,x99193),x99194),x99195),f866(f866(f158(x99191),x99194),x99195))+P107(f866(f866(f336(x99191),f752(x99194,x99193,x99195,x99191,x99192)),f866(f179(x99191),x99195)))
% 157.76/157.52 [9923]~P60(x99231,x99234,x99233,x99232)+~P107(f866(f866(f336(x99231),x99235),x99233))+P107(f866(f866(f336(x99231),f521(x99232,x99233,x99234,x99231,x99235)),x99232))
% 157.76/157.52 [9924]~P60(x99241,x99244,x99243,x99242)+~P107(f866(f866(f336(x99241),x99245),x99243))+P107(f866(f866(f336(x99241),f810(x99242,x99243,x99244,x99241,x99245)),x99242))
% 157.76/157.52 [10040]~P107(f866(f866(f336(f936(f937(x100401,a925),f937(x100401,a925))),f866(f866(f260(f937(x100401,a925),f937(x100401,a925)),x100404),x100403)),f325(x100401,x100402)))+~P107(f866(f866(f336(x100401),x100405),x100404))+P107(f866(f866(f336(x100401),f577(x100402,x100403,x100404,x100401,x100405)),x100403))
% 157.76/157.52 [10050]~P110(x100502)+E(f866(f866(f155(x100501,x100502,x100503),x100504),x100505),f866(f866(f158(x100501),x100504),x100505))+~P107(f866(f866(f243(x100502),f866(x100503,x100504)),f866(x100503,f752(x100504,x100503,x100505,x100501,x100502))))
% 157.76/157.52 [10099]~P25(x100993,x100994,x100995,f250(f937(x100993,a925)))+P107(f866(x100991,x100992))+~P107(f866(x100991,f866(f97(x100993,x100994,f250(f937(x100993,a925)),x100995),f729(x100992,x100991,x100995,x100994,x100993))))
% 157.76/157.52 [10236]P34(x102361,x102362,x102363,x102364,x102365)+~E(f866(f196(f931(x102361)),x102364),f866(f196(f931(x102362)),x102365))+~P107(f866(f866(x102363,f866(f866(f171(x102361),x102364),f709(x102365,x102364,x102363,x102362,x102361))),f866(f866(f171(x102362),x102365),f709(x102365,x102364,x102363,x102362,x102361))))
% 157.76/157.52 [10237]P34(x102371,x102372,x102373,x102374,x102375)+~E(f866(f196(f931(x102371)),x102374),f866(f196(f931(x102372)),x102375))+~P107(f866(f866(x102373,f866(f866(f171(x102371),x102374),f744(x102373,x102375,x102372,x102374,x102371))),f866(f866(f171(x102372),x102375),f744(x102373,x102375,x102372,x102374,x102371))))
% 157.76/157.52 [6832]~P17(x68322,x68325,x68321)+~P107(f866(f66(x68322),x68324))+E(f866(x68321,f866(f866(f316(x68322),x68323),x68324)),f866(f866(f69(x68322,x68322,x68325),x68323),x68324))
% 157.76/157.52 [6833]~E(x68333,x68334)+~E(x68332,x68335)+E(f866(f866(f316(x68331),x68332),f866(f866(f316(x68331),x68333),f195(f937(x68331,a925)))),f866(f866(f316(x68331),x68334),f866(f866(f316(x68331),x68335),f195(f937(x68331,a925)))))
% 157.76/157.52 [6843]P107(f866(x68432,x68435))+E(f184(x68431,x68432,f866(f866(f141(x68431),x68433),x68434)),f184(x68431,x68432,x68433))+~P107(f866(f866(f336(x68431),x68435),f866(f179(x68431),x68433)))
% 157.76/157.52 [6879]E(f866(x68791,x68792),f195(f937(x68793,a925)))+~E(f866(f866(f44(x68794,f937(x68793,a925)),x68795),x68791),f195(f937(x68793,a925)))+~P107(f866(f866(f336(x68794),x68792),x68795))
% 157.76/157.52 [6880]E(f866(x68801,x68802),f250(f937(x68803,a925)))+~E(f866(f866(f45(x68804,f937(x68803,a925)),x68805),x68801),f250(f937(x68803,a925)))+~P107(f866(f866(f336(x68804),x68802),x68805))
% 157.76/157.52 [7380]~E(x73802,x73804)+~P144(x73801)+E(f866(f866(f86(x73801),f866(f866(f87(x73801),x73802),x73803)),f866(f866(f87(x73801),x73804),x73805)),f866(f866(f86(x73801),f866(f866(f87(x73801),x73802),x73805)),f866(f866(f87(x73801),x73804),x73803)))
% 157.76/157.52 [7440]~P5(x74401)+~P107(f866(f866(f336(x74404),x74403),x74405))+P107(f866(f866(f243(x74401),f866(x74402,x74403)),f866(f866(f44(x74404,x74401),x74405),x74402)))
% 157.76/157.52 [7492]~P109(x74921)+P107(f866(f866(f243(x74921),f866(x74922,x74923)),f866(x74924,x74923)))+~P107(f866(f866(f243(f937(x74925,x74921)),x74922),x74924))
% 157.76/157.52 [7613]E(x76131,x76132)+E(x76133,x76131)+~E(f866(f866(f316(x76134),x76131),f866(f866(f316(x76134),x76135),f195(f937(x76134,a925)))),f866(f866(f316(x76134),x76132),f866(f866(f316(x76134),x76133),f195(f937(x76134,a925)))))
% 157.76/157.52 [7614]E(x76141,x76142)+E(x76143,x76141)+~E(f866(f866(f316(x76144),x76143),f866(f866(f316(x76144),x76142),f195(f937(x76144,a925)))),f866(f866(f316(x76144),x76145),f866(f866(f316(x76144),x76141),f195(f937(x76144,a925)))))
% 157.76/157.52 [7615]E(x76151,x76152)+E(x76151,x76153)+~E(f866(f866(f316(x76154),x76153),f866(f866(f316(x76154),x76152),f195(f937(x76154,a925)))),f866(f866(f316(x76154),x76155),f866(f866(f316(x76154),x76151),f195(f937(x76154,a925)))))
% 157.76/157.52 [7616]E(x76161,x76162)+E(x76161,x76163)+~E(f866(f866(f316(x76164),x76161),f866(f866(f316(x76164),x76165),f195(f937(x76164,a925)))),f866(f866(f316(x76164),x76162),f866(f866(f316(x76164),x76163),f195(f937(x76164,a925)))))
% 157.76/157.52 [8137]P25(x81371,x81372,x81373,x81374)+~P25(x81371,x81372,x81373,x81375)+~P107(f866(f866(f243(f937(x81371,a925)),x81374),x81375))
% 157.76/157.52 [8166]~E(f866(x81663,x81665),x81664)+~P25(x81661,x81662,x81663,f250(f937(x81661,a925)))+E(f866(f97(x81661,x81662,f250(f937(x81661,a925)),x81663),x81664),x81665)
% 157.76/157.52 [8313]E(x83131,x83132)+~E(f866(f317(x83133,x83134,x83135),x83131),f866(f317(x83133,x83134,x83135),x83132))+~P25(x83133,x83134,x83135,f866(f866(f117(f937(x83133,a925)),x83131),x83132))
% 157.76/157.52 [8383]P107(f866(x83832,x83834))+E(f866(f866(f145(x83831),f866(f196(f931(x83831)),f184(x83831,x83832,x83833))),x83833),f866(f866(f158(x83831),x83834),x83835))+~E(f866(f866(f141(x83831),f184(x83831,x83832,x83833)),f866(f866(f158(x83831),x83834),x83835)),x83833)
% 157.76/157.52 [8411]~P25(x84111,x84112,x84113,x84115)+~P25(x84111,x84112,x84113,x84114)+P25(x84111,x84112,x84113,f866(f866(f108(f937(x84111,a925)),x84114),x84115))
% 157.76/157.52 [8519]~P72(x85191)+E(f866(f866(f86(x85191),f866(x85192,x85193)),f866(f172(x85191),f866(f866(f161(x85194,x85191),x85192),f177(x85194,x85193,x85195)))),f866(f172(x85191),f866(f866(f161(x85194,x85191),x85192),x85195)))+~P107(f866(f866(f336(x85194),x85193),f866(f179(x85194),x85195)))
% 157.76/157.52 [8606]~P110(x86061)+~P13(x86061,f866(f866(f161(x86062,x86061),x86063),x86065))+P13(x86061,f866(f866(f161(x86062,x86061),x86063),f866(f866(f155(x86062,x86061,x86063),x86064),x86065)))
% 157.76/157.52 [8690]~P5(x86901)+P107(f866(f866(f243(x86901),f866(f866(f44(x86902,x86901),x86903),x86904)),f866(f866(f44(x86902,x86901),x86905),x86904)))+~P107(f866(f866(f243(f937(x86902,a925)),x86903),x86905))
% 157.76/157.52 [8691]~P5(x86911)+P107(f866(f866(f243(x86911),f866(f866(f45(x86912,x86911),x86913),x86914)),f866(f866(f45(x86912,x86911),x86915),x86914)))+~P107(f866(f866(f243(f937(x86912,a925)),x86915),x86913))
% 157.76/157.52 [8724]~P110(x87243)+P107(f866(f144(x87241),x87242))+~P107(f866(f144(x87241),f866(f866(f155(x87241,x87243,x87244),x87245),x87242)))
% 157.76/157.52 [8870]~P110(x88701)+~P107(f866(f866(f336(x88702),x88703),f866(f179(x88702),x88704)))+~P107(f866(f144(x88702),f866(f866(f155(x88702,x88701,x88705),x88703),x88704)))
% 157.76/157.52 [8960]~P110(x89601)+P13(x89601,f866(f866(f161(x89602,x89601),x89603),x89604))+~P13(x89601,f866(f866(f161(x89602,x89601),x89603),f866(f866(f155(x89602,x89601,x89603),x89605),x89604)))
% 157.76/157.52 [9006]~P25(x90062,x90061,x90064,x90063)+E(f866(f317(x90061,x90062,f97(x90062,x90061,x90063,x90064)),f866(f317(x90062,x90061,x90064),x90065)),x90065)+~P107(f866(f866(f243(f937(x90062,a925)),x90065),x90063))
% 157.76/157.52 [9059]~P110(x90592)+E(f866(f866(f155(x90591,x90592,x90593),x90594),x90595),f156(x90591,x90592,x90593,x90594,x90595))+P107(f866(f866(f336(x90592),f866(x90593,x90594)),f866(f317(x90591,x90592,x90593),f866(f179(x90591),x90595))))
% 157.76/157.52 [9142]~P110(x91422)+E(f156(x91421,x91422,x91423,x91424,x91425),x91425)+~P107(f866(f866(f336(x91422),f866(x91423,x91424)),f866(f317(x91421,x91422,x91423),f866(f179(x91421),x91425))))
% 157.76/157.52 [9158]~P25(x91582,x91581,x91583,x91585)+P107(f866(f866(f244(f937(x91581,a925)),f866(f317(x91582,x91581,x91583),x91584)),f866(f317(x91582,x91581,x91583),x91585)))+~P107(f866(f866(f244(f937(x91582,a925)),x91584),x91585))
% 157.76/157.52 [9317]~P25(x93171,x93172,x93173,f250(f937(x93171,a925)))+~P107(f866(f866(f243(f937(x93172,a925)),x93174),f866(f317(x93171,x93172,x93173),x93175)))+P107(f866(f866(f243(f937(x93171,a925)),f866(f318(x93171,x93172,x93173),x93174)),x93175))
% 157.76/157.52 [9341]~E(f866(f317(x93413,x93411,x93414),f250(f937(x93413,a925))),f250(f937(x93411,a925)))+P107(f866(f866(f243(f937(x93411,a925)),x93412),f866(f317(x93413,x93411,x93414),x93415)))+~P107(f866(f866(f243(f937(x93413,a925)),f866(f318(x93413,x93411,x93414),x93412)),x93415))
% 157.76/157.52 [9445]~P25(x94451,x94454,x94455,f250(f937(x94451,a925)))+~P107(f866(f866(f243(f937(x94454,a925)),f866(f317(x94451,x94454,x94455),x94452)),f866(f317(x94451,x94454,x94455),x94453)))+P107(f866(f866(f243(f937(x94451,a925)),x94452),x94453))
% 157.76/157.52 [9569]~P82(x95691)+~E(f866(x95693,f727(x95693,x95694,x95695,x95692,x95691)),f2(x95691))+E(f866(f172(x95691),f866(f866(f161(x95692,x95691),x95693),f866(f143(x95692,x95694),x95695))),f866(f172(x95691),f866(f866(f161(x95692,x95691),x95693),x95695)))
% 157.76/157.52 [9596]~P26(x95961,x95962,x95963,f250(f937(x95961,a925)),f250(f937(x95962,a925)))+~P107(f866(f866(f243(f937(x95962,a925)),x95964),f866(f317(x95961,x95962,x95963),x95965)))+P107(f866(f866(f243(f937(x95961,a925)),f866(f318(x95961,x95962,x95963),x95964)),x95965))
% 157.76/157.52 [9625]~P26(x96253,x96251,x96254,f250(f937(x96253,a925)),f250(f937(x96251,a925)))+P107(f866(f866(f243(f937(x96251,a925)),x96252),f866(f317(x96253,x96251,x96254),x96255)))+~P107(f866(f866(f243(f937(x96253,a925)),f866(f318(x96253,x96251,x96254),x96252)),x96255))
% 157.76/157.52 [9749]~P16(x97491,x97492,x97493)+~P107(f866(f66(x97491),x97495))+P107(f866(f71(x97491,x97492,x97493,x97494,x97495),f866(f866(f69(x97491,x97492,x97493),x97494),x97495)))
% 157.76/157.52 [9828]~P26(x98282,x98281,x98284,f250(f937(x98282,a925)),f250(f937(x98281,a925)))+~P26(x98281,x98283,x98285,f250(f937(x98281,a925)),f250(f937(x98283,a925)))+E(f866(f78(x98281,x98282,x98283,f97(x98282,x98281,f250(f937(x98282,a925)),x98284)),f97(x98281,x98283,f250(f937(x98281,a925)),x98285)),f97(x98282,x98283,f250(f937(x98282,a925)),f866(f78(x98281,x98283,x98282,x98285),x98284)))
% 157.76/157.52 [9829]P107(f866(x98291,f647(x98292,x98291,x98293,x98294,x98295)))+~P107(f866(f866(f243(f937(x98295,a925)),x98294),x98293))+P107(f866(f866(f243(f937(x98295,a925)),f866(f866(f108(f937(x98295,a925)),x98294),f866(f270(x98295),x98291))),f866(f866(f108(f937(x98295,a925)),x98293),f866(f270(x98295),x98292))))
% 157.76/157.52 [9843]~P82(x98431)+~P107(f866(x98434,f727(x98433,x98434,x98435,x98432,x98431)))+E(f866(f172(x98431),f866(f866(f161(x98432,x98431),x98433),f866(f143(x98432,x98434),x98435))),f866(f172(x98431),f866(f866(f161(x98432,x98431),x98433),x98435)))
% 157.76/157.52 [9921]~P5(x99215)+P107(f866(f866(f336(x99211),f615(x99212,x99213,x99211,x99214,x99215)),x99213))+P107(f866(f866(f243(x99215),x99214),f866(f866(f45(x99211,x99215),x99213),x99212)))
% 157.76/157.52 [9925]~P82(x99251)+E(f866(f172(x99251),f866(f866(f161(x99252,x99251),x99253),f866(f143(x99252,x99254),x99255))),f866(f172(x99251),f866(f866(f161(x99252,x99251),x99253),x99255)))+P107(f866(f866(f336(x99252),f727(x99253,x99254,x99255,x99252,x99251)),f866(f179(x99252),x99255)))
% 157.76/157.52 [9935]~P107(f866(x99355,f647(x99355,x99353,x99354,x99352,x99351)))+~P107(f866(f866(f243(f937(x99351,a925)),x99352),x99354))+P107(f866(f866(f243(f937(x99351,a925)),f866(f866(f108(f937(x99351,a925)),x99352),f866(f270(x99351),x99353))),f866(f866(f108(f937(x99351,a925)),x99354),f866(f270(x99351),x99355))))
% 157.76/157.52 [9951]~P25(x99515,x99513,x99514,f250(f937(x99515,a925)))+P107(f866(x99511,x99512))+P107(f866(f866(f336(x99513),f729(x99512,x99511,x99514,x99513,x99515)),f866(f317(x99515,x99513,x99514),f250(f937(x99515,a925)))))
% 157.76/157.52 [9975]P34(x99751,x99752,x99753,x99754,x99755)+~E(f866(f196(f931(x99752)),x99755),f866(f196(f931(x99751)),x99754))+P107(f866(f866(f244(a930),f709(x99755,x99754,x99753,x99752,x99751)),f866(f196(f931(x99751)),x99754)))
% 157.76/157.52 [9976]P34(x99761,x99762,x99763,x99764,x99765)+~E(f866(f196(f931(x99762)),x99765),f866(f196(f931(x99761)),x99764))+P107(f866(f866(f244(a930),f744(x99763,x99765,x99762,x99764,x99761)),f866(f196(f931(x99761)),x99764)))
% 157.76/157.52 [10008]P107(f866(f866(f336(x100081),f647(x100082,x100083,x100084,x100085,x100081)),x100085))+~P107(f866(f866(f243(f937(x100081,a925)),x100085),x100084))+P107(f866(f866(f243(f937(x100081,a925)),f866(f866(f108(f937(x100081,a925)),x100085),f866(f270(x100081),x100083))),f866(f866(f108(f937(x100081,a925)),x100084),f866(f270(x100081),x100082))))
% 157.76/157.52 [10051]~P5(x100511)+~P107(f866(f866(f243(x100511),x100512),f866(x100515,f615(x100515,x100514,x100513,x100512,x100511))))+P107(f866(f866(f243(x100511),x100512),f866(f866(f45(x100513,x100511),x100514),x100515)))
% 157.76/157.52 [10088]~P71(x100881)+~P107(f866(f66(x100882),x100885))+E(f866(f866(f866(f70(x100881,x100882,f87(x100881)),f866(f866(f18(x100882,x100881,x100881),f866(f866(f8(x100881,f937(x100881,x100881),x100882),f87(x100881)),x100883)),x100884)),f84(x100881)),x100885),f866(f866(f87(x100881),f866(f866(f866(f70(x100881,x100882,f87(x100881)),x100883),f84(x100881)),x100885)),f866(f866(f866(f70(x100881,x100882,f87(x100881)),x100884),f84(x100881)),x100885)))
% 157.76/157.52 [10144]~P107(f866(f866(f336(f936(f937(x101441,a925),f937(x101441,a925))),f866(f866(f260(f937(x101441,a925),f937(x101441,a925)),x101445),x101444)),f325(x101441,x101443)))+~P107(f866(f866(f336(x101441),x101442),x101445))+P107(f866(f866(f336(f936(x101441,x101441)),f866(f866(f260(x101441,x101441),x101442),f577(x101443,x101444,x101445,x101441,x101442))),x101443))
% 157.76/157.52 [10269]~P107(f866(f866(f336(f936(f931(x102691),f931(x102691))),f866(f866(f260(f931(x102691),f931(x102691)),f866(f866(f141(x102691),x102695),x102692)),f866(f866(f141(x102691),x102695),x102693))),f154(x102691,x102694)))+P107(f866(f866(f336(f936(f931(x102691),f931(x102691))),f866(f866(f260(f931(x102691),f931(x102691)),x102692),x102693)),f154(x102691,x102694)))+P107(f866(f866(f336(f936(x102691,x102691)),f866(f866(f260(x102691,x102691),f697(x102694,x102693,x102692,x102695,x102691)),f697(x102694,x102693,x102692,x102695,x102691))),x102694))
% 157.76/157.52 [7495]~E(x74953,x74955)+E(f866(f866(f171(x74951),f866(f866(f166(x74951,x74952),x74953),x74954)),x74955),x74954)+~P107(f866(f866(f244(a930),x74953),f866(f196(f931(x74951)),x74952)))
% 157.76/157.52 [7610]~E(f866(f866(f141(x76101),x76102),x76104),f866(f866(f141(x76101),x76103),x76105))+E(f866(f866(f182(x76101),f866(f196(f931(x76101)),x76102)),x76103),x76102)+P107(f866(f866(f243(a930),f866(f196(f931(x76101)),x76103)),f866(f196(f931(x76101)),x76102)))
% 157.76/157.52 [8098]~E(f866(f866(f141(x80981),x80982),x80984),f866(f866(f141(x80981),x80983),x80985))+E(f866(f866(f182(x80981),f866(f196(f931(x80981)),x80982)),x80983),x80982)+~P107(f866(f866(f243(a930),f866(f196(f931(x80981)),x80982)),f866(f196(f931(x80981)),x80983)))
% 157.76/157.52 [8122]~P107(f866(f66(x81221),f866(x81224,x81225)))+~P107(f866(f866(f336(x81222),x81225),x81223))+P107(f866(f66(x81221),f866(f866(f45(x81222,f937(x81221,a925)),x81223),x81224)))
% 157.76/157.52 [8297]~P53(x82971,x82973,x82975)+~P53(x82971,x82972,x82974)+P53(x82971,f866(f866(f117(f937(x82971,a925)),x82972),x82973),f866(f866(f117(f937(f936(x82971,x82971),a925)),x82974),x82975))
% 157.76/157.52 [8298]~P53(x82981,x82983,x82985)+~P53(x82981,x82982,x82984)+P53(x82981,f866(f866(f108(f937(x82981,a925)),x82982),x82983),f866(f866(f108(f937(f936(x82981,x82981),a925)),x82984),x82985))
% 157.76/157.52 [8645]E(f866(f866(f260(x86451,x86452),f866(f866(f171(x86451),x86453),x86454)),f866(f866(f171(x86452),x86455),x86454)),f866(f866(f171(f936(x86451,x86452)),f866(f866(f188(x86451,x86452),x86453),x86455)),x86454))+~P107(f866(f866(f244(a930),x86454),f866(f196(f931(x86451)),x86453)))+~P107(f866(f866(f244(a930),x86454),f866(f196(f931(x86452)),x86455)))
% 157.76/157.52 [8799]~P53(x87991,x87993,x87994)+P107(f866(f866(f336(x87991),x87992),x87993))+~P107(f866(f866(f336(f936(x87991,x87991)),f866(f866(f260(x87991,x87991),x87995),x87992)),x87994))
% 157.76/157.52 [8800]~P53(x88001,x88003,x88004)+P107(f866(f866(f336(x88001),x88002),x88003))+~P107(f866(f866(f336(f936(x88001,x88001)),f866(f866(f260(x88001,x88001),x88002),x88005)),x88004))
% 157.76/157.52 [8801]~P8(x88011,x88013,x88014)+P107(f866(f866(f336(x88011),x88012),x88013))+~P107(f866(f866(f336(f936(x88011,x88011)),f866(f866(f260(x88011,x88011),x88015),x88012)),x88014))
% 157.76/157.52 [8802]~P8(x88021,x88023,x88024)+P107(f866(f866(f336(x88021),x88022),x88023))+~P107(f866(f866(f336(f936(x88021,x88021)),f866(f866(f260(x88021,x88021),x88022),x88025)),x88024))
% 157.76/157.52 [9083]~P8(x90831,x90835,x90832)+E(f866(f293(x90831,x90831,x90832),f866(f866(f316(x90831),x90833),f195(f937(x90831,a925)))),f866(f293(x90831,x90831,x90832),f866(f866(f316(x90831),x90834),f195(f937(x90831,a925)))))+~P107(f866(f866(f336(f936(x90831,x90831)),f866(f866(f260(x90831,x90831),x90833),x90834)),x90832))
% 157.76/157.52 [9273]P107(f866(x92731,x92732))+~P107(f866(f866(f336(x92733),x92732),x92735))+P107(f866(f866(f336(x92733),f596(x92731,x92734,x92735,x92733)),f866(f866(f117(f937(x92733,a925)),x92735),x92734)))
% 157.76/157.52 [9274]P107(f866(x92741,x92742))+~P107(f866(f866(f336(x92743),x92742),x92744))+P107(f866(f866(f336(x92743),f596(x92741,x92744,x92745,x92743)),f866(f866(f117(f937(x92743,a925)),x92745),x92744)))
% 157.76/157.52 [9282]~P107(f866(x92822,x92825))+~P107(f866(f866(f336(x92821),x92825),x92824))+P107(f866(f866(f336(x92821),f648(x92822,x92823,x92824,x92821)),f866(f866(f117(f937(x92821,a925)),x92824),x92823)))
% 157.76/157.52 [9283]~P107(f866(x92832,x92835))+~P107(f866(f866(f336(x92831),x92835),x92833))+P107(f866(f866(f336(x92831),f648(x92832,x92833,x92834,x92831)),f866(f866(f117(f937(x92831,a925)),x92834),x92833)))
% 157.76/157.52 [9298]~P107(f866(f866(f243(f937(x92981,a925)),x92985),x92983))+~P107(f866(f866(f243(f937(x92981,a925)),x92982),x92984))+P107(f866(f866(f243(f937(x92981,a925)),f866(f866(f23(f937(x92981,a925)),x92982),x92983)),f866(f866(f23(f937(x92981,a925)),x92984),x92985)))
% 157.76/157.52 [9299]~P107(f866(f866(f243(f937(x92991,a925)),x92993),x92995))+~P107(f866(f866(f243(f937(x92991,a925)),x92992),x92994))+P107(f866(f866(f243(f937(x92991,a925)),f866(f866(f117(f937(x92991,a925)),x92992),x92993)),f866(f866(f117(f937(x92991,a925)),x92994),x92995)))
% 157.76/157.52 [9300]~P107(f866(f866(f243(f937(x93001,a925)),x93003),x93005))+~P107(f866(f866(f243(f937(x93001,a925)),x93002),x93004))+P107(f866(f866(f243(f937(x93001,a925)),f866(f866(f108(f937(x93001,a925)),x93002),x93003)),f866(f866(f108(f937(x93001,a925)),x93004),x93005)))
% 157.76/157.52 [9395]P107(f866(f866(f336(f936(x93951,x93951)),f866(f866(f260(x93951,x93951),x93952),x93953)),f328(x93951,x93954,x93955)))+~P107(f866(f866(f243(a930),f866(x93954,x93952)),f866(x93954,x93953)))+~P107(f866(f866(f336(f936(x93951,x93951)),f866(f866(f260(x93951,x93951),x93952),x93953)),x93955))
% 157.76/157.52 [9579]P107(f866(f866(f336(f936(x95791,x95791)),f866(f866(f260(x95791,x95791),x95792),x95793)),f314(x95791,x95794)))+~P107(f866(f866(f336(f936(x95791,x95791)),f866(f866(f260(x95791,x95791),x95792),x95795)),f314(x95791,x95794)))+~P107(f866(f866(f336(f936(x95791,x95791)),f866(f866(f260(x95791,x95791),x95795),x95793)),x95794))
% 157.76/157.52 [9580]P107(f866(f866(f336(f936(x95801,x95801)),f866(f866(f260(x95801,x95801),x95802),x95803)),f314(x95801,x95804)))+~P107(f866(f866(f336(f936(x95801,x95801)),f866(f866(f260(x95801,x95801),x95805),x95803)),f314(x95801,x95804)))+~P107(f866(f866(f336(f936(x95801,x95801)),f866(f866(f260(x95801,x95801),x95802),x95805)),x95804))
% 157.76/157.52 [9678]E(x96781,x96782)+E(f866(a119,f598(x96783,x96784,x96781,x96782,x96785)),x96784)+~P107(f866(f866(f336(f936(x96785,x96785)),f866(f866(f260(x96785,x96785),x96782),x96781)),f866(f866(f190(f936(x96785,x96785),a925),x96784),x96783)))
% 157.76/157.52 [9679]E(x96791,x96792)+E(f866(a119,f602(x96793,x96794,x96791,x96792,x96795)),x96794)+~P107(f866(f866(f336(f936(x96795,x96795)),f866(f866(f260(x96795,x96795),x96792),x96791)),f866(f866(f190(f936(x96795,x96795),a925),x96794),x96793)))
% 157.76/157.52 [9680]E(x96801,f2(a930))+E(f866(a119,f598(x96802,x96801,x96803,x96804,x96805)),x96801)+~P107(f866(f866(f336(f936(x96805,x96805)),f866(f866(f260(x96805,x96805),x96804),x96803)),f866(f866(f190(f936(x96805,x96805),a925),x96801),x96802)))
% 157.76/157.52 [9681]E(x96811,f2(a930))+E(f866(a119,f602(x96812,x96811,x96813,x96814,x96815)),x96811)+~P107(f866(f866(f336(f936(x96815,x96815)),f866(f866(f260(x96815,x96815),x96814),x96813)),f866(f866(f190(f936(x96815,x96815),a925),x96811),x96812)))
% 157.76/157.52 [9702]P107(f866(f866(f336(f936(x97021,x97021)),f866(f866(f260(x97021,x97021),x97022),x97023)),f866(f866(f296(x97021,x97021,x97021),x97024),f314(x97021,x97024))))+~P107(f866(f866(f336(f936(x97021,x97021)),f866(f866(f260(x97021,x97021),x97022),x97025)),x97024))+~P107(f866(f866(f336(f936(x97021,x97021)),f866(f866(f260(x97021,x97021),x97025),x97023)),x97024))
% 157.76/157.52 [9709]~P107(f866(f866(f336(f936(x97091,x97091)),f866(f866(f260(x97091,x97091),x97092),x97095)),f314(x97091,x97094)))+P107(f866(f866(f336(f936(x97091,x97091)),f866(f866(f260(x97091,x97091),x97092),x97093)),f866(f866(f296(x97091,x97091,x97091),x97094),f314(x97091,x97094))))+~P107(f866(f866(f336(f936(x97091,x97091)),f866(f866(f260(x97091,x97091),x97095),x97093)),x97094))
% 157.76/157.52 [9743]~P8(x97431,x97435,x97432)+~P107(f866(f866(f336(f936(x97431,x97431)),f866(f866(f260(x97431,x97431),x97433),x97434)),x97432))+P107(f866(f866(f243(f937(x97431,a925)),f866(f293(x97431,x97431,x97432),f866(f866(f316(x97431),x97433),f195(f937(x97431,a925))))),f866(f293(x97431,x97431,x97432),f866(f866(f316(x97431),x97434),f195(f937(x97431,a925))))))
% 157.76/157.52 [9801]P107(f866(f866(f336(f936(x98011,x98011)),f866(f866(f260(x98011,x98011),x98012),x98013)),f866(f866(f296(x98011,x98011,x98011),x98014),f314(x98011,x98014))))+~P107(f866(f866(f336(f936(x98011,x98011)),f866(f866(f260(x98011,x98011),x98012),x98015)),f866(f866(f296(x98011,x98011,x98011),x98014),f314(x98011,x98014))))+~P107(f866(f866(f336(f936(x98011,x98011)),f866(f866(f260(x98011,x98011),x98015),x98013)),x98014))
% 157.76/157.52 [9802]P107(f866(f866(f336(f936(x98021,x98021)),f866(f866(f260(x98021,x98021),x98022),x98023)),f866(f866(f296(x98021,x98021,x98021),x98024),f314(x98021,x98024))))+~P107(f866(f866(f336(f936(x98021,x98021)),f866(f866(f260(x98021,x98021),x98025),x98023)),f866(f866(f296(x98021,x98021,x98021),x98024),f314(x98021,x98024))))+~P107(f866(f866(f336(f936(x98021,x98021)),f866(f866(f260(x98021,x98021),x98022),x98025)),x98024))
% 157.76/157.52 [9852]~P107(f866(f71(x98521,x98521,x98524,x98522,x98523),x98525))+P107(f866(f866(f336(x98521),x98522),x98523))+P107(f866(f67(x98521,x98524,f866(f866(f316(x98521),x98522),x98523)),x98525))
% 157.76/157.52 [9890]~E(f866(f317(x98903,x98902,x98905),x98904),x98901)+E(x98901,f195(f937(x98902,a925)))+P107(f866(f866(f243(f937(x98903,a925)),f866(f317(x98902,x98903,f485(x98904,x98903,x98902,x98901)),x98901)),x98904))
% 157.76/157.52 [9938]~P5(x99385)+P107(f866(f866(f336(x99381),f856(x99382,x99383,x99384,x99381,x99385)),x99384))+P107(f866(f866(f243(x99385),f866(f866(f44(x99381,x99385),x99384),x99383)),x99382))
% 157.76/157.52 [9995]P34(x99951,x99952,x99953,x99954,x99955)+~E(f866(f196(f931(x99951)),x99954),f866(f196(f931(x99952)),x99955))+P107(f866(f866(f336(f936(x99951,x99952)),f707(x99955,x99954,x99953,x99952,x99951)),f866(f179(f936(x99951,x99952)),f866(f866(f188(x99951,x99952),x99954),x99955))))
% 157.76/157.52 [9996]P34(x99961,x99962,x99963,x99964,x99965)+~E(f866(f196(f931(x99961)),x99964),f866(f196(f931(x99962)),x99965))+P107(f866(f866(f336(f936(x99961,x99962)),f708(x99963,x99965,x99964,x99962,x99961)),f866(f179(f936(x99961,x99962)),f866(f866(f188(x99961,x99962),x99964),x99965))))
% 157.76/157.52 [10122]E(x101221,x101222)+P107(f866(f866(f336(f936(x101223,x101223)),f866(f866(f260(x101223,x101223),x101221),f600(x101224,x101225,x101222,x101221,x101223))),x101224))+~P107(f866(f866(f336(f936(x101223,x101223)),f866(f866(f260(x101223,x101223),x101221),x101222)),f866(f866(f190(f936(x101223,x101223),a925),x101225),x101224)))
% 157.76/157.52 [10123]E(x101231,f2(a930))+P107(f866(f866(f336(f936(x101232,x101232)),f866(f866(f260(x101232,x101232),x101233),f600(x101234,x101231,x101235,x101233,x101232))),x101234))+~P107(f866(f866(f336(f936(x101232,x101232)),f866(f866(f260(x101232,x101232),x101233),x101235)),f866(f866(f190(f936(x101232,x101232),a925),x101231),x101234)))
% 157.76/157.52 [10163]~P5(x101631)+~P107(f866(f866(f243(x101631),f866(x101634,f856(x101635,x101634,x101633,x101632,x101631))),x101635))+P107(f866(f866(f243(x101631),f866(f866(f44(x101632,x101631),x101633),x101634)),x101635))
% 157.76/157.52 [10206]E(x102061,x102062)+P107(f866(f866(f336(f936(x102063,x102063)),f866(f866(f260(x102063,x102063),f599(x102064,x102065,x102061,x102062,x102063)),x102061)),x102064))+~P107(f866(f866(f336(f936(x102063,x102063)),f866(f866(f260(x102063,x102063),x102062),x102061)),f866(f866(f190(f936(x102063,x102063),a925),x102065),x102064)))
% 157.76/157.52 [10207]E(x102071,f2(a930))+P107(f866(f866(f336(f936(x102072,x102072)),f866(f866(f260(x102072,x102072),f599(x102073,x102071,x102074,x102075,x102072)),x102074)),x102073))+~P107(f866(f866(f336(f936(x102072,x102072)),f866(f866(f260(x102072,x102072),x102075),x102074)),f866(f866(f190(f936(x102072,x102072),a925),x102071),x102073)))
% 157.76/157.52 [10211]E(x102111,x102112)+P107(f866(f866(f336(f936(x102113,x102113)),f866(f866(f260(x102113,x102113),x102111),f599(x102114,x102115,x102112,x102111,x102113))),f866(f866(f190(f936(x102113,x102113),a925),f598(x102114,x102115,x102112,x102111,x102113)),x102114)))+~P107(f866(f866(f336(f936(x102113,x102113)),f866(f866(f260(x102113,x102113),x102111),x102112)),f866(f866(f190(f936(x102113,x102113),a925),x102115),x102114)))
% 157.76/157.52 [10212]E(x102121,f2(a930))+P107(f866(f866(f336(f936(x102122,x102122)),f866(f866(f260(x102122,x102122),x102123),f599(x102124,x102121,x102125,x102123,x102122))),f866(f866(f190(f936(x102122,x102122),a925),f598(x102124,x102121,x102125,x102123,x102122)),x102124)))+~P107(f866(f866(f336(f936(x102122,x102122)),f866(f866(f260(x102122,x102122),x102123),x102125)),f866(f866(f190(f936(x102122,x102122),a925),x102121),x102124)))
% 157.76/157.52 [10260]E(x102601,x102602)+P107(f866(f866(f336(f936(x102603,x102603)),f866(f866(f260(x102603,x102603),f600(x102604,x102605,x102601,x102602,x102603)),x102601)),f866(f866(f190(f936(x102603,x102603),a925),f602(x102604,x102605,x102601,x102602,x102603)),x102604)))+~P107(f866(f866(f336(f936(x102603,x102603)),f866(f866(f260(x102603,x102603),x102602),x102601)),f866(f866(f190(f936(x102603,x102603),a925),x102605),x102604)))
% 157.76/157.52 [10261]E(x102611,f2(a930))+P107(f866(f866(f336(f936(x102612,x102612)),f866(f866(f260(x102612,x102612),f600(x102613,x102611,x102614,x102615,x102612)),x102614)),f866(f866(f190(f936(x102612,x102612),a925),f602(x102613,x102611,x102614,x102615,x102612)),x102613)))+~P107(f866(f866(f336(f936(x102612,x102612)),f866(f866(f260(x102612,x102612),x102615),x102614)),f866(f866(f190(f936(x102612,x102612),a925),x102611),x102613)))
% 157.76/157.52 [10296]~P72(x102962)+~P107(f866(f66(x102961),x102965))+E(f866(f866(f6(x102961,x102962),f866(f866(f7(x102961,x102962,x102962),f866(f866(f18(x102961,x102962,f937(x102962,x102962)),f866(f866(f8(a925,f937(x102962,f937(x102962,x102962)),x102961),f103(x102962)),f866(f866(f7(x102961,f937(x102961,a925),a925),f336(x102961)),x102963))),x102964)),f2(x102962))),x102965),f866(f866(f6(x102961,x102962),x102964),f866(f866(f108(f937(x102961,a925)),x102965),x102963)))
% 157.76/157.52 [8867]~P71(x88671)+~P107(f866(f66(x88674),x88675))+E(f866(f866(f87(x88671),f866(x88672,x88673)),f866(f866(f9(x88674,x88671),x88672),f866(f866(f23(f937(x88674,a925)),x88675),f866(f866(f316(x88674),x88673),f195(f937(x88674,a925)))))),f866(f866(f9(x88674,x88671),x88672),f866(f866(f316(x88674),x88673),x88675)))
% 157.76/157.52 [8868]~P72(x88681)+~P107(f866(f66(x88684),x88685))+E(f866(f866(f86(x88681),f866(x88682,x88683)),f866(f866(f6(x88684,x88681),x88682),f866(f866(f23(f937(x88684,a925)),x88685),f866(f866(f316(x88684),x88683),f195(f937(x88684,a925)))))),f866(f866(f6(x88684,x88681),x88682),f866(f866(f316(x88684),x88683),x88685)))
% 157.76/157.53 [9206]~P110(x92062)+~P13(x92062,f866(f175(x92062),f866(f866(f161(x92061,x92062),x92064),x92065)))+E(f866(f143(x92061,f866(f866(f8(x92062,a925,x92061),f866(f244(x92062),x92063)),x92064)),x92065),f184(x92061,f866(f866(f8(x92062,a925,x92061),f866(f244(x92062),x92063)),x92064),x92065))
% 157.76/157.53 [9230]~P72(x92301)+E(f866(f866(f86(x92301),f866(f866(f6(a930,x92301),x92302),f310(a930,x92303,x92304))),f866(f866(f6(a930,x92301),x92302),f310(a930,f866(f866(f86(a930),x92304),f84(a930)),f866(f866(f86(a930),x92304),x92305)))),f866(f866(f6(a930,x92301),x92302),f310(a930,x92303,f866(f866(f86(a930),x92304),x92305))))+~P107(f866(f866(f243(a930),x92303),f866(f866(f86(a930),x92304),f84(a930))))
% 157.76/157.53 [9231]~P107(f866(f866(f336(x92311),x92314),x92315))+~P107(f866(f866(f243(f937(x92311,a925)),f866(f179(x92311),x92312)),x92315))+P107(f866(f866(f243(f937(x92311,a925)),f866(f179(x92311),f866(f866(f166(x92311,x92312),x92313),x92314))),x92315))
% 157.76/157.53 [9453]~P5(x94532)+~P107(f866(f66(x94531),x94535))+E(f866(f866(f69(x94531,x94532,f866(f866(f8(x94532,f937(x94532,x94532),x94531),f117(x94532)),x94533)),x94534),x94535),f866(f866(f117(x94532),x94534),f866(f866(f44(x94531,x94532),x94535),x94533)))
% 157.76/157.53 [9454]~P5(x94542)+~P107(f866(f66(x94541),x94545))+E(f866(f866(f69(x94541,x94542,f866(f866(f8(x94542,f937(x94542,x94542),x94541),f108(x94542)),x94543)),x94544),x94545),f866(f866(f108(x94542),x94544),f866(f866(f45(x94541,x94542),x94545),x94543)))
% 157.76/157.53 [9503]E(f866(x95031,x95032),f866(x95031,x95033))+P107(f866(f866(f244(a930),f866(x95031,x95032)),f866(x95031,x95033)))+~P107(f866(f866(f336(f936(x95034,x95034)),f866(f866(f260(x95034,x95034),x95032),x95033)),f160(x95034,f866(f866(f158(f937(x95034,a930)),x95031),x95035))))
% 157.76/157.53 [9537]~E(f866(x95374,x95372),f866(x95374,x95373))+~P107(f866(f866(f336(f936(x95371,x95371)),f866(f866(f260(x95371,x95371),x95372),x95373)),f160(x95371,x95375)))+P107(f866(f866(f336(f936(x95371,x95371)),f866(f866(f260(x95371,x95371),x95372),x95373)),f160(x95371,f866(f866(f158(f937(x95371,a930)),x95374),x95375))))
% 157.76/157.53 [9557]~P25(x95571,x95572,x95573,x95575)+P25(x95571,x95572,x95573,f866(f866(f316(x95571),x95574),x95575))+P107(f866(f866(f336(x95572),f866(x95573,x95574)),f866(f317(x95571,x95572,x95573),f866(f866(f23(f937(x95571,a925)),x95575),f866(f866(f316(x95571),x95574),f195(f937(x95571,a925)))))))
% 157.76/157.53 [9560]P107(f866(x95602,x95605))+~P107(f866(f866(f336(x95601),x95605),f866(f179(x95601),x95603)))+E(f866(f866(f145(x95601),f866(f196(f931(x95601)),f184(x95601,x95602,f866(f866(f141(x95601),x95603),x95604)))),f866(f866(f141(x95601),x95603),x95604)),f866(f866(f141(x95601),f866(f866(f145(x95601),f866(f196(f931(x95601)),f184(x95601,x95602,x95603))),x95603)),x95604))
% 157.76/157.53 [9565]~P107(f866(f866(f336(f936(x95651,x95651)),f866(f866(f260(x95651,x95651),x95652),x95653)),f160(x95651,x95655)))+~P107(f866(f866(f243(a930),f866(x95654,x95652)),f866(x95654,x95653)))+P107(f866(f866(f336(f936(x95651,x95651)),f866(f866(f260(x95651,x95651),x95652),x95653)),f160(x95651,f866(f866(f158(f937(x95651,a930)),x95654),x95655))))
% 157.76/157.53 [9630]P107(f866(f866(f336(f936(x96304,x96304)),f866(f866(f260(x96304,x96304),x96302),x96303)),f160(x96304,x96305)))+P107(f866(f866(f244(a930),f866(x96301,x96302)),f866(x96301,x96303)))+~P107(f866(f866(f336(f936(x96304,x96304)),f866(f866(f260(x96304,x96304),x96302),x96303)),f160(x96304,f866(f866(f158(f937(x96304,a930)),x96301),x96305))))
% 157.76/157.53 [9773]~P107(f866(f866(f336(f936(f931(x97731),f931(x97731))),f866(f866(f260(f931(x97731),f931(x97731)),x97732),x97734)),f165(x97731,x97735)))+~P107(f866(f866(f244(a930),x97733),f866(f196(f931(x97731)),x97732)))+P107(f866(f866(f336(f936(x97731,x97731)),f866(f866(f260(x97731,x97731),f866(f866(f171(x97731),x97732),x97733)),f866(f866(f171(x97731),x97734),x97733))),x97735))
% 157.76/157.53 [10018]E(x100181,f2(a1))+~P107(f866(f54(x100183,x100181),f866(f866(f260(a1,a1),x100184),x100185)))+P107(f866(f54(f866(f866(f87(a1),x100182),x100183),x100181),f866(f866(f260(a1,a1),f866(f866(f86(a1),f866(f866(f87(a1),x100182),x100184)),f866(f866(f41(a1),f866(f866(f87(a1),x100182),x100185)),x100181))),f50(a1,f866(f866(f87(a1),x100182),x100185),x100181))))
% 157.76/157.53 [10019]~P107(f866(f866(f244(a930),f2(a930)),x100193))+~P107(f866(f53(x100192,x100193),f866(f866(f260(a930,a930),x100194),x100195)))+P107(f866(f53(f866(f866(f87(a930),x100191),x100192),x100193),f866(f866(f260(a930,a930),f866(f866(f86(a930),f866(f866(f87(a930),x100191),x100194)),f866(f866(f41(a930),f866(f866(f87(a930),x100191),x100195)),x100193))),f50(a930,f866(f866(f87(a930),x100191),x100195),x100193))))
% 157.76/157.53 [10319]~P72(x103192)+~P107(f866(f66(x103191),x103194))+E(f866(f866(f6(x103191,x103192),x103193),f866(f270(x103191),f866(f866(f18(x103191,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103191),a333),f866(f866(f7(x103191,f937(x103191,a925),a925),f336(x103191)),x103194))),f866(f866(f7(x103191,f937(x103191,a925),a925),f336(x103191)),x103195)))),f866(f866(f6(x103191,x103192),f866(f866(f7(x103191,x103192,x103192),f866(f866(f18(x103191,x103192,f937(x103192,x103192)),f866(f866(f8(a925,f937(x103192,f937(x103192,x103192)),x103191),f103(x103192)),f866(f866(f7(x103191,f937(x103191,a925),a925),f336(x103191)),x103195))),x103193)),f2(x103192))),x103194))
% 157.76/157.53 [8497]~E(f866(f866(f141(x84971),x84972),x84975),f866(f866(f141(x84971),x84973),x84974))+E(f866(f866(f141(x84971),f866(f866(f145(x84971),f866(f196(f931(x84971)),x84972)),x84973)),x84974),x84975)+P107(f866(f866(f243(a930),f866(f196(f931(x84971)),x84973)),f866(f196(f931(x84971)),x84972)))
% 157.76/157.53 [8693]~E(f866(f866(f141(x86932),x86933),x86931),f866(f866(f141(x86932),x86934),x86935))+E(x86931,f866(f866(f141(x86932),f866(f866(f145(x86932),f866(f196(f931(x86932)),x86933)),x86934)),x86935))+~P107(f866(f866(f243(a930),f866(f196(f931(x86932)),x86933)),f866(f196(f931(x86932)),x86934)))
% 157.76/157.53 [8782]~E(f866(f866(f86(a930),f866(f866(f87(a930),x87823),x87824)),x87821),f866(f866(f86(a930),f866(f866(f87(a930),x87822),x87824)),x87825))+~P107(f866(f866(f243(a930),x87823),x87822))+E(x87821,f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x87822),x87823)),x87824)),x87825))
% 157.76/157.53 [8783]~E(f866(f866(f86(a930),f866(f866(f87(a930),x87831),x87833)),x87834),f866(f866(f86(a930),f866(f866(f87(a930),x87832),x87833)),x87835))+~P107(f866(f866(f243(a930),x87832),x87831))+E(f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x87831),x87832)),x87833)),x87834),x87835)
% 157.76/157.53 [8951]E(f866(f866(f86(a930),f866(f866(f87(a930),x89511),x89512)),x89513),f866(f866(f86(a930),f866(f866(f87(a930),x89514),x89512)),x89515))+~P107(f866(f866(f243(a930),x89514),x89511))+~E(x89515,f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x89511),x89514)),x89512)),x89513))
% 157.76/157.53 [8952]E(f866(f866(f86(a930),f866(f866(f87(a930),x89521),x89522)),x89523),f866(f866(f86(a930),f866(f866(f87(a930),x89524),x89522)),x89525))+~P107(f866(f866(f243(a930),x89524),x89521))+~E(f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x89521),x89524)),x89522)),x89523),x89525)
% 157.76/157.53 [9826]~P65(x98262)+~P107(f866(f66(x98261),x98265))+E(f866(f866(f9(x98261,x98262),f866(f866(f18(x98261,x98262,x98262),f866(f866(f8(x98262,f937(x98262,x98262),x98261),f297(x98262)),x98263)),x98264)),x98265),f866(f866(f297(x98262),f866(f866(f9(x98261,x98262),x98263),x98265)),f866(f866(f9(x98261,x98262),x98264),x98265)))
% 157.76/157.53 [9958]~E(f604(x99585,x99584,x99583,x99582,x99581),f605(x99585,x99584,x99583,x99582,x99581))+P107(f866(f866(f336(f936(x99581,x99581)),f866(f866(f260(x99581,x99581),x99582),x99583)),f314(x99581,x99584)))+~P107(f866(f866(f336(f936(x99581,x99581)),f866(f866(f260(x99581,x99581),x99582),x99583)),f314(x99581,f866(f866(f117(f937(f936(x99581,x99581),a925)),x99584),x99585))))
% 157.76/157.53 [9959]~E(f606(x99595,x99594,x99593,x99592,x99591),f607(x99595,x99594,x99593,x99592,x99591))+P107(f866(f866(f336(f936(x99591,x99591)),f866(f866(f260(x99591,x99591),x99592),x99593)),f314(x99591,x99594)))+~P107(f866(f866(f336(f936(x99591,x99591)),f866(f866(f260(x99591,x99591),x99592),x99593)),f314(x99591,f866(f866(f117(f937(f936(x99591,x99591),a925)),x99594),x99595))))
% 157.76/157.53 [10153]P107(f866(f866(f336(f936(x101531,x101531)),f866(f866(f260(x101531,x101531),x101532),f607(x101535,x101534,x101533,x101532,x101531))),f314(x101531,x101534)))+P107(f866(f866(f336(f936(x101531,x101531)),f866(f866(f260(x101531,x101531),x101532),x101533)),f314(x101531,x101534)))+~P107(f866(f866(f336(f936(x101531,x101531)),f866(f866(f260(x101531,x101531),x101532),x101533)),f314(x101531,f866(f866(f117(f937(f936(x101531,x101531),a925)),x101534),x101535))))
% 157.76/157.53 [10233]P107(f866(f866(f336(f936(x102331,x102331)),f866(f866(f260(x102331,x102331),f605(x102335,x102334,x102333,x102332,x102331)),x102333)),f314(x102331,x102334)))+P107(f866(f866(f336(f936(x102331,x102331)),f866(f866(f260(x102331,x102331),x102332),x102333)),f314(x102331,x102334)))+~P107(f866(f866(f336(f936(x102331,x102331)),f866(f866(f260(x102331,x102331),x102332),x102333)),f314(x102331,f866(f866(f117(f937(f936(x102331,x102331),a925)),x102334),x102335))))
% 157.76/157.53 [10267]P107(f866(f866(f336(f936(x102671,x102671)),f866(f866(f260(x102671,x102671),x102672),x102673)),f314(x102671,x102674)))+P107(f866(f866(f336(f936(x102671,x102671)),f866(f866(f260(x102671,x102671),f604(x102675,x102674,x102673,x102672,x102671)),f605(x102675,x102674,x102673,x102672,x102671))),x102675))+~P107(f866(f866(f336(f936(x102671,x102671)),f866(f866(f260(x102671,x102671),x102672),x102673)),f314(x102671,f866(f866(f117(f937(f936(x102671,x102671),a925)),x102674),x102675))))
% 157.76/157.53 [10268]P107(f866(f866(f336(f936(x102681,x102681)),f866(f866(f260(x102681,x102681),x102682),x102683)),f314(x102681,x102684)))+P107(f866(f866(f336(f936(x102681,x102681)),f866(f866(f260(x102681,x102681),f607(x102685,x102684,x102683,x102682,x102681)),f606(x102685,x102684,x102683,x102682,x102681))),x102685))+~P107(f866(f866(f336(f936(x102681,x102681)),f866(f866(f260(x102681,x102681),x102682),x102683)),f314(x102681,f866(f866(f117(f937(f936(x102681,x102681),a925)),x102684),x102685))))
% 157.76/157.53 [10415]~P107(f866(f866(f336(f936(f931(x104151),f931(x104151))),f866(f866(f260(f931(x104151),f931(x104151)),x104154),x104155)),f165(x104151,x104152)))+~P107(f866(f866(f336(f936(x104151,x104151)),x104153),f866(f179(f936(x104151,x104151)),f866(f866(f188(x104151,x104151),x104154),x104155))))+P107(f866(f866(f265(x104151,x104151,a925),f866(f866(f7(x104151,f937(f936(x104151,x104151),a925),f937(x104151,a925)),f866(f866(f8(f937(x104151,f937(f937(f936(x104151,x104151),a925),a925)),f937(f937(f936(x104151,x104151),a925),f937(x104151,a925)),x104151),f7(x104151,f937(f936(x104151,x104151),a925),a925)),f866(f866(f8(f937(x104151,f936(x104151,x104151)),f937(x104151,f937(f937(f936(x104151,x104151),a925),a925)),x104151),f866(f8(f936(x104151,x104151),f937(f937(f936(x104151,x104151),a925),a925),x104151),f336(f936(x104151,x104151)))),f260(x104151,x104151)))),x104152)),x104153))
% 157.76/157.53 [9856]~P107(f866(f866(f243(a930),x98563),x98562))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),x98563),x98564)),x98561)),f866(f866(f86(a930),f866(f866(f87(a930),x98562),x98564)),x98565)))+P107(f866(f866(f243(a930),x98561),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x98562),x98563)),x98564)),x98565)))
% 157.76/157.53 [9857]~P107(f866(f866(f243(a930),x98573),x98572))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),x98573),x98574)),x98571)),f866(f866(f86(a930),f866(f866(f87(a930),x98572),x98574)),x98575)))+P107(f866(f866(f244(a930),x98571),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x98572),x98573)),x98574)),x98575)))
% 157.76/157.53 [9874]~P107(f866(f866(f243(a930),x98741),x98744))+P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),x98741),x98742)),x98743)),f866(f866(f86(a930),f866(f866(f87(a930),x98744),x98742)),x98745)))+~P107(f866(f866(f243(a930),x98743),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x98744),x98741)),x98742)),x98745)))
% 157.76/157.53 [9875]~P107(f866(f866(f243(a930),x98751),x98754))+P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),x98751),x98752)),x98753)),f866(f866(f86(a930),f866(f866(f87(a930),x98754),x98752)),x98755)))+~P107(f866(f866(f244(a930),x98753),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x98754),x98751)),x98752)),x98755)))
% 157.76/157.53 [9993]~P107(f866(f866(f243(a930),x99932),x99931))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),x99931),x99933)),x99934)),f866(f866(f86(a930),f866(f866(f87(a930),x99932),x99933)),x99935)))+P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x99931),x99932)),x99933)),x99934)),x99935))
% 157.76/157.53 [9994]~P107(f866(f866(f243(a930),x99942),x99941))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),x99941),x99943)),x99944)),f866(f866(f86(a930),f866(f866(f87(a930),x99942),x99943)),x99945)))+P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x99941),x99942)),x99943)),x99944)),x99945))
% 157.76/157.53 [10037]~P107(f866(f866(f243(a930),x100374),x100371))+P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),x100371),x100372)),x100373)),f866(f866(f86(a930),f866(f866(f87(a930),x100374),x100372)),x100375)))+~P107(f866(f866(f243(a930),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x100371),x100374)),x100372)),x100373)),x100375))
% 157.76/157.53 [10038]~P107(f866(f866(f243(a930),x100384),x100381))+P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),x100381),x100382)),x100383)),f866(f866(f86(a930),f866(f866(f87(a930),x100384),x100382)),x100385)))+~P107(f866(f866(f244(a930),f866(f866(f86(a930),f866(f866(f87(a930),f866(f866(f23(a930),x100381),x100384)),x100382)),x100383)),x100385))
% 157.76/157.53 [10255]~P11(x102551,x102552,x102555,x102553)+~P107(f866(f866(f336(f936(x102551,x102551)),x102554),x102555))+P107(f866(f866(f265(x102551,x102551,a925),f866(f866(f7(x102551,f937(x102551,x102552),f937(x102551,a925)),f866(f866(f8(f937(x102552,a925),f937(f937(x102551,x102552),f937(x102551,a925)),x102551),f8(x102552,a925,x102551)),f866(f866(f8(x102552,f937(x102552,a925),x102551),a332),x102553))),x102553)),x102554))
% 157.76/157.53 [8657]~P19(x86576,x86571,x86572,x86574)+E(f866(f78(x86571,x86571,x86571,f866(x86572,x86573)),f866(x86574,x86575)),f866(f78(x86571,x86571,x86571,f866(x86574,x86575)),f866(x86572,x86573)))+~P107(f866(f66(x86576),x86575))
% 157.76/157.53 [9095]~P25(x90951,x90953,x90955,x90956)+~P25(x90953,x90952,x90954,f866(f317(x90951,x90953,x90955),x90956))+P25(x90951,x90952,f866(f78(x90953,x90952,x90951,x90954),x90955),x90956)
% 157.76/157.53 [9662]~P107(f866(f866(x96623,x96622),x96626))+~P107(f866(f866(x96624,x96625),x96622))+P107(f866(f866(f336(x96621),x96622),f307(x96621,x96623,x96624,x96625,x96626)))
% 157.76/157.53 [9663]~P107(f866(f866(x96634,x96632),x96636))+~P107(f866(f866(x96633,x96635),x96632))+P107(f866(f866(f336(x96631),x96632),f304(x96631,x96633,x96634,x96635,x96636)))
% 157.76/157.53 [9774]E(x97741,x97742)+E(x97743,x97744)+~P107(f866(f866(f336(f936(f931(x97745),f931(x97745))),f866(f866(f260(f931(x97745),f931(x97745)),f866(f866(f158(x97745),x97743),x97741)),f866(f866(f158(x97745),x97744),x97742))),f164(x97745,x97746)))
% 157.76/157.53 [9783]~E(x97832,x97834)+P107(f866(f866(f336(f936(f931(x97831),f931(x97831))),f866(f866(f260(f931(x97831),f931(x97831)),f866(f866(f158(x97831),x97832),x97833)),f866(f866(f158(x97831),x97834),x97835))),f152(x97831,x97836)))+~P107(f866(f866(f336(f936(f931(x97831),f931(x97831))),f866(f866(f260(f931(x97831),f931(x97831)),x97833),x97835)),f152(x97831,x97836)))
% 157.76/157.53 [9784]~E(x97842,x97844)+P107(f866(f866(f336(f936(f931(x97841),f931(x97841))),f866(f866(f260(f931(x97841),f931(x97841)),f866(f866(f158(x97841),x97842),x97843)),f866(f866(f158(x97841),x97844),x97845))),f154(x97841,x97846)))+~P107(f866(f866(f336(f936(f931(x97841),f931(x97841))),f866(f866(f260(f931(x97841),f931(x97841)),x97843),x97845)),f154(x97841,x97846)))
% 157.76/157.53 [9785]~E(x97852,x97854)+P107(f866(f866(f336(f936(f931(x97851),f931(x97851))),f866(f866(f260(f931(x97851),f931(x97851)),f866(f866(f158(x97851),x97852),x97853)),f866(f866(f158(x97851),x97854),x97855))),f164(x97851,x97856)))+~P107(f866(f866(f336(f936(f931(x97851),f931(x97851))),f866(f866(f260(f931(x97851),f931(x97851)),x97853),x97855)),f164(x97851,x97856)))
% 157.76/157.53 [9786]~E(x97862,x97864)+P107(f866(f866(f336(f936(f931(x97861),f931(x97861))),f866(f866(f260(f931(x97861),f931(x97861)),f866(f866(f141(x97861),x97862),x97863)),f866(f866(f141(x97861),x97864),x97865))),f164(x97861,x97866)))+~P107(f866(f866(f336(f936(f931(x97861),f931(x97861))),f866(f866(f260(f931(x97861),f931(x97861)),x97863),x97865)),f164(x97861,x97866)))
% 157.76/157.53 [9787]~E(x97873,x97875)+P107(f866(f866(f336(f936(f931(x97871),f931(x97871))),f866(f866(f260(f931(x97871),f931(x97871)),f866(f866(f141(x97871),x97872),x97873)),f866(f866(f141(x97871),x97874),x97875))),f164(x97871,x97876)))+~P107(f866(f866(f336(f936(f931(x97871),f931(x97871))),f866(f866(f260(f931(x97871),f931(x97871)),x97872),x97874)),f164(x97871,x97876)))
% 157.76/157.53 [9844]E(x98441,x98442)+P107(f866(f866(f336(f936(f931(x98443),f931(x98443))),f866(f866(f260(f931(x98443),f931(x98443)),x98441),x98442)),f164(x98443,x98444)))+~P107(f866(f866(f336(f936(f931(x98443),f931(x98443))),f866(f866(f260(f931(x98443),f931(x98443)),f866(f866(f158(x98443),x98445),x98441)),f866(f866(f158(x98443),x98446),x98442))),f164(x98443,x98444)))
% 157.76/157.53 [9997]~E(x99973,x99975)+P107(f866(f866(f336(f936(f931(x99971),f931(x99971))),f866(f866(f260(f931(x99971),f931(x99971)),f866(f866(f141(x99971),x99972),f866(f866(f158(x99971),x99973),f120(x99971)))),f866(f866(f141(x99971),x99974),f866(f866(f158(x99971),x99975),f120(x99971))))),f164(x99971,x99976)))+~P107(f866(f866(f336(f936(f931(x99971),f931(x99971))),f866(f866(f260(f931(x99971),f931(x99971)),x99972),x99974)),f164(x99971,x99976)))
% 157.76/157.53 [10041]E(x100411,x100412)+E(x100413,x100414)+~P107(f866(f866(f336(f936(f931(x100415),f931(x100415))),f866(f866(f260(f931(x100415),f931(x100415)),f866(f866(f141(x100415),x100413),f866(f866(f158(x100415),x100411),f120(x100415)))),f866(f866(f141(x100415),x100414),f866(f866(f158(x100415),x100412),f120(x100415))))),f164(x100415,x100416)))
% 157.76/157.53 [10067]E(x100671,x100672)+~P107(f866(f866(f336(f936(f931(x100673),f931(x100673))),f866(f866(f260(f931(x100673),f931(x100673)),f866(f866(f141(x100673),x100671),f866(f866(f158(x100673),x100675),f120(x100673)))),f866(f866(f141(x100673),x100672),f866(f866(f158(x100673),x100676),f120(x100673))))),f164(x100673,x100674)))+P107(f866(f866(f336(f936(f931(x100673),f931(x100673))),f866(f866(f260(f931(x100673),f931(x100673)),x100671),x100672)),f164(x100673,x100674)))
% 157.76/157.53 [10105]~P107(f866(f866(f336(f936(f937(x101051,a925),f937(x101051,a925))),f866(f866(f260(f937(x101051,a925),f937(x101051,a925)),x101052),x101054)),f325(x101051,x101056)))+~P107(f866(f866(f336(f936(f937(x101051,a925),f937(x101051,a925))),f866(f866(f260(f937(x101051,a925),f937(x101051,a925)),x101053),x101055)),f325(x101051,x101056)))+P107(f866(f866(f336(f936(f937(x101051,a925),f937(x101051,a925))),f866(f866(f260(f937(x101051,a925),f937(x101051,a925)),f866(f866(f117(f937(x101051,a925)),x101052),x101053)),f866(f866(f117(f937(x101051,a925)),x101054),x101055))),f325(x101051,x101056)))
% 157.76/157.53 [5915]~E(f866(f866(f141(x59151),x59156),x59153),x59155)+E(f866(f866(f141(x59151),x59152),x59153),f866(f866(f158(x59151),x59154),x59155))+~E(x59152,f866(f866(f158(x59151),x59154),x59156))
% 157.76/157.53 [5916]~E(f866(f866(f141(x59161),x59166),x59163),x59165)+E(f866(f866(f141(x59161),x59162),x59163),f866(f866(f141(x59161),x59164),x59165))+~E(x59162,f866(f866(f141(x59161),x59164),x59166))
% 157.76/157.53 [5918]E(f866(f866(f141(x59181),x59182),x59183),f866(f866(f158(x59181),x59184),x59185))+~E(f866(f866(f158(x59181),x59184),x59186),x59182)+~E(x59185,f866(f866(f141(x59181),x59186),x59183))
% 157.76/157.53 [5920]~E(f866(f866(f141(x59201),x59202),x59206),x59204)+E(f866(f866(f141(x59201),x59202),x59203),f866(f866(f141(x59201),x59204),x59205))+~E(x59203,f866(f866(f141(x59201),x59206),x59205))
% 157.76/157.53 [7062]E(f866(x70621,x70622),f866(x70623,x70622))+~E(f866(f866(f161(x70624,x70625),x70621),x70626),f866(f866(f161(x70624,x70625),x70623),x70626))+~P107(f866(f866(f336(x70624),x70622),f866(f179(x70624),x70626)))
% 157.76/157.53 [7442]~P19(x74424,x74425,x74426,x74421)+E(f866(f866(x74421,x74422),x74423),f866(f866(f69(x74424,x74425,x74426),x74423),x74422))+~P107(f866(f66(x74424),x74422))
% 157.76/157.53 [7513]~E(x75132,f866(x75134,x75136))+~P107(f866(f866(f336(x75133),x75136),x75135))+P107(f866(f866(f336(x75131),x75132),f866(f317(x75133,x75131,x75134),x75135)))
% 157.76/157.53 [7514]~E(f866(x75144,x75142),x75146)+~P107(f866(f866(f336(x75143),x75146),x75145))+P107(f866(f866(f336(x75141),x75142),f866(f318(x75141,x75143,x75144),x75145)))
% 157.76/157.53 [7957]~P32(x79571,x79572,x79574,x79576)+P32(x79571,x79572,f866(f866(f158(x79571),x79573),x79574),f866(f866(f158(x79571),x79575),x79576))+~P107(f866(f866(x79572,x79573),x79575))
% 157.76/157.53 [8961]~P58(x89614,x89615,x89611,x89612,x89616)+E(f866(x89611,f866(x89612,x89613)),x89613)+~P107(f866(f866(f336(x89615),x89613),x89616))
% 157.76/157.53 [9462]~P26(x94622,x94621,x94625,x94624,x94623)+E(f866(f97(x94621,x94622,x94623,f97(x94622,x94621,x94624,x94625)),x94626),f866(x94625,x94626))+~P107(f866(f866(f336(x94622),x94626),x94624))
% 157.76/157.53 [9473]~P25(x94731,x94732,x94733,x94736)+P25(x94731,x94732,f80(x94731,x94732,x94733,x94734,x94735),x94736)+P107(f866(f866(f336(x94732),x94735),f866(f317(x94731,x94732,x94733),x94736)))
% 157.76/157.53 [9776]E(x97761,x97762)+E(f866(f196(f931(x97763)),x97764),f866(f196(f931(x97763)),x97765))+~P107(f866(f866(f336(f936(f931(x97763),f931(x97763))),f866(f866(f260(f931(x97763),f931(x97763)),f866(f866(f158(x97763),x97761),x97764)),f866(f866(f158(x97763),x97762),x97765))),f152(x97763,x97766)))
% 157.76/157.53 [9839]~P16(x98391,x98392,x98393)+E(f866(f866(f69(x98391,x98392,x98393),x98394),x98395),x98396)+~P107(f866(f71(x98391,x98392,x98393,x98394,x98395),x98396))
% 157.76/157.53 [9847]E(f866(f196(f931(x98471)),x98472),f866(f196(f931(x98471)),x98473))+P107(f866(f866(f336(f936(f931(x98471),f931(x98471))),f866(f866(f260(f931(x98471),f931(x98471)),x98472),x98473)),f152(x98471,x98474)))+~P107(f866(f866(f336(f936(f931(x98471),f931(x98471))),f866(f866(f260(f931(x98471),f931(x98471)),f866(f866(f158(x98471),x98475),x98472)),f866(f866(f158(x98471),x98476),x98473))),f152(x98471,x98474)))
% 157.76/157.53 [9868]~P107(f866(f866(f336(f936(x98681,x98681)),f866(f866(f260(x98681,x98681),x98682),x98684)),f314(x98681,x98686)))+P107(f866(f866(f336(f936(f931(x98681),f931(x98681))),f866(f866(f260(f931(x98681),f931(x98681)),f866(f866(f158(x98681),x98682),x98683)),f866(f866(f158(x98681),x98684),x98685))),f314(f931(x98681),f164(x98681,x98686))))+~P107(f866(f866(f336(f936(f931(x98681),f931(x98681))),f866(f866(f260(f931(x98681),f931(x98681)),x98683),x98685)),f314(f931(x98681),f164(x98681,x98686))))
% 157.76/157.53 [10047]~P107(f866(x100472,x100476))+~E(f866(f143(x100471,x100472),x100473),f866(f866(f158(x100471),x100474),x100475))+~P107(f866(f866(f336(x100471),x100476),f866(f179(x100471),f754(x100475,x100474,x100473,x100472,x100471))))
% 157.76/157.53 [10048]~P107(f866(x100484,x100486))+~E(f866(f866(f158(x100481),x100482),x100483),f866(f143(x100481,x100484),x100485))+~P107(f866(f866(f336(x100481),x100486),f866(f179(x100481),f751(x100485,x100484,x100483,x100482,x100481))))
% 157.76/157.53 [10354]~P72(x103542)+E(f866(f866(f6(x103541,x103542),f866(f866(f8(f937(x103543,a925),x103542,x103541),f866(f6(x103543,x103542),x103544)),f866(f866(f8(f937(x103543,a925),f937(x103543,a925),x103541),f270(x103543)),f866(f866(f8(f937(x103543,a925),f937(x103543,a925),x103541),f866(f18(x103543,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103543),a333),f866(f866(f7(x103543,f937(x103543,a925),a925),f336(x103543)),x103545)))),f866(f7(x103543,x103541,a925),f866(f866(f8(x103541,f937(x103541,a925),x103543),a332),x103546)))))),f866(f317(x103543,x103541,x103546),x103545)),f866(f866(f6(x103543,x103542),x103544),x103545))+~P107(f866(f66(x103543),x103545))
% 157.76/157.53 [7119]~P110(x71193)+P107(f866(x71192,x71195))+E(f866(f143(x71191,x71192),f866(f866(f155(x71191,x71193,x71194),x71195),x71196)),f866(f143(x71191,x71192),x71196))
% 157.76/157.53 [7121]P107(f866(x71211,x71212))+~E(f173(x71213,x71211,x71214),f866(f866(f260(f931(x71213),f931(x71213)),x71215),x71216))+~P107(f866(f866(f336(x71213),x71212),f866(f179(x71213),x71215)))
% 157.76/157.53 [7165]~P107(f866(x71652,x71656))+~E(f173(x71651,x71652,x71653),f866(f866(f260(f931(x71651),f931(x71651)),x71654),x71655))+~P107(f866(f866(f336(x71651),x71656),f866(f179(x71651),x71655)))
% 157.76/157.53 [7823]~P14(x78231,x78232,x78233)+~P107(f866(f66(x78231),x78236))+E(f866(f866(f69(x78231,x78232,x78233),x78234),f866(f866(f316(x78231),x78235),x78236)),f866(f866(f69(x78231,x78232,x78233),f866(f866(x78233,x78235),x78234)),x78236))
% 157.76/157.53 [7874]~P110(x78742)+~P107(f866(f866(f243(x78742),f866(x78743,x78744)),f866(x78743,x78745)))+E(f866(f866(f155(x78741,x78742,x78743),x78744),f866(f866(f158(x78741),x78745),x78746)),f866(f866(f158(x78741),x78744),f866(f866(f158(x78741),x78745),x78746)))
% 157.76/157.53 [7987]E(x79871,x79872)+~E(f866(f866(f262(x79873,x79874),x79871),f866(f16(f937(x79874,a925),x79873),x79875)),f866(f866(f262(x79873,x79874),x79872),f866(f16(f937(x79874,a925),x79873),x79875)))+~P107(f866(f866(f336(x79874),x79876),x79875))
% 157.76/157.53 [8052]~P14(x80521,x80522,x80523)+~P107(f866(f66(x80521),x80526))+E(f866(f866(f69(x80521,x80522,x80523),x80524),f866(f866(f316(x80521),x80525),x80526)),f866(f866(x80523,x80525),f866(f866(f69(x80521,x80522,x80523),x80524),x80526)))
% 157.76/157.53 [8167]~P16(x81671,x81672,x81673)+~P107(f866(f66(x81671),x81676))+E(f866(f866(f69(x81671,x81672,x81673),f866(f866(x81673,x81674),x81675)),x81676),f866(f866(x81673,x81674),f866(f866(f69(x81671,x81672,x81673),x81675),x81676)))
% 157.76/157.53 [8236]~P20(x82362,x82365,x82366,x82361)+~P107(f866(f66(x82362),x82364))+E(f866(x82361,f866(f866(f316(x82362),x82363),x82364)),f866(f78(x82365,x82365,x82365,f866(x82361,x82364)),f866(x82366,x82363)))
% 157.76/157.53 [8268]~P110(x82682)+P107(f866(f866(f243(x82682),f866(x82683,x82684)),f866(x82683,x82685)))+E(f866(f866(f155(x82681,x82682,x82683),x82684),f866(f866(f158(x82681),x82685),x82686)),f866(f866(f158(x82681),x82685),f866(f866(f155(x82681,x82682,x82683),x82684),x82686)))
% 157.76/157.53 [8404]~E(f866(f196(f931(x84041)),x84045),f866(f196(f931(x84042)),x84046))+~E(f866(f196(f931(x84041)),x84043),f866(f196(f931(x84042)),x84044))+E(f866(f866(f141(f936(x84041,x84042)),f866(f866(f188(x84041,x84042),x84043),x84044)),f866(f866(f188(x84041,x84042),x84045),x84046)),f866(f866(f188(x84041,x84042),f866(f866(f141(x84041),x84043),x84045)),f866(f866(f141(x84042),x84044),x84046)))
% 157.76/157.53 [8515]~E(x85152,f866(f317(x85153,x85151,x85154),x85156))+P107(f866(f866(f243(f937(x85151,a925)),x85152),f866(f317(x85153,x85151,x85154),x85155)))+~P107(f866(f866(f243(f937(x85153,a925)),x85156),x85155))
% 157.76/157.53 [8617]~P110(x86175)+E(f866(x86171,x86172),f866(x86171,x86173))+E(f866(f866(f155(x86174,x86175,x86171),x86172),f866(f866(f155(x86174,x86175,x86171),x86173),x86176)),f866(f866(f155(x86174,x86175,x86171),x86173),f866(f866(f155(x86174,x86175,x86171),x86172),x86176)))
% 157.76/157.53 [8791]~P107(f866(f866(f336(x87912),x87914),f866(x87916,x87913)))+~P107(f866(f866(f336(x87911),x87913),x87915))+P107(f866(f866(f336(f936(x87911,x87912)),f866(f866(f260(x87911,x87912),x87913),x87914)),f866(f866(f262(x87911,x87912),x87915),x87916)))
% 157.76/157.53 [9271]~P71(x92712)+~P25(x92714,x92711,x92715,x92716)+E(f866(f866(f9(x92711,x92712),x92713),f866(f317(x92714,x92711,x92715),x92716)),f866(f866(f9(x92714,x92712),f866(f78(x92711,x92712,x92714,x92713),x92715)),x92716))
% 157.76/157.53 [9272]~P72(x92722)+~P25(x92724,x92721,x92725,x92726)+E(f866(f866(f6(x92721,x92722),x92723),f866(f317(x92724,x92721,x92725),x92726)),f866(f866(f6(x92724,x92722),f866(f78(x92721,x92722,x92724,x92723),x92725)),x92726))
% 157.76/157.53 [9319]~P34(x93192,x93195,x93191,x93193,x93196)+P107(f866(f866(x93191,f866(f866(f171(x93192),x93193),x93194)),f866(f866(f171(x93195),x93196),x93194)))+~P107(f866(f866(f244(a930),x93194),f866(f196(f931(x93195)),x93196)))
% 157.76/157.53 [9320]~P34(x93202,x93205,x93201,x93203,x93206)+P107(f866(f866(x93201,f866(f866(f171(x93202),x93203),x93204)),f866(f866(f171(x93205),x93206),x93204)))+~P107(f866(f866(f244(a930),x93204),f866(f196(f931(x93202)),x93203)))
% 157.76/157.53 [9331]~E(f866(f317(x93311,x93312,x93313),x93314),x93316)+E(f866(f317(x93311,x93312,x93313),f866(f317(x93312,x93311,f97(x93311,x93312,x93314,x93313)),x93315)),x93315)+~P107(f866(f866(f243(f937(x93312,a925)),x93315),x93316))
% 157.76/157.53 [9532]~P19(x95323,x95321,x95326,x95322)+~P107(f866(f66(x95323),x95324))+E(f866(f78(x95321,x95321,x95321,f866(x95322,f866(f866(f23(f937(x95323,a925)),x95324),f866(f866(f316(x95323),x95325),f195(f937(x95323,a925)))))),f866(x95326,x95325)),f866(x95322,f866(f866(f316(x95323),x95325),x95324)))
% 157.76/157.53 [10135]~E(f866(f317(x101352,x101354,x101356),f250(f937(x101352,a925))),f250(f937(x101354,a925)))+~E(f866(f317(x101351,x101353,x101355),f250(f937(x101351,a925))),f250(f937(x101353,a925)))+E(f866(f317(f936(x101351,x101352),f936(x101353,x101354),f266(x101351,x101353,x101352,x101354,x101355,x101356)),f250(f937(f936(x101351,x101352),a925))),f250(f937(f936(x101353,x101354),a925)))
% 157.76/157.53 [10183]~P25(x101833,x101834,x101835,f866(x101836,f637(x101836,x101835,x101834,x101833,x101832,x101831)))+P25(x101833,x101834,x101835,f866(f866(f45(x101832,f937(x101833,a925)),x101831),x101836))+E(x101831,f195(f937(x101832,a925)))
% 157.76/157.53 [10240]P25(x102406,x102405,x102404,f866(f866(f45(x102402,f937(x102406,a925)),x102401),x102403))+E(x102401,f195(f937(x102402,a925)))+P107(f866(f866(f336(x102402),f637(x102403,x102404,x102405,x102406,x102402,x102401)),x102401))
% 157.76/157.53 [10245]P107(f866(f866(f336(x102451),f568(x102452,x102453,x102454,x102455,x102456,x102451)),x102456))+P107(f866(f866(f243(f937(f936(x102451,x102454),a925)),f866(f866(f262(x102451,x102454),x102456),x102453)),f866(f866(f262(x102451,x102454),x102455),x102452)))+~P107(f866(f866(f243(f937(x102451,a925)),x102456),x102455))
% 157.76/157.53 [10284]P24(x102846,x102845,f866(f866(f316(f929(x102846)),f98(x102846,x102844,x102843,x102842)),f195(f937(f929(x102846),a925))))+~P24(x102846,x102845,f866(f866(f316(f929(x102846)),f98(x102846,x102844,x102843,x102841)),f195(f937(f929(x102846),a925))))+P107(f866(f866(x102841,f562(x102842,x102841,x102843,x102844,x102845,x102846)),f673(x102842,x102841,x102843,x102844,x102845,x102846)))
% 157.76/157.53 [10285]P24(x102856,x102855,f866(f866(f316(f929(x102856)),f98(x102856,x102851,x102853,x102852)),f195(f937(f929(x102856),a925))))+~P24(x102856,x102855,f866(f866(f316(f929(x102856)),f98(x102856,x102854,x102853,x102852)),f195(f937(f929(x102856),a925))))+P107(f866(f866(x102851,f786(x102851,x102852,x102853,x102854,x102855,x102856)),f884(x102851,x102852,x102853,x102854,x102855,x102856)))
% 157.76/157.53 [10328]~P24(x103281,x103282,f866(f866(f316(f929(x103281)),f98(x103281,x103283,x103284,x103286)),f195(f937(f929(x103281),a925))))+P24(x103281,x103282,f866(f866(f316(f929(x103281)),f98(x103281,x103283,x103284,x103285)),f195(f937(f929(x103281),a925))))+~P107(f866(f866(x103285,f562(x103285,x103286,x103284,x103283,x103282,x103281)),f673(x103285,x103286,x103284,x103283,x103282,x103281)))
% 157.76/157.53 [10329]~P24(x103291,x103292,f866(f866(f316(f929(x103291)),f98(x103291,x103296,x103294,x103295)),f195(f937(f929(x103291),a925))))+P24(x103291,x103292,f866(f866(f316(f929(x103291)),f98(x103291,x103293,x103294,x103295)),f195(f937(f929(x103291),a925))))+~P107(f866(f866(x103296,f786(x103293,x103295,x103294,x103296,x103292,x103291)),f884(x103293,x103295,x103294,x103296,x103292,x103291)))
% 157.76/157.53 [10368]~P107(f866(f866(f243(f937(x103682,a925)),f866(x103684,f568(x103686,x103684,x103682,x103685,x103683,x103681))),f866(x103686,f568(x103686,x103684,x103682,x103685,x103683,x103681))))+~P107(f866(f866(f243(f937(x103681,a925)),x103683),x103685))+P107(f866(f866(f243(f937(f936(x103681,x103682),a925)),f866(f866(f262(x103681,x103682),x103683),x103684)),f866(f866(f262(x103681,x103682),x103685),x103686)))
% 157.76/157.53 [8009]~P107(f866(x80091,x80095))+~P107(f866(x80096,x80094))+P107(f866(x80091,f866(f264(x80092,x80093),f866(f866(f260(x80092,x80093),x80094),x80095))))
% 157.76/157.53 [8010]~P107(f866(x80101,x80104))+~P107(f866(x80106,x80105))+P107(f866(x80101,f866(f259(x80102,x80103),f866(f866(f260(x80102,x80103),x80104),x80105))))
% 157.76/157.53 [8057]~P107(f866(f866(x80574,x80576),x80575))+~P107(f866(f866(f336(x80571),x80576),x80573))+P107(f866(f866(f866(f44(x80571,f937(x80572,a925)),x80573),x80574),x80575))
% 157.76/157.53 [8357]~P107(f866(f866(f336(x83571),x83572),f866(x83575,x83576)))+~P107(f866(f866(f336(x83573),x83576),x83574))+P107(f866(f866(f336(x83571),x83572),f866(f866(f44(x83573,f937(x83571,a925)),x83574),x83575)))
% 157.76/157.53 [8398]P107(f866(f866(x83981,x83982),x83983))+~P107(f866(f866(x83984,x83982),x83983))+~P107(f866(f866(f243(f937(x83985,f937(x83986,a925))),x83984),x83981))
% 157.76/157.53 [8539]P107(f866(f866(x85391,x85392),x85393))+~P107(f866(f866(f336(x85394),x85392),x85395))+~P107(f866(f866(f866(f45(x85394,f937(x85396,a925)),x85395),x85391),x85393))
% 157.76/157.53 [8672]P107(f866(f866(f336(x86721),x86722),f866(x86723,x86724)))+~P107(f866(f866(f336(x86725),x86724),x86726))+~P107(f866(f866(f336(x86721),x86722),f866(f866(f45(x86725,f937(x86721,a925)),x86726),x86723)))
% 157.76/157.53 [8940]~P11(x89404,x89405,x89406,x89401)+E(f866(x89401,x89402),f866(x89401,x89403))+~P107(f866(f866(f336(f936(x89404,x89404)),f866(f866(f260(x89404,x89404),x89402),x89403)),x89406))
% 157.76/157.53 [8975]P107(f866(f866(f243(f937(x89751,a925)),x89752),f866(x89753,x89754)))+~P107(f866(f866(f336(x89755),x89754),x89756))+~P107(f866(f866(f243(f937(x89751,a925)),x89752),f866(f866(f45(x89755,f937(x89751,a925)),x89756),x89753)))
% 157.76/157.53 [9008]~P55(x90083,x90084,f866(f294(x90084,x90083),x90085))+E(x90081,f195(f937(x90082,a925)))+E(f866(f866(f45(x90082,f937(x90083,a925)),x90081),f866(f866(f8(f937(x90084,a925),f937(x90083,a925),x90082),f293(x90084,x90083,x90085)),x90086)),f866(f293(x90084,x90083,x90085),f866(f866(f45(x90082,f937(x90084,a925)),x90081),x90086)))
% 157.76/157.53 [9086]P107(f866(f866(f336(x90861),x90862),f866(f293(x90863,x90861,x90864),x90865)))+~P107(f866(f866(f336(x90863),x90866),x90865))+~P107(f866(f866(f336(f936(x90863,x90861)),f866(f866(f260(x90863,x90861),x90866),x90862)),x90864))
% 157.76/157.53 [9397]P107(f866(f866(f243(f937(x93971,a925)),f866(f293(x93972,x93971,x93973),x93974)),f866(f293(x93972,x93971,x93975),x93976)))+~P107(f866(f866(f243(f937(x93972,a925)),x93974),x93976))+~P107(f866(f866(f243(f937(f936(x93972,x93971),a925)),x93973),x93975))
% 157.76/157.53 [9581]~P107(f866(f866(f336(x95812),x95816),x95814))+~P107(f866(f866(f243(f937(x95811,a925)),x95813),x95815))+P107(f866(f866(f243(f937(f936(x95811,x95812),a925)),f866(f866(f262(x95811,x95812),x95813),f866(f16(f937(x95812,a925),x95811),x95814))),f866(f866(f262(x95811,x95812),x95815),f866(f16(f937(x95812,a925),x95811),x95814))))
% 157.76/157.53 [9593]~P34(x95931,x95932,x95933,x95935,x95936)+P107(f866(f866(f265(x95931,x95932,a925),x95933),x95934))+~P107(f866(f866(f336(f936(x95931,x95932)),x95934),f866(f179(f936(x95931,x95932)),f866(f866(f188(x95931,x95932),x95935),x95936))))
% 157.76/157.53 [9730]~E(x97303,x97305)+P107(f866(f866(f336(f936(f931(x97301),f931(x97301))),f866(f866(f260(f931(x97301),f931(x97301)),f866(f866(f158(x97301),x97302),x97303)),f866(f866(f158(x97301),x97304),x97305))),f164(x97301,x97306)))+~P107(f866(f866(f336(f936(x97301,x97301)),f866(f866(f260(x97301,x97301),x97302),x97304)),x97306))
% 157.76/157.53 [9736]~E(f866(f196(f931(x97361)),x97363),f866(f196(f931(x97361)),x97365))+P107(f866(f866(f336(f936(f931(x97361),f931(x97361))),f866(f866(f260(f931(x97361),f931(x97361)),f866(f866(f158(x97361),x97362),x97363)),f866(f866(f158(x97361),x97364),x97365))),f152(x97361,x97366)))+~P107(f866(f866(f336(f936(x97361,x97361)),f866(f866(f260(x97361,x97361),x97362),x97364)),x97366))
% 157.76/157.53 [9768]P107(f866(f866(f336(f936(x97681,x97681)),f866(f866(f260(x97681,x97681),x97682),x97683)),f866(f866(f190(f936(x97681,x97681),a925),f866(a119,x97684)),x97685)))+~P107(f866(f866(f336(f936(x97681,x97681)),f866(f866(f260(x97681,x97681),x97686),x97683)),x97685))+~P107(f866(f866(f336(f936(x97681,x97681)),f866(f866(f260(x97681,x97681),x97682),x97686)),f866(f866(f190(f936(x97681,x97681),a925),x97684),x97685)))
% 157.76/157.53 [9769]P107(f866(f866(f336(f936(x97691,x97691)),f866(f866(f260(x97691,x97691),x97692),x97693)),f866(f866(f190(f936(x97691,x97691),a925),f866(a119,x97694)),x97695)))+~P107(f866(f866(f336(f936(x97691,x97691)),f866(f866(f260(x97691,x97691),x97692),x97696)),x97695))+~P107(f866(f866(f336(f936(x97691,x97691)),f866(f866(f260(x97691,x97691),x97696),x97693)),f866(f866(f190(f936(x97691,x97691),a925),x97694),x97695)))
% 157.76/157.53 [9772]~P107(f866(f866(f336(x97724),x97725),x97726))+P107(f866(f866(f243(f937(x97721,a925)),x97722),x97723))+~P107(f866(f866(f243(f937(f936(x97721,x97724),a925)),f866(f866(f262(x97721,x97724),x97722),f866(f16(f937(x97724,a925),x97721),x97726))),f866(f866(f262(x97721,x97724),x97723),f866(f16(f937(x97724,a925),x97721),x97726))))
% 157.76/157.53 [9817]E(x98171,x98172)+~P107(f866(f866(f336(f936(f931(x98173),f931(x98173))),f866(f866(f260(f931(x98173),f931(x98173)),f866(f866(f158(x98173),x98171),x98175)),f866(f866(f158(x98173),x98172),x98176))),f152(x98173,x98174)))+P107(f866(f866(f336(f936(x98173,x98173)),f866(f866(f260(x98173,x98173),x98171),x98172)),x98174))
% 157.76/157.53 [9818]E(x98181,x98182)+~P107(f866(f866(f336(f936(f931(x98183),f931(x98183))),f866(f866(f260(f931(x98183),f931(x98183)),f866(f866(f158(x98183),x98181),x98185)),f866(f866(f158(x98183),x98182),x98186))),f154(x98183,x98184)))+P107(f866(f866(f336(f936(x98183,x98183)),f866(f866(f260(x98183,x98183),x98181),x98182)),x98184))
% 157.76/157.53 [9819]E(x98191,x98192)+~P107(f866(f866(f336(f936(f931(x98193),f931(x98193))),f866(f866(f260(f931(x98193),f931(x98193)),f866(f866(f158(x98193),x98191),x98195)),f866(f866(f158(x98193),x98192),x98196))),f164(x98193,x98194)))+P107(f866(f866(f336(f936(x98193,x98193)),f866(f866(f260(x98193,x98193),x98191),x98192)),x98194))
% 157.76/157.53 [9855]P107(f866(f866(f336(f936(f931(x98551),f931(x98551))),f866(f866(f260(f931(x98551),f931(x98551)),f866(f866(f158(x98551),x98552),x98553)),f866(f866(f158(x98551),x98554),x98555))),f165(x98551,x98556)))+~P107(f866(f866(f336(f936(f931(x98551),f931(x98551))),f866(f866(f260(f931(x98551),f931(x98551)),x98553),x98555)),f165(x98551,x98556)))+~P107(f866(f866(f336(f936(x98551,x98551)),f866(f866(f260(x98551,x98551),x98552),x98554)),x98556))
% 157.76/157.53 [9872]P107(f866(x98721,x98722))+~P107(f866(x98721,f841(x98721,x98723,x98724,x98725,x98726)))+~P107(f866(f866(f336(x98726),x98722),f866(f866(f44(x98725,f937(x98726,a925)),x98724),x98723)))
% 157.76/157.53 [9877]~P107(f866(f866(f336(f936(f931(x98771),f931(x98771))),f866(f866(f260(f931(x98771),f931(x98771)),f866(f866(f158(x98771),x98772),x98775)),f866(f866(f158(x98771),x98773),x98776))),f152(x98771,x98774)))+P107(f866(f866(f336(f936(f931(x98771),f931(x98771))),f866(f866(f260(f931(x98771),f931(x98771)),x98775),x98776)),f152(x98771,x98774)))+P107(f866(f866(f336(f936(x98771,x98771)),f866(f866(f260(x98771,x98771),x98772),x98773)),x98774))
% 157.76/157.53 [9878]~P107(f866(f866(f336(f936(f931(x98781),f931(x98781))),f866(f866(f260(f931(x98781),f931(x98781)),f866(f866(f158(x98781),x98782),x98785)),f866(f866(f158(x98781),x98783),x98786))),f154(x98781,x98784)))+P107(f866(f866(f336(f936(f931(x98781),f931(x98781))),f866(f866(f260(f931(x98781),f931(x98781)),x98785),x98786)),f154(x98781,x98784)))+P107(f866(f866(f336(f936(x98781,x98781)),f866(f866(f260(x98781,x98781),x98782),x98783)),x98784))
% 157.76/157.53 [9879]~P107(f866(f866(f336(f936(f931(x98791),f931(x98791))),f866(f866(f260(f931(x98791),f931(x98791)),f866(f866(f158(x98791),x98792),x98795)),f866(f866(f158(x98791),x98793),x98796))),f164(x98791,x98794)))+P107(f866(f866(f336(f936(f931(x98791),f931(x98791))),f866(f866(f260(f931(x98791),f931(x98791)),x98795),x98796)),f164(x98791,x98794)))+P107(f866(f866(f336(f936(x98791,x98791)),f866(f866(f260(x98791,x98791),x98792),x98793)),x98794))
% 157.76/157.53 [9969]P107(f866(x99691,x99692))+P107(f866(f866(f336(x99693),f839(x99691,x99694,x99695,x99693,x99696)),x99695))+~P107(f866(f866(f336(x99696),x99692),f866(f866(f44(x99693,f937(x99696,a925)),x99695),x99694)))
% 157.76/157.53 [9980]~E(x99802,x99804)+P107(f866(f866(f336(f936(f931(x99801),f931(x99801))),f866(f866(f260(f931(x99801),f931(x99801)),f866(f866(f141(x99801),x99802),f866(f866(f158(x99801),x99803),f120(x99801)))),f866(f866(f141(x99801),x99804),f866(f866(f158(x99801),x99805),f120(x99801))))),f164(x99801,x99806)))+~P107(f866(f866(f336(f936(x99801,x99801)),f866(f866(f260(x99801,x99801),x99803),x99805)),x99806))
% 157.76/157.53 [10055]E(x100551,x100552)+~P107(f866(f866(f336(f936(f931(x100553),f931(x100553))),f866(f866(f260(f931(x100553),f931(x100553)),f866(f866(f141(x100553),x100555),f866(f866(f158(x100553),x100551),f120(x100553)))),f866(f866(f141(x100553),x100556),f866(f866(f158(x100553),x100552),f120(x100553))))),f164(x100553,x100554)))+P107(f866(f866(f336(f936(x100553,x100553)),f866(f866(f260(x100553,x100553),x100551),x100552)),x100554))
% 157.76/157.53 [10086]~P107(f866(f866(f336(f936(f931(x100861),f931(x100861))),f866(f866(f260(f931(x100861),f931(x100861)),f866(f866(f141(x100861),x100865),f866(f866(f158(x100861),x100862),f120(x100861)))),f866(f866(f141(x100861),x100866),f866(f866(f158(x100861),x100863),f120(x100861))))),f164(x100861,x100864)))+P107(f866(f866(f336(f936(f931(x100861),f931(x100861))),f866(f866(f260(f931(x100861),f931(x100861)),x100865),x100866)),f164(x100861,x100864)))+P107(f866(f866(f336(f936(x100861,x100861)),f866(f866(f260(x100861,x100861),x100862),x100863)),x100864))
% 157.76/157.53 [10106]P107(f866(x101061,x101062))+P107(f866(f866(f336(x101063),f841(x101061,x101064,x101065,x101066,x101063)),f866(x101064,f839(x101061,x101064,x101065,x101066,x101063))))+~P107(f866(f866(f336(x101063),x101062),f866(f866(f44(x101066,f937(x101063,a925)),x101065),x101064)))
% 157.76/157.53 [10249]P107(f866(f866(f336(x102491),f845(x102492,x102493,x102494,x102495,x102496,x102491)),x102495))+~P107(f866(f866(f243(f937(x102491,a925)),x102496),x102495))+P107(f866(f866(f243(f937(x102494,a925)),f866(f866(f45(x102491,f937(x102494,a925)),x102495),x102493)),f866(f866(f45(x102491,f937(x102494,a925)),x102495),x102492)))
% 157.76/157.53 [10369]~P107(f866(f866(f243(f937(x103691,a925)),f866(x103694,f845(x103695,x103694,x103691,x103693,x103696,x103692))),f866(x103695,f845(x103695,x103694,x103691,x103693,x103696,x103692))))+~P107(f866(f866(f243(f937(x103692,a925)),x103696),x103693))+P107(f866(f866(f243(f937(x103691,a925)),f866(f866(f45(x103692,f937(x103691,a925)),x103693),x103694)),f866(f866(f45(x103692,f937(x103691,a925)),x103693),x103695)))
% 157.76/157.53 [9108]~P16(x91083,x91084,x91081)+~P107(f866(f66(x91083),x91086))+E(f866(f866(x91081,x91082),f866(f866(f69(x91083,x91084,x91081),x91085),f866(f866(f23(f937(x91083,a925)),x91086),f866(f866(f316(x91083),x91082),f195(f937(x91083,a925)))))),f866(f866(f69(x91083,x91084,x91081),x91085),f866(f866(f316(x91083),x91082),x91086)))
% 157.76/157.53 [9406]~P107(f866(f866(f336(x94065),x94063),x94066))+P107(f866(f866(f243(f937(x94061,a925)),f866(x94062,x94063)),x94064))+~P107(f866(f866(f243(f937(x94061,a925)),f866(f866(f44(x94065,f937(x94061,a925)),x94066),x94062)),x94064))
% 157.76/157.53 [10030]~P8(x100301,x100305,x100304)+P107(f866(f866(f336(f936(x100301,x100301)),f866(f866(f260(x100301,x100301),x100302),x100303)),x100304))+~P107(f866(f866(f336(x100301),x100306),f866(f866(f108(f937(x100301,a925)),f866(f293(x100301,x100301,x100304),f866(f866(f316(x100301),x100302),f195(f937(x100301,a925))))),f866(f293(x100301,x100301,x100304),f866(f866(f316(x100301),x100303),f195(f937(x100301,a925)))))))
% 157.76/157.53 [8828]~P136(x88282)+~E(f866(f866(f86(x88282),f866(f866(f87(x88282),x88284),x88285)),x88281),f866(f866(f86(x88282),f866(f866(f87(x88282),x88283),x88285)),x88286))+E(x88281,f866(f866(f86(x88282),f866(f866(f87(x88282),f866(f866(f23(x88282),x88283),x88284)),x88285)),x88286))
% 157.76/157.53 [8829]~P136(x88291)+~E(f866(f866(f86(x88291),f866(f866(f87(x88291),x88292),x88294)),x88295),f866(f866(f86(x88291),f866(f866(f87(x88291),x88293),x88294)),x88296))+E(f866(f866(f86(x88291),f866(f866(f87(x88291),f866(f866(f23(x88291),x88292),x88293)),x88294)),x88295),x88296)
% 157.76/157.53 [9011]~P136(x90111)+E(f866(f866(f86(x90111),f866(f866(f87(x90111),x90112),x90113)),x90114),f866(f866(f86(x90111),f866(f866(f87(x90111),x90115),x90113)),x90116))+~E(x90116,f866(f866(f86(x90111),f866(f866(f87(x90111),f866(f866(f23(x90111),x90112),x90115)),x90113)),x90114))
% 157.76/157.53 [9012]~P136(x90121)+E(f866(f866(f86(x90121),f866(f866(f87(x90121),x90122),x90123)),x90124),f866(f866(f86(x90121),f866(f866(f87(x90121),x90125),x90123)),x90126))+~E(f866(f866(f86(x90121),f866(f866(f87(x90121),f866(f866(f23(x90121),x90122),x90125)),x90123)),x90124),x90126)
% 157.76/157.53 [9343]~P107(f866(f866(x93434,x93435),x93436))+~P107(f866(f866(x93433,x93435),x93436))+P107(f866(f866(f866(f866(f108(f937(x93431,f937(x93432,a925))),x93433),x93434),x93435),x93436))
% 157.76/157.53 [9602]P107(f866(f866(x96021,x96022),x96023))+P107(f866(f866(x96024,x96022),x96023))+~P107(f866(f866(f866(f866(f117(f937(x96025,f937(x96026,a925))),x96024),x96021),x96022),x96023))
% 157.76/157.53 [9892]~P138(x98921)+~P107(f866(f866(f243(x98921),f866(f866(f86(x98921),f866(f866(f87(x98921),x98924),x98925)),x98922)),f866(f866(f86(x98921),f866(f866(f87(x98921),x98923),x98925)),x98926)))+P107(f866(f866(f243(x98921),x98922),f866(f866(f86(x98921),f866(f866(f87(x98921),f866(f866(f23(x98921),x98923),x98924)),x98925)),x98926)))
% 157.76/157.53 [9893]~P138(x98931)+~P107(f866(f866(f244(x98931),f866(f866(f86(x98931),f866(f866(f87(x98931),x98934),x98935)),x98932)),f866(f866(f86(x98931),f866(f866(f87(x98931),x98933),x98935)),x98936)))+P107(f866(f866(f244(x98931),x98932),f866(f866(f86(x98931),f866(f866(f87(x98931),f866(f866(f23(x98931),x98933),x98934)),x98935)),x98936)))
% 157.76/157.53 [9917]~P138(x99171)+P107(f866(f866(f243(x99171),f866(f866(f86(x99171),f866(f866(f87(x99171),x99172),x99173)),x99174)),f866(f866(f86(x99171),f866(f866(f87(x99171),x99175),x99173)),x99176)))+~P107(f866(f866(f243(x99171),x99174),f866(f866(f86(x99171),f866(f866(f87(x99171),f866(f866(f23(x99171),x99175),x99172)),x99173)),x99176)))
% 157.76/157.53 [9918]~P138(x99181)+P107(f866(f866(f244(x99181),f866(f866(f86(x99181),f866(f866(f87(x99181),x99182),x99183)),x99184)),f866(f866(f86(x99181),f866(f866(f87(x99181),x99185),x99183)),x99186)))+~P107(f866(f866(f244(x99181),x99184),f866(f866(f86(x99181),f866(f866(f87(x99181),f866(f866(f23(x99181),x99185),x99182)),x99183)),x99186)))
% 157.76/157.53 [10022]~P138(x100221)+~P107(f866(f866(f243(x100221),f866(f866(f86(x100221),f866(f866(f87(x100221),x100222),x100224)),x100225)),f866(f866(f86(x100221),f866(f866(f87(x100221),x100223),x100224)),x100226)))+P107(f866(f866(f243(x100221),f866(f866(f86(x100221),f866(f866(f87(x100221),f866(f866(f23(x100221),x100222),x100223)),x100224)),x100225)),x100226))
% 157.76/157.53 [10023]~P138(x100231)+~P107(f866(f866(f244(x100231),f866(f866(f86(x100231),f866(f866(f87(x100231),x100232),x100234)),x100235)),f866(f866(f86(x100231),f866(f866(f87(x100231),x100233),x100234)),x100236)))+P107(f866(f866(f244(x100231),f866(f866(f86(x100231),f866(f866(f87(x100231),f866(f866(f23(x100231),x100232),x100233)),x100234)),x100235)),x100236))
% 157.76/157.53 [10069]~P138(x100691)+P107(f866(f866(f243(x100691),f866(f866(f86(x100691),f866(f866(f87(x100691),x100692),x100693)),x100694)),f866(f866(f86(x100691),f866(f866(f87(x100691),x100695),x100693)),x100696)))+~P107(f866(f866(f243(x100691),f866(f866(f86(x100691),f866(f866(f87(x100691),f866(f866(f23(x100691),x100692),x100695)),x100693)),x100694)),x100696))
% 157.76/157.53 [10070]~P138(x100701)+P107(f866(f866(f244(x100701),f866(f866(f86(x100701),f866(f866(f87(x100701),x100702),x100703)),x100704)),f866(f866(f86(x100701),f866(f866(f87(x100701),x100705),x100703)),x100706)))+~P107(f866(f866(f244(x100701),f866(f866(f86(x100701),f866(f866(f87(x100701),f866(f866(f23(x100701),x100702),x100705)),x100703)),x100704)),x100706))
% 157.76/157.53 [10234]~P72(x102342)+~P107(f866(f66(x102341),x102346))+E(f866(f866(f6(x102341,x102342),f866(f866(f18(x102341,x102342,x102342),f866(f866(f18(x102341,x102342,f937(x102342,x102342)),f866(f866(f8(a925,f937(x102342,f937(x102342,x102342)),x102341),f103(x102342)),x102343)),x102344)),x102345)),x102346),f866(f866(f86(x102342),f866(f866(f6(x102341,x102342),x102344),f866(f866(f108(f937(x102341,a925)),x102346),f866(f270(x102341),x102343)))),f866(f866(f6(x102341,x102342),x102345),f866(f866(f108(f937(x102341,a925)),x102346),f866(f85(f937(x102341,a925)),f866(f270(x102341),x102343))))))
% 157.76/157.53 [10292]P107(f866(f866(f336(x102922),x102924),x102926))+P107(f866(f866(f336(x102922),x102925),x102926))+E(f866(f318(x102921,x102922,f866(f866(f7(x102921,x102922,x102922),f866(f866(f7(x102921,x102922,f937(x102922,x102922)),f866(f866(f8(a925,f937(x102922,f937(x102922,x102922)),x102921),f103(x102922)),f866(f866(f7(x102921,f937(x102921,a925),a925),f336(x102921)),x102923))),x102924)),x102925)),x102926),f195(f937(x102921,a925)))
% 157.76/157.53 [10293]P107(f866(f866(f336(x102932),x102935),x102936))+~P107(f866(f866(f336(x102932),x102934),x102936))+E(f866(f318(x102931,x102932,f866(f866(f7(x102931,x102932,x102932),f866(f866(f7(x102931,x102932,f937(x102932,x102932)),f866(f866(f8(a925,f937(x102932,f937(x102932,x102932)),x102931),f103(x102932)),f866(f866(f7(x102931,f937(x102931,a925),a925),f336(x102931)),x102933))),x102934)),x102935)),x102936),x102933)
% 157.76/157.53 [10294]P107(f866(f866(f336(x102942),x102944),x102946))+~P107(f866(f866(f336(x102942),x102945),x102946))+E(f866(f318(x102941,x102942,f866(f866(f7(x102941,x102942,x102942),f866(f866(f7(x102941,x102942,f937(x102942,x102942)),f866(f866(f8(a925,f937(x102942,f937(x102942,x102942)),x102941),f103(x102942)),f866(f866(f7(x102941,f937(x102941,a925),a925),f336(x102941)),x102943))),x102944)),x102945)),x102946),f866(f85(f937(x102941,a925)),x102943))
% 157.76/157.53 [10295]~P107(f866(f866(f336(x102952),x102954),x102956))+~P107(f866(f866(f336(x102952),x102955),x102956))+E(f866(f318(x102951,x102952,f866(f866(f7(x102951,x102952,x102952),f866(f866(f7(x102951,x102952,f937(x102952,x102952)),f866(f866(f8(a925,f937(x102952,f937(x102952,x102952)),x102951),f103(x102952)),f866(f866(f7(x102951,f937(x102951,a925),a925),f336(x102951)),x102953))),x102954)),x102955)),x102956),f250(f937(x102951,a925)))
% 157.76/157.53 [8861]E(x88611,x88612)+~P58(x88614,x88615,x88613,x88616,x88617)+~E(f866(x88613,x88611),f866(x88613,x88612))
% 157.76/157.53 [8890]~P10(x88906,x88905,x88907,x88904,x88901)+E(f866(f866(x88901,x88902),x88903),x88904)+P107(f866(f66(x88905),x88903))
% 157.76/157.53 [9759]P42(x97591,x97592,x97593,x97594,x97595,f866(f866(x97593,x97596),x97597))+~E(f866(f866(x97593,x97596),x97597),x97594)+~E(x97595,f195(f937(x97591,a925)))
% 157.76/157.53 [9939]~P107(f866(x99396,x99393))+~P107(f866(f866(f336(f936(x99392,x99392)),f866(f866(f260(x99392,x99392),x99394),x99395)),f866(x99397,x99393)))+P107(f866(f866(f336(f936(f936(x99391,x99392),f936(x99391,x99392))),f866(f866(f260(f936(x99391,x99392),f936(x99391,x99392)),f866(f866(f260(x99391,x99392),x99393),x99394)),f866(f866(f260(x99391,x99392),x99393),x99395))),f288(x99391,x99392,x99396,x99397)))
% 157.76/157.53 [10357]~P42(x103572,x103577,x103573,x103576,x103571,f866(f866(x103573,x103575),x103574))+E(f866(f866(x103573,f497(x103574,x103575,x103571,x103576,x103573,x103577,x103572)),f508(x103574,x103575,x103571,x103576,x103573,x103577,x103572)),f866(f866(x103573,x103575),x103574))+E(x103571,f195(f937(x103572,a925)))
% 157.76/157.53 [10358]~P42(x103587,x103586,x103581,x103584,x103585,f866(f866(x103581,x103582),x103583))+E(f866(f866(x103581,f497(x103583,x103582,x103585,x103584,x103581,x103586,x103587)),f508(x103583,x103582,x103585,x103584,x103581,x103586,x103587)),f866(f866(x103581,x103582),x103583))+E(f866(f866(x103581,x103582),x103583),x103584)
% 157.76/157.53 [9439]~P34(x94391,x94392,x94393,x94395,x94397)+P34(x94391,x94392,x94393,f866(f866(f158(x94391),x94394),x94395),f866(f866(f158(x94392),x94396),x94397))+~P107(f866(f866(x94393,x94394),x94396))
% 157.76/157.53 [9455]P34(x94551,x94552,x94553,x94554,x94555)+~P34(x94551,x94552,x94553,f866(f866(f141(x94551),x94556),x94554),f866(f866(f141(x94552),x94557),x94555))+~E(f866(f196(f931(x94551)),x94556),f866(f196(f931(x94552)),x94557))
% 157.76/157.53 [9456]P34(x94561,x94562,x94563,x94564,x94565)+~P34(x94561,x94562,x94563,f866(f866(f141(x94561),x94564),x94566),f866(f866(f141(x94562),x94565),x94567))+~E(f866(f196(f931(x94561)),x94564),f866(f196(f931(x94562)),x94565))
% 157.76/157.53 [9666]~P34(x96661,x96662,x96663,x96665,x96667)+~P34(x96661,x96662,x96663,x96664,x96666)+P34(x96661,x96662,x96663,f866(f866(f141(x96661),x96664),x96665),f866(f866(f141(x96662),x96666),x96667))
% 157.76/157.53 [10015]~P107(f866(f71(x100151,x100154,x100155,x100156,x100153),x100157))+P107(f866(f71(x100151,x100154,x100155,x100156,f866(f866(f316(x100151),x100152),x100153)),f866(f866(x100155,x100152),x100157)))+P107(f866(f866(f336(x100151),x100152),x100153))
% 157.76/157.53 [10385]~P42(x103852,x103857,x103856,x103855,x103851,f866(f866(x103856,x103854),x103853))+E(x103851,f195(f937(x103852,a925)))+P107(f866(f866(f336(x103852),f497(x103853,x103854,x103851,x103855,x103856,x103857,x103852)),x103851))
% 157.76/157.53 [10386]~P42(x103865,x103867,x103861,x103864,x103866,f866(f866(x103861,x103862),x103863))+E(f866(f866(x103861,x103862),x103863),x103864)+P107(f866(f866(f336(x103865),f497(x103863,x103862,x103866,x103864,x103861,x103867,x103865)),x103866))
% 157.76/157.53 [10477]E(f866(f866(f260(x104771,x104772),x104773),x104774),f866(f866(f260(x104771,x104772),x104775),x104776))+P107(f866(f866(f336(f936(f936(x104771,x104772),f936(x104771,x104772))),f866(f866(f260(f936(x104771,x104772),f936(x104771,x104772)),f866(f866(f260(x104771,x104772),f847(x104777,x104774,x104773,x104776,x104775,x104772,x104771)),f848(x104777,x104774,x104773,x104776,x104775,x104772,x104771))),f866(f866(f260(x104771,x104772),x104773),x104774))),f314(f936(x104771,x104772),x104777)))+~P107(f866(f866(f336(f936(f936(x104771,x104772),f936(x104771,x104772))),f866(f866(f260(f936(x104771,x104772),f936(x104771,x104772)),f866(f866(f260(x104771,x104772),x104775),x104776)),f866(f866(f260(x104771,x104772),x104773),x104774))),f314(f936(x104771,x104772),x104777)))
% 157.76/157.53 [9133]~P21(x91334,x91335,x91336,x91337,x91331)+~P107(f866(f66(x91335),x91333))+E(f866(f866(x91331,x91332),x91333),f866(f866(f866(f70(x91334,x91335,x91336),x91332),x91337),x91333))
% 157.76/157.53 [9134]~P10(x91344,x91345,x91346,x91347,x91341)+~P107(f866(f66(x91345),x91343))+E(f866(f866(x91341,x91342),x91343),f866(f866(f866(f70(x91344,x91345,x91346),x91342),x91347),x91343))
% 157.76/157.53 [9903]~P24(x99031,x99032,f866(f866(f316(f929(x99031)),f98(x99031,x99033,x99034,x99037)),f195(f937(f929(x99031),a925))))+P24(x99031,x99032,f866(f866(f316(f929(x99031)),f98(x99031,x99033,f31(x99034,x99035),x99036)),f195(f937(f929(x99031),a925))))+~P24(x99031,x99032,f866(f866(f316(f929(x99031)),f98(x99031,x99037,x99035,x99036)),f195(f937(f929(x99031),a925))))
% 157.76/157.53 [9912]~P23(x99123,x99124,x99125,x99127,x99126,x99121)+~P107(f866(f66(x99124),x99122))+E(f866(x99121,x99122),f866(f866(f866(f70(x99123,x99124,x99125),x99126),x99127),x99122))
% 157.76/157.53 [10064]P42(x100641,x100642,x100643,x100644,x100645,f866(f866(x100643,x100646),x100647))+~P42(x100641,x100642,x100643,x100644,f866(f866(f23(f937(x100641,a925)),x100645),f866(f866(f316(x100641),x100646),f195(f937(x100641,a925)))),x100647)+~P107(f866(f866(f336(x100641),x100646),x100645))
% 157.76/157.53 [10180]~P24(x101801,x101802,f866(f866(f316(f929(x101801)),f98(x101801,f99(x101801,x101803,x101804),x101805,x101807)),f195(f937(f929(x101801),a925))))+P24(x101801,x101802,f866(f866(f316(f929(x101801)),f98(x101801,x101803,f28(x101804,x101805,x101806),x101807)),f195(f937(f929(x101801),a925))))+~P24(x101801,x101802,f866(f866(f316(f929(x101801)),f98(x101801,f99(x101801,x101803,f866(f78(a925,a925,a926,a329),x101804)),x101806,x101807)),f195(f937(f929(x101801),a925))))
% 157.76/157.53 [10410]P107(f866(f866(x104107,f800(x104104,x104105,x104101,x104106,x104103,x104102,x104107)),f801(x104104,x104105,x104101,x104106,x104103,x104102,x104107)))+~P107(f866(f866(x104107,f866(f264(x104102,x104103),x104106)),f866(f259(x104102,x104103),x104106)))+P107(f866(x104101,f866(f866(f265(x104102,x104103,x104104),x104105),x104106)))
% 157.76/157.53 [10411]P24(x104117,x104116,f866(f866(f316(f929(x104117)),f98(x104117,x104111,x104114,x104112)),f195(f937(f929(x104117),a925))))+~P24(x104117,x104116,f866(f866(f316(f929(x104117)),f98(x104117,x104115,x104114,x104113)),f195(f937(f929(x104117),a925))))+P107(f866(f866(x104111,f895(x104112,x104111,x104113,x104114,x104115,x104116,x104117)),f903(x104112,x104111,x104113,x104114,x104115,x104116,x104117)))
% 157.76/157.53 [10422]~P42(x104222,x104223,x104224,x104225,x104221,f866(f866(x104224,x104227),x104226))+P42(x104222,x104223,x104224,x104225,f866(f866(f23(f937(x104222,a925)),x104221),f866(f866(f316(x104222),f497(x104226,x104227,x104221,x104225,x104224,x104223,x104222)),f195(f937(x104222,a925)))),f508(x104226,x104227,x104221,x104225,x104224,x104223,x104222))+E(x104221,f195(f937(x104222,a925)))
% 157.76/157.53 [10423]~P42(x104235,x104236,x104231,x104234,x104237,f866(f866(x104231,x104232),x104233))+P42(x104235,x104236,x104231,x104234,f866(f866(f23(f937(x104235,a925)),x104237),f866(f866(f316(x104235),f497(x104233,x104232,x104237,x104234,x104231,x104236,x104235)),f195(f937(x104235,a925)))),f508(x104233,x104232,x104237,x104234,x104231,x104236,x104235))+E(f866(f866(x104231,x104232),x104233),x104234)
% 157.76/157.53 [10424]~P24(x104241,x104242,f866(f866(f316(f929(x104241)),f98(x104241,x104247,x104244,x104246)),f195(f937(f929(x104241),a925))))+P24(x104241,x104242,f866(f866(f316(f929(x104241)),f98(x104241,x104243,x104244,x104245)),f195(f937(f929(x104241),a925))))+~P107(f866(f866(x104245,f895(x104245,x104243,x104246,x104244,x104247,x104242,x104241)),f914(x104245,x104243,x104246,x104244,x104247,x104242,x104241)))
% 157.76/157.53 [10444]~P107(f866(x104441,f866(f866(x104445,f801(x104444,x104445,x104441,x104446,x104443,x104442,x104447)),f800(x104444,x104445,x104441,x104446,x104443,x104442,x104447))))+~P107(f866(f866(x104447,f866(f264(x104442,x104443),x104446)),f866(f259(x104442,x104443),x104446)))+P107(f866(x104441,f866(f866(f265(x104442,x104443,x104444),x104445),x104446)))
% 157.76/157.53 [9744]P107(f866(f866(f243(f937(f936(x97441,x97442),a925)),f866(f866(f296(x97441,x97443,x97442),x97444),x97445)),f866(f866(f296(x97441,x97443,x97442),x97446),x97447)))+~P107(f866(f866(f243(f937(f936(x97443,x97442),a925)),x97445),x97447))+~P107(f866(f866(f243(f937(f936(x97441,x97443),a925)),x97444),x97446))
% 157.76/157.53 [10471]E(f866(f866(f260(x104711,x104712),x104713),x104714),f866(f866(f260(x104711,x104712),x104715),x104716))+~P107(f866(f866(f336(f936(f936(x104711,x104712),f936(x104711,x104712))),f866(f866(f260(f936(x104711,x104712),f936(x104711,x104712)),f866(f866(f260(x104711,x104712),x104713),x104714)),f866(f866(f260(x104711,x104712),x104715),x104716))),f314(f936(x104711,x104712),x104717)))+P107(f866(f866(f336(f936(f936(x104711,x104712),f936(x104711,x104712))),f866(f866(f260(f936(x104711,x104712),f936(x104711,x104712)),f866(f866(f260(x104711,x104712),x104713),x104714)),f866(f866(f260(x104711,x104712),f847(x104717,x104716,x104715,x104714,x104713,x104712,x104711)),f848(x104717,x104716,x104715,x104714,x104713,x104712,x104711)))),x104717))
% 157.76/157.53 [10075]~P107(f866(f866(f336(x100751),x100756),x100755))+P107(f866(f71(x100751,x100752,x100753,x100754,x100755),f866(f866(x100753,x100756),x100757)))+~P107(f866(f71(x100751,x100752,x100753,x100754,f866(f866(f23(f937(x100751,a925)),x100755),f866(f866(f316(x100751),x100756),f195(f937(x100751,a925))))),x100757))
% 157.76/157.53 [10484]~P147(x104841)+~P25(f936(x104842,x104843),x104841,f866(f265(x104842,x104843,x104841),f866(f866(f7(x104842,f937(x104843,x104841),f937(x104843,x104841)),f866(f866(f8(f937(x104841,x104841),f937(f937(x104843,x104841),f937(x104843,x104841)),x104842),f8(x104841,x104841,x104843)),f866(f866(f8(x104841,f937(x104841,x104841),x104842),f87(x104841)),x104844))),x104845)),f866(f866(f262(x104842,x104843),x104846),f866(f16(f937(x104843,a925),x104842),x104847)))+E(f866(f866(f6(x104841,x104841),f32(x104841)),f866(f270(x104841),f866(f866(f8(f937(x104842,a925),a925,x104841),f93(x104842)),f866(f866(f8(f937(x104842,f937(x104843,a925)),f937(x104842,a925),x104841),f866(f8(f937(x104843,a925),a925,x104842),f93(x104843))),f866(f866(f7(x104841,f937(x104842,f937(x104843,a925)),f937(x104842,f937(x104843,a925))),f866(f866(f8(f937(x104842,f937(f937(x104843,a925),f937(x104843,a925))),f937(f937(x104842,f937(x104843,a925)),f937(x104842,f937(x104843,a925))),x104841),f18(x104842,f937(x104843,a925),f937(x104843,a925))),f866(f866(f8(f937(x104842,f937(x104843,f937(a925,a925))),f937(x104842,f937(f937(x104843,a925),f937(x104843,a925))),x104841),f866(f8(f937(x104843,f937(a925,a925)),f937(f937(x104843,a925),f937(x104843,a925)),x104842),f18(x104843,a925,a925))),f866(f866(f8(f937(x104842,f937(x104843,a925)),f937(x104842,f937(x104843,f937(a925,a925))),x104841),f866(f8(f937(x104843,a925),f937(x104843,f937(a925,a925)),x104842),f866(f8(a925,f937(a925,a925),x104843),a333))),f866(f866(f7(x104841,f937(x104842,f937(x104843,x104841)),f937(x104842,f937(x104843,a925))),f866(f866(f8(f937(f937(x104843,x104841),f937(x104843,a925)),f937(f937(x104842,f937(x104843,x104841)),f937(x104842,f937(x104843,a925))),x104841),f8(f937(x104843,x104841),f937(x104843,a925),x104842)),f866(f866(f8(f937(x104841,a925),f937(f937(x104843,x104841),f937(x104843,a925)),x104841),f8(x104841,a925,x104843)),a332))),f866(f866(f7(x104842,f937(x104843,x104841),f937(x104843,x104841)),f866(f866(f8(f937(x104841,x104841),f937(f937(x104843,x104841),f937(x104843,x104841)),x104842),f8(x104841,x104841,x104843)),f866(f866(f8(x104841,f937(x104841,x104841),x104842),f87(x104841)),x104844))),x104845)))))),f866(f866(f7(x104842,f937(x104843,a925),f937(x104843,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x104843,a925),f937(x104843,a925)),x104842),f8(a925,a925,x104843)),f866(f866(f8(a925,f937(a925,a925),x104842),a333),f866(f866(f7(x104842,f937(x104842,a925),a925),f336(x104842)),x104846)))),f866(f866(f7(x104843,f937(x104843,a925),a925),f336(x104843)),x104847))))))),f866(f866(f87(x104841),f866(f866(f6(x104842,x104841),x104844),x104846)),f866(f866(f6(x104843,x104841),x104845),x104847)))
% 157.76/157.53 [9748]~P26(x97481,x97483,x97485,x97486,x97488)+~P26(x97483,x97482,x97484,x97488,x97487)+P26(x97481,x97482,f866(f78(x97483,x97482,x97481,x97484),x97485),x97486,x97487)
% 157.76/157.53 [9777]P26(x97771,x97772,x97773,x97774,x97775)+~P26(x97776,x97771,x97777,x97778,x97774)+~P26(x97776,x97772,f866(f78(x97771,x97772,x97776,x97773),x97777),x97778,x97775)
% 157.76/157.53 [9910]~P107(f866(f866(x99104,x99106),x99108))+~P107(f866(f866(x99105,x99108),x99107))+P107(f866(f866(f261(x99101,x99102,x99103,x99104,x99105),x99106),x99107))
% 157.76/157.53 [9509]~P19(x95098,x95091,x95093,x95095)+~P107(f866(f66(x95098),x95096))+E(f866(f78(x95091,x95091,x95092,f866(x95093,x95094)),f866(f78(x95091,x95091,x95092,f866(x95095,x95096)),x95097)),f866(f78(x95091,x95091,x95092,f866(x95095,x95096)),f866(f78(x95091,x95091,x95092,f866(x95093,x95094)),x95097)))
% 157.76/157.53 [9899]~P22(x98997,x98992,x98995,x98998,x98996,x98991)+~P107(f866(f66(x98992),x98994))+E(f866(x98991,f866(f866(f316(x98992),x98993),x98994)),f866(f866(x98995,f866(x98996,x98993)),f866(x98991,x98994)))
% 157.76/157.53 [10020]~P25(x100202,x100204,x100206,x100208)+~P25(x100201,x100203,x100205,x100207)+P25(f936(x100201,x100202),f936(x100203,x100204),f266(x100201,x100203,x100202,x100204,x100205,x100206),f866(f866(f262(x100201,x100202),x100207),f866(f16(f937(x100202,a925),x100201),x100208)))
% 157.76/157.53 [9692]P107(f866(f866(f336(f936(x96921,x96922)),f866(f866(f260(x96921,x96922),x96923),x96924)),f866(f866(f296(x96921,x96925,x96922),x96926),x96927)))+~P107(f866(f866(f336(f936(x96921,x96925)),f866(f866(f260(x96921,x96925),x96923),x96928)),x96926))+~P107(f866(f866(f336(f936(x96925,x96922)),f866(f866(f260(x96925,x96922),x96928),x96924)),x96927))
% 157.76/157.53 [9880]~P107(f866(f866(f243(f937(f936(x98803,x98802),a925)),x98805),f866(f866(f262(x98803,x98802),x98808),f866(f16(f937(x98802,a925),x98803),x98807))))+~P107(f866(f866(f243(f937(f936(x98801,x98803),a925)),x98804),f866(f866(f262(x98801,x98803),x98806),f866(f16(f937(x98803,a925),x98801),x98808))))+P107(f866(f866(f243(f937(f936(x98801,x98802),a925)),f866(f866(f296(x98801,x98803,x98802),x98804),x98805)),f866(f866(f262(x98801,x98802),x98806),f866(f16(f937(x98802,a925),x98801),x98807))))
% 157.76/157.53 [9934]~E(x99343,x99345)+P107(f866(f866(f336(f936(f936(x99341,x99342),f936(x99341,x99342))),f866(f866(f260(f936(x99341,x99342),f936(x99341,x99342)),f866(f866(f260(x99341,x99342),x99343),x99344)),f866(f866(f260(x99341,x99342),x99345),x99346))),f326(x99341,x99342,x99347,x99348)))+~P107(f866(f866(f336(f936(x99342,x99342)),f866(f866(f260(x99342,x99342),x99344),x99346)),x99348))
% 157.76/157.53 [10039]E(x100391,x100392)+~P107(f866(f866(f336(f936(f936(x100393,x100395),f936(x100393,x100395))),f866(f866(f260(f936(x100393,x100395),f936(x100393,x100395)),f866(f866(f260(x100393,x100395),x100391),x100396)),f866(f866(f260(x100393,x100395),x100392),x100397))),f326(x100393,x100395,x100394,x100398)))+P107(f866(f866(f336(f936(x100393,x100393)),f866(f866(f260(x100393,x100393),x100391),x100392)),x100394))
% 157.76/157.53 [10054]~P107(f866(f866(f336(f936(f936(x100541,x100545),f936(x100541,x100545))),f866(f866(f260(f936(x100541,x100545),f936(x100541,x100545)),f866(f866(f260(x100541,x100545),x100542),x100546)),f866(f866(f260(x100541,x100545),x100543),x100547))),f326(x100541,x100545,x100544,x100548)))+P107(f866(f866(f336(f936(x100541,x100541)),f866(f866(f260(x100541,x100541),x100542),x100543)),x100544))+P107(f866(f866(f336(f936(x100545,x100545)),f866(f866(f260(x100545,x100545),x100546),x100547)),x100548))
% 157.76/157.53 [9970]~P23(x99707,x99705,x99701,x99708,x99702,x99704)+~P107(f866(f66(x99705),x99706))+E(f866(f866(x99701,f866(x99702,x99703)),f866(x99704,f866(f866(f23(f937(x99705,a925)),x99706),f866(f866(f316(x99705),x99703),f195(f937(x99705,a925)))))),f866(x99704,f866(f866(f316(x99705),x99703),x99706)))
% 157.76/157.53 [9461]~P107(f866(f866(f866(x94615,x94618),x94616),x94617))+~P107(f866(f866(f336(x94611),x94618),x94614))+P107(f866(f866(f866(f866(f44(x94611,f937(x94612,f937(x94613,a925))),x94614),x94615),x94616),x94617))
% 157.76/157.53 [9677]P107(f866(f866(f866(x96771,x96772),x96773),x96774))+~P107(f866(f866(f336(x96775),x96772),x96776))+~P107(f866(f866(f866(f866(f45(x96775,f937(x96777,f937(x96778,a925))),x96776),x96771),x96773),x96774))
% 157.76/157.53 [9873]~P21(x98733,x98732,x98734,x98738,x98731)+~P107(f866(f66(x98732),x98737))+E(f866(f866(x98731,f866(f866(f18(x98732,x98733,x98733),f866(f866(f8(x98733,f937(x98733,x98733),x98732),x98734),x98735)),x98736)),x98737),f866(f866(x98734,f866(f866(x98731,x98735),x98737)),f866(f866(x98731,x98736),x98737)))
% 157.76/157.53 [10141]~E(f866(f317(x101412,x101414,x101416),x101418),x1014110)+~E(f866(f317(x101411,x101413,x101415),x101417),x101419)+E(f866(f317(f936(x101411,x101412),f936(x101413,x101414),f266(x101411,x101413,x101412,x101414,x101415,x101416)),f866(f866(f262(x101411,x101412),x101417),f866(f16(f937(x101412,a925),x101411),x101418))),f866(f866(f262(x101413,x101414),x101419),f866(f16(f937(x101414,a925),x101413),x1014110)))
% 157.76/157.53 [5124]~P48(x51241,x51242)+~P50(x51241,x51242)+~P51(x51241,x51242)+P7(x51241,x51242)
% 157.76/157.53 [5080]~P110(x50802)+~P13(x50802,x50801)+P13(x50802,f121(x50802,x50801))+E(x50801,f120(x50802))
% 157.76/157.53 [5081]~P110(x50812)+~P13(x50812,x50811)+P13(x50812,f715(x50811,x50812))+E(x50811,f120(x50812))
% 157.76/157.53 [5321]~P5(x53212)+E(f10(x53212,x53211),f43(x53212,x53211))+E(x53211,f195(f937(x53212,a925)))+~P107(f866(f66(x53212),x53211))
% 157.76/157.53 [5322]~P5(x53222)+E(f13(x53222,x53221),f42(x53222,x53221))+E(x53221,f195(f937(x53222,a925)))+~P107(f866(f66(x53222),x53221))
% 157.76/157.53 [5481]~P110(x54812)+~P13(x54812,x54811)+E(x54811,f120(x54812))+E(f866(f866(f158(x54812),f735(x54811,x54812)),f715(x54811,x54812)),x54811)
% 157.76/157.53 [6299]~P83(x62992)+E(x62991,f195(f937(x62992,a925)))+P107(f866(f866(f243(x62992),f10(x62992,x62991)),f13(x62992,x62991)))+~P107(f866(f66(x62992),x62991))
% 157.76/157.53 [6308]~P40(x63082)+~P40(x63081)+E(x63081,x63082)+~E(f866(f317(a1,a930,a111),x63081),f866(f317(a1,a930,a111),x63082))
% 157.76/157.53 [9321]~P128(x93211)+~P107(f866(f866(f336(x93211),x93212),f116(x93211)))+P107(f866(f866(f244(x93211),f866(f866(f86(x93211),f866(f866(f86(x93211),f84(x93211)),x93212)),x93212)),f2(x93211)))+~P107(f866(f866(f244(x93211),x93212),f2(x93211)))
% 157.76/157.53 [9562]~P128(x95621)+~P107(f866(f866(f336(x95621),x95622),f116(x95621)))+~P107(f866(f866(f244(x95621),f866(f866(f86(x95621),f866(f866(f86(x95621),f84(x95621)),x95622)),x95622)),f2(x95621)))+P107(f866(f866(f244(x95621),x95622),f2(x95621)))
% 157.76/157.53 [5139]~P116(x51392)+~P147(x51392)+E(x51391,f2(a930))+E(f866(f866(f252(x51392),f2(x51392)),x51391),f2(x51392))
% 157.76/157.53 [5142]~P116(x51421)+~P147(x51421)+~E(x51422,f2(a930))+E(f866(f866(f252(x51421),f2(x51421)),x51422),f84(x51421))
% 157.76/157.53 [5307]~P143(x53072)+E(x53071,f84(x53072))+E(x53071,f866(f85(x53072),f84(x53072)))+~E(f866(f866(f87(x53072),x53071),x53071),f84(x53072))
% 157.76/157.53 [5561]~P93(x55612)+E(x55611,f2(x55612))+E(f88(x55612,x55611),f866(f85(x55612),f84(x55612)))+P107(f866(f866(f244(x55612),f2(x55612)),x55611))
% 157.76/157.53 [5802]~P93(x58022)+E(f88(x58022,x58021),f84(x58022))+E(x58021,f2(x58022))+~P107(f866(f866(f244(x58022),f2(x58022)),x58021))
% 157.76/157.53 [5811]E(x58111,x58112)+~E(f866(f110(a930),x58111),f866(f110(a930),x58112))+P107(f866(a200,f866(f110(a1),x58112)))+P107(f866(a200,f866(f110(a1),x58111)))
% 157.76/157.53 [5865]~P95(x58651)+~E(x58652,f2(x58651))+E(f866(f866(f86(x58651),x58652),x58652),f2(x58651))+~P107(f866(f866(f336(x58651),x58652),f116(x58651)))
% 157.76/157.53 [5904]E(x59041,f2(a1))+~E(f866(f866(f41(a1),x59042),x59041),f2(a1))+P107(f866(f866(f244(a1),x59041),x59042))+P107(f866(f866(f244(a1),x59042),x59041))
% 157.76/157.53 [5936]E(x59361,f2(a1))+~E(f866(f866(f41(a1),x59362),x59361),f2(a1))+P107(f866(f866(f243(a1),x59362),f2(a1)))+P107(f866(f866(f244(a1),x59362),x59361))
% 157.76/157.53 [5970]E(x59701,f2(a1))+~E(f866(f866(f41(a1),x59702),x59701),f2(a1))+P107(f866(f866(f243(a1),f2(a1)),x59702))+P107(f866(f866(f244(a1),x59701),x59702))
% 157.76/157.53 [6005]~P95(x60052)+E(x60051,f2(x60052))+~E(f866(f866(f86(x60052),x60051),x60051),f2(x60052))+~P107(f866(f866(f336(x60052),x60051),f116(x60052)))
% 157.76/157.53 [6067]E(f866(f110(a930),x60671),f866(f110(a930),x60672))+~E(f866(f110(a1),x60672),f2(a1))+P107(f866(a200,f866(f110(a1),x60672)))+~P107(f866(a200,f866(f110(a1),x60671)))
% 157.76/157.53 [6098]~E(f866(f110(a930),x60982),f866(f110(a930),x60981))+E(f866(f110(a1),x60981),f2(a1))+P107(f866(a200,f866(f110(a1),x60981)))+~P107(f866(a200,f866(f110(a1),x60982)))
% 157.76/157.53 [6108]~P110(x61082)+E(x61081,f195(f937(x61082,a925)))+~P107(f866(f66(x61082),x61081))+P107(f866(f866(f336(x61082),f14(x61082,x61081)),x61081))
% 157.76/157.53 [6109]~P110(x61092)+E(x61091,f195(f937(x61092,a925)))+~P107(f866(f66(x61092),x61091))+P107(f866(f866(f336(x61092),f15(x61092,x61091)),x61091))
% 157.76/157.53 [6276]~P128(x62761)+~P96(x62761)+P107(f866(f866(f243(x62761),f2(x62761)),f866(f110(x62761),x62762)))+~P107(f866(f866(f243(a1),a89),x62762))
% 157.76/157.53 [6277]~P128(x62771)+~P96(x62771)+P107(f866(f866(f244(x62771),f2(x62771)),f866(f110(x62771),x62772)))+~P107(f866(f866(f244(a1),a89),x62772))
% 157.76/157.53 [6298]~P128(x62981)+~P96(x62981)+E(f866(f81(x62981),f866(f110(x62981),x62982)),f866(f110(x62981),x62982))+P107(f866(f866(f244(x62981),f866(f110(x62981),x62982)),f2(x62981)))
% 157.76/157.53 [6332]E(x63321,x63322)+~E(f866(a111,x63321),f866(a111,x63322))+~P107(f866(f866(f243(a1),f2(a1)),x63322))+~P107(f866(f866(f243(a1),f2(a1)),x63321))
% 157.76/157.53 [6525]~P96(x65252)+~P128(x65252)+~P107(f866(f866(f243(x65252),f2(x65252)),f866(f110(x65252),x65251)))+P107(f866(f866(f243(a1),a89),x65251))
% 157.76/157.53 [6526]~P96(x65262)+~P128(x65262)+~P107(f866(f866(f244(x65262),f2(x65262)),f866(f110(x65262),x65261)))+P107(f866(f866(f244(a1),a89),x65261))
% 157.76/157.53 [6531]~P128(x65311)+~P96(x65311)+P107(f866(f866(f243(x65311),f866(f110(x65311),x65312)),f2(x65311)))+~P107(f866(f866(f243(a1),x65312),a89))
% 157.76/157.53 [6532]~P128(x65321)+~P96(x65321)+P107(f866(f866(f244(x65321),f866(f110(x65321),x65322)),f2(x65321)))+~P107(f866(f866(f244(a1),x65322),a89))
% 157.76/157.53 [6853]~P96(x68532)+~P128(x68532)+~P107(f866(f866(f243(x68532),f866(f110(x68532),x68531)),f2(x68532)))+P107(f866(f866(f243(a1),x68531),a89))
% 157.76/157.53 [6854]~P96(x68542)+~P128(x68542)+~P107(f866(f866(f244(x68542),f866(f110(x68542),x68541)),f2(x68542)))+P107(f866(f866(f244(a1),x68541),a89))
% 157.76/157.53 [6944]~P128(x69441)+~P96(x69441)+E(f866(f81(x69441),f866(f110(x69441),x69442)),f866(f85(x69441),f866(f110(x69441),x69442)))+~P107(f866(f866(f244(x69441),f866(f110(x69441),x69442)),f2(x69441)))
% 157.76/157.53 [6963]E(f866(f110(a930),x69631),f866(f110(a930),x69632))+~E(f866(f110(a1),x69632),f2(a1))+~P107(f866(f866(f243(a1),f866(f110(a1),x69631)),f2(a1)))+~P107(f866(a200,f866(f110(a1),x69631)))
% 157.76/157.53 [7830]~P110(x78302)+E(x78301,f195(f937(x78302,a925)))+~P107(f866(f66(x78302),x78301))+P107(f866(f866(f243(x78302),f11(x78302,f241(x78302),x78301)),f12(x78302,f242(x78302),x78301)))
% 157.76/157.53 [8143]~P40(x81432)+~P6(x81431)+P107(f866(f866(f336(a1),x81431),x81432))+~P107(f866(f866(f336(a930),f866(a111,x81431)),f866(f317(a1,a930,a111),x81432)))
% 157.76/157.53 [6104]~P142(x61042)+E(x61041,f2(a1))+E(f866(f85(x61042),f866(f109(x61042),f866(f85(a1),x61041))),f866(f109(x61042),x61041))+~P107(f866(f866(f244(a1),x61041),f2(a1)))
% 157.76/157.53 [6179]~P95(x61791)+~P96(x61791)+~P28(x61791,f866(f110(x61791),x61792))+P28(x61791,f866(f110(x61791),f866(f866(f86(a1),x61792),x61792)))
% 157.76/157.53 [6514]~P76(x65142)+E(x65141,f195(f937(x65142,a925)))+E(f15(x65142,f866(f317(x65142,x65142,f85(x65142)),x65141)),f866(f85(x65142),f14(x65142,x65141)))+~P107(f866(f66(x65142),x65141))
% 157.76/157.53 [6515]~P76(x65152)+E(x65151,f195(f937(x65152,a925)))+E(f14(x65152,f866(f317(x65152,x65152,f85(x65152)),x65151)),f866(f85(x65152),f15(x65152,x65151)))+~P107(f866(f66(x65152),x65151))
% 157.76/157.53 [6548]~P95(x65481)+~P96(x65481)+P28(x65481,f866(f110(x65481),x65482))+~P28(x65481,f866(f110(x65481),f866(f866(f86(a1),x65482),x65482)))
% 157.76/157.53 [6640]E(x66401,f2(a1))+E(f866(a56,f55(f866(f85(a1),x66401),f866(f85(a1),x66402))),f51(x66401,x66402))+P107(f866(f866(f243(a1),f2(a1)),x66402))+~P107(f866(f866(f243(a1),f2(a1)),x66401))
% 157.76/157.53 [8918]~P40(x89182)+~P40(x89181)+P107(f866(f866(f244(f937(a930,a925)),f866(f317(a1,a930,a111),x89181)),f866(f317(a1,a930,a111),x89182)))+~P107(f866(f866(f244(f937(a1,a925)),x89181),x89182))
% 157.76/157.53 [9153]~E(f738(x91532,x91531),f739(x91532,x91531))+~P107(f866(f144(x91531),f740(x91532,x91531)))+~P107(f866(f144(f931(x91531)),x91532))+P107(f866(f144(x91531),f866(f149(f931(x91531),f931(x91531),f141(x91531),f120(x91531)),x91532)))
% 157.76/157.53 [9241]~P40(x92412)+~P40(x92411)+~P107(f866(f866(f243(f937(a930,a925)),f866(f317(a1,a930,a111),x92411)),f866(f317(a1,a930,a111),x92412)))+P107(f866(f866(f243(f937(a1,a925)),x92411),x92412))
% 157.76/157.53 [9242]~P40(x92422)+~P40(x92421)+~P107(f866(f866(f244(f937(a930,a925)),f866(f317(a1,a930,a111),x92421)),f866(f317(a1,a930,a111),x92422)))+P107(f866(f866(f244(f937(a1,a925)),x92421),x92422))
% 157.76/157.53 [9248]~E(f738(x92482,x92481),f739(x92482,x92481))+~P107(f866(f144(f931(x92481)),x92482))+P107(f866(f144(x92481),f866(f149(f931(x92481),f931(x92481),f141(x92481),f120(x92481)),x92482)))+P107(f866(f866(f336(f931(x92481)),f740(x92482,x92481)),f866(f179(f931(x92481)),x92482)))
% 157.76/157.53 [9289]~P107(f866(f144(x92891),f740(x92892,x92891)))+~P107(f866(f144(f931(x92891)),x92892))+P107(f866(f144(x92891),f866(f149(f931(x92891),f931(x92891),f141(x92891),f120(x92891)),x92892)))+P107(f866(f866(f336(f931(x92891)),f739(x92892,x92891)),f866(f179(f931(x92891)),x92892)))
% 157.76/157.53 [9290]~P107(f866(f144(x92901),f740(x92902,x92901)))+~P107(f866(f144(f931(x92901)),x92902))+P107(f866(f144(x92901),f866(f149(f931(x92901),f931(x92901),f141(x92901),f120(x92901)),x92902)))+P107(f866(f866(f336(f931(x92901)),f738(x92902,x92901)),f866(f179(f931(x92901)),x92902)))
% 157.76/157.53 [9368]~P107(f866(f144(f931(x93681)),x93682))+P107(f866(f144(x93681),f866(f149(f931(x93681),f931(x93681),f141(x93681),f120(x93681)),x93682)))+P107(f866(f866(f336(f931(x93681)),f739(x93682,x93681)),f866(f179(f931(x93681)),x93682)))+P107(f866(f866(f336(f931(x93681)),f740(x93682,x93681)),f866(f179(f931(x93681)),x93682)))
% 157.76/157.53 [9369]~P107(f866(f144(f931(x93691)),x93692))+P107(f866(f144(x93691),f866(f149(f931(x93691),f931(x93691),f141(x93691),f120(x93691)),x93692)))+P107(f866(f866(f336(f931(x93691)),f738(x93692,x93691)),f866(f179(f931(x93691)),x93692)))+P107(f866(f866(f336(f931(x93691)),f740(x93692,x93691)),f866(f179(f931(x93691)),x93692)))
% 157.76/157.53 [9383]~E(f866(f866(f108(f937(x93831,a925)),f866(f179(x93831),f739(x93832,x93831))),f866(f179(x93831),f738(x93832,x93831))),f195(f937(x93831,a925)))+~P107(f866(f144(x93831),f740(x93832,x93831)))+~P107(f866(f144(f931(x93831)),x93832))+P107(f866(f144(x93831),f866(f149(f931(x93831),f931(x93831),f141(x93831),f120(x93831)),x93832)))
% 157.76/157.53 [9443]~E(f866(f866(f108(f937(x94431,a925)),f866(f179(x94431),f739(x94432,x94431))),f866(f179(x94431),f738(x94432,x94431))),f195(f937(x94431,a925)))+~P107(f866(f144(f931(x94431)),x94432))+P107(f866(f144(x94431),f866(f149(f931(x94431),f931(x94431),f141(x94431),f120(x94431)),x94432)))+P107(f866(f866(f336(f931(x94431)),f740(x94432,x94431)),f866(f179(f931(x94431)),x94432)))
% 157.76/157.53 [9717]E(x97171,f2(a1))+E(x97172,f2(a1))+E(f866(f866(f92(a1,f936(a1,a1)),f866(f866(a226,x97172),x97171)),f866(f866(f18(a1,a1,f936(a1,a1)),f866(f866(f8(a1,f937(a1,f936(a1,a1)),a1),f260(a1,a1)),f866(f41(a1),x97172))),f866(f41(a1),x97171))),f224(x97172,x97171))+P107(f866(f866(f244(a1),x97171),f2(a1)))
% 157.76/157.53 [8463]~P96(x84632)+~P128(x84632)+~P107(f866(f866(f243(x84632),f866(f110(x84632),x84631)),f84(x84632)))+P107(f866(f866(f243(a1),x84631),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))
% 157.76/157.53 [8464]~P96(x84642)+~P128(x84642)+~P107(f866(f866(f244(x84642),f866(f110(x84642),x84641)),f84(x84642)))+P107(f866(f866(f244(a1),x84641),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))
% 157.76/157.53 [8733]~P128(x87331)+~P96(x87331)+P107(f866(f866(f243(x87331),f866(f110(x87331),x87332)),f84(x87331)))+~P107(f866(f866(f243(a1),x87332),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))
% 157.76/157.53 [8734]~P128(x87341)+~P96(x87341)+P107(f866(f866(f244(x87341),f866(f110(x87341),x87342)),f84(x87341)))+~P107(f866(f866(f244(a1),x87342),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))
% 157.76/157.53 [8946]~P96(x89462)+~P128(x89462)+~P107(f866(f866(f243(x89462),f84(x89462)),f866(f110(x89462),x89461)))+P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),x89461))
% 157.76/157.53 [8947]~P96(x89472)+~P128(x89472)+~P107(f866(f866(f244(x89472),f84(x89472)),f866(f110(x89472),x89471)))+P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),x89471))
% 157.76/157.53 [9327]~P128(x93271)+~P96(x93271)+P107(f866(f866(f243(x93271),f84(x93271)),f866(f110(x93271),x93272)))+~P107(f866(f866(f243(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),x93272))
% 157.76/157.53 [9328]~P128(x93281)+~P96(x93281)+P107(f866(f866(f244(x93281),f84(x93281)),f866(f110(x93281),x93282)))+~P107(f866(f866(f244(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),x93282))
% 157.76/157.53 [9846]~P143(x98462)+E(x98461,f84(x98462))+E(x98461,f866(f85(x98462),f84(x98462)))+~E(f866(f866(f252(x98462),x98461),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f84(x98462))
% 157.76/157.53 [10116]~P67(x101161)+~P96(x101161)+~P107(f866(f866(f244(x101161),f2(x101161)),x101162))+P107(f866(f866(f244(x101161),f2(x101161)),f866(f866(f297(x101161),x101162),f866(f110(x101161),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.76/157.53 [10170]~P67(x101701)+~P96(x101701)+P107(f866(f866(f244(x101701),f2(x101701)),x101702))+~P107(f866(f866(f244(x101701),f2(x101701)),f866(f866(f297(x101701),x101702),f866(f110(x101701),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.76/157.53 [10451]~P142(x104512)+E(x104511,f2(a1))+P107(f866(f866(f244(a1),x104511),f2(a1)))+E(f866(f866(f265(a1,a1,x104512),f866(f866(f7(a1,f937(a1,f937(x104512,x104512)),f937(a1,x104512)),f866(f866(f8(f937(f937(x104512,x104512),x104512),f937(f937(a1,f937(x104512,x104512)),f937(a1,x104512)),a1),f8(f937(x104512,x104512),x104512,a1)),f866(f866(f8(x104512,f937(f937(x104512,x104512),x104512),a1),f92(x104512,x104512)),f109(x104512)))),f866(f866(f7(a1,f937(x104512,x104512),f937(x104512,x104512)),f866(f866(f8(f937(x104512,f937(x104512,x104512)),f937(f937(x104512,x104512),f937(x104512,x104512)),a1),f18(x104512,x104512,x104512)),f866(f866(f7(a1,f937(x104512,x104512),f937(x104512,f937(x104512,x104512))),f866(f866(f8(f937(x104512,f937(x104512,x104512)),f937(f937(x104512,x104512),f937(x104512,f937(x104512,x104512))),a1),f8(x104512,f937(x104512,x104512),x104512)),f866(f866(f8(a925,f937(x104512,f937(x104512,x104512)),a1),f103(x104512)),f866(f866(f7(a1,a1,a925),a332),f2(a1))))),f866(f866(f18(x104512,x104512,x104512),f86(x104512)),f5(x104512))))),f866(f866(f7(x104512,x104512,x104512),f866(f866(f8(x104512,f937(x104512,x104512),x104512),f86(x104512)),f866(f866(f18(x104512,x104512,x104512),f86(x104512)),f5(x104512)))),f84(x104512))))),f51(x104511,f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f109(x104512),x104511))
% 157.76/157.53 [5570]~P38(x55701,x55703)+~P52(x55701,x55703)+~P53(x55701,x55702,x55703)+P8(x55701,x55702,x55703)
% 157.76/157.53 [5108]~P95(x51083)+~P96(x51083)+E(x51081,x51082)+~E(f866(f110(x51083),x51081),f866(f110(x51083),x51082))
% 157.76/157.53 [5580]~P50(x55801,x55802)+~P51(x55801,x55802)+P15(x55801,x55802)+~P107(f866(f866(x55802,x55803),x55803))
% 157.76/157.53 [6082]P15(x60822,x60821)+E(f866(x60821,f817(x60821)),f866(x60821,f818(x60821)))+P107(f866(f866(x60821,f817(x60821)),f818(x60821)))+~P107(f866(f866(x60821,x60823),x60823))
% 157.76/157.53 [6286]~P107(f866(x62861,x62862))+~P107(f866(x62861,x62863))+~P107(f866(f866(f243(a930),x62863),f906(x62862,x62861)))+P107(f866(x62861,f2(a930)))
% 157.76/157.53 [6351]P15(x63511,x63512)+P107(f866(f866(x63512,f817(x63512)),f817(x63512)))+P107(f866(f866(x63512,f817(x63512)),f818(x63512)))+~P107(f866(f866(x63512,x63513),x63513))
% 157.76/157.53 [6352]P15(x63521,x63522)+P107(f866(f866(x63522,f817(x63522)),f818(x63522)))+P107(f866(f866(x63522,f818(x63522)),f818(x63522)))+~P107(f866(f866(x63522,x63523),x63523))
% 157.76/157.53 [6708]P150(x67082,x67083,x67081)+E(x67081,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f872(x67081,x67083,x67082)))+P107(f866(f866(f244(a1),x67081),f2(a1)))
% 157.76/157.53 [6709]P149(x67092,x67093,x67091)+E(x67091,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f878(x67091,x67093,x67092)))+P107(f866(f866(f244(a1),x67091),f2(a1)))
% 157.76/157.53 [6834]P149(x68341,x68342,x68343)+~P107(f866(x68341,x68342))+P107(f866(f866(f243(a1),f2(a1)),f878(x68343,x68342,x68341)))+P107(f866(f866(f244(a1),x68343),f2(a1)))
% 157.76/157.53 [6859]P150(x68591,x68592,x68593)+P107(f866(f866(f243(a1),f2(a1)),f872(x68593,x68592,x68591)))+~P107(f866(x68591,f2(a1)))+P107(f866(f866(f244(a1),x68593),f2(a1)))
% 157.76/157.53 [6887]P150(x68872,x68873,x68871)+E(x68871,f2(a1))+~P107(f866(x68872,f873(x68871,x68873,x68872)))+P107(f866(f866(f244(a1),x68871),f2(a1)))
% 157.76/157.53 [6888]P149(x68882,x68883,x68881)+E(x68881,f2(a1))+~P107(f866(x68882,f878(x68881,x68883,x68882)))+P107(f866(f866(f244(a1),x68881),f2(a1)))
% 157.76/157.53 [6987]~P110(x69871)+~P5(x69871)+~P107(f866(f866(f244(x69871),x69872),f42(x69871,x69873)))+P107(f866(f866(f244(x69871),x69872),f592(x69873,x69872,x69871)))
% 157.76/157.53 [6996]P149(x69961,x69962,x69963)+~P107(f866(x69961,x69962))+~P107(f866(x69961,f878(x69963,x69962,x69961)))+P107(f866(f866(f244(a1),x69963),f2(a1)))
% 157.76/157.53 [7026]P150(x70261,x70262,x70263)+~P107(f866(x70261,f873(x70263,x70262,x70261)))+~P107(f866(x70261,f2(a1)))+P107(f866(f866(f244(a1),x70263),f2(a1)))
% 157.76/157.53 [7272]P150(x72722,x72723,x72721)+E(x72721,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f872(x72721,x72723,x72722)))+P107(f866(f866(f244(a1),x72721),f871(x72721,x72723,x72722)))
% 157.76/157.53 [7273]P149(x72732,x72733,x72731)+E(x72731,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f878(x72731,x72733,x72732)))+P107(f866(f866(f244(a1),x72731),f877(x72731,x72733,x72732)))
% 157.76/157.53 [7392]P149(x73921,x73922,x73923)+~P107(f866(x73921,x73922))+P107(f866(f866(f243(a1),f2(a1)),f878(x73923,x73922,x73921)))+P107(f866(f866(f244(a1),x73923),f877(x73923,x73922,x73921)))
% 157.76/157.53 [7411]P150(x74111,x74112,x74113)+P107(f866(f866(f243(a1),f2(a1)),f872(x74113,x74112,x74111)))+P107(f866(f866(f244(a1),x74113),f871(x74113,x74112,x74111)))+~P107(f866(x74111,f2(a1)))
% 157.76/157.53 [7443]P150(x74432,x74433,x74431)+E(x74431,f2(a1))+~P107(f866(x74432,f873(x74431,x74433,x74432)))+P107(f866(f866(f244(a1),x74431),f871(x74431,x74433,x74432)))
% 157.76/157.53 [7444]P149(x74442,x74443,x74441)+E(x74441,f2(a1))+~P107(f866(x74442,f878(x74441,x74443,x74442)))+P107(f866(f866(f244(a1),x74441),f877(x74441,x74443,x74442)))
% 157.76/157.53 [7488]P150(x74882,x74883,x74881)+E(x74881,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f872(x74881,x74883,x74882)))+~P107(f866(x74882,f876(x74881,x74883,x74882)))
% 157.76/157.53 [7489]P149(x74892,x74893,x74891)+E(x74891,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f878(x74891,x74893,x74892)))+~P107(f866(x74892,f877(x74891,x74893,x74892)))
% 157.76/157.53 [7585]P149(x75851,x75852,x75853)+~P107(f866(x75851,x75852))+~P107(f866(x75851,f878(x75853,x75852,x75851)))+P107(f866(f866(f244(a1),x75853),f877(x75853,x75852,x75851)))
% 157.76/157.53 [7600]P150(x76001,x76002,x76003)+~P107(f866(x76001,f873(x76003,x76002,x76001)))+P107(f866(f866(f244(a1),x76003),f871(x76003,x76002,x76001)))+~P107(f866(x76001,f2(a1)))
% 157.76/157.53 [7603]P149(x76031,x76032,x76033)+~P107(f866(x76031,x76032))+P107(f866(f866(f243(a1),f2(a1)),f878(x76033,x76032,x76031)))+~P107(f866(x76031,f877(x76033,x76032,x76031)))
% 157.76/157.53 [7619]P150(x76191,x76192,x76193)+P107(f866(f866(f243(a1),f2(a1)),f872(x76193,x76192,x76191)))+~P107(f866(x76191,f876(x76193,x76192,x76191)))+~P107(f866(x76191,f2(a1)))
% 157.76/157.53 [7641]P150(x76412,x76413,x76411)+E(x76411,f2(a1))+~P107(f866(x76412,f873(x76411,x76413,x76412)))+~P107(f866(x76412,f876(x76411,x76413,x76412)))
% 157.76/157.53 [7642]P149(x76422,x76423,x76421)+E(x76421,f2(a1))+~P107(f866(x76422,f878(x76421,x76423,x76422)))+~P107(f866(x76422,f877(x76421,x76423,x76422)))
% 157.76/157.53 [7728]P149(x77281,x77282,x77283)+~P107(f866(x77281,x77282))+~P107(f866(x77281,f878(x77283,x77282,x77281)))+~P107(f866(x77281,f877(x77283,x77282,x77281)))
% 157.76/157.53 [7745]P150(x77451,x77452,x77453)+~P107(f866(x77451,f873(x77453,x77452,x77451)))+~P107(f866(x77451,f876(x77453,x77452,x77451)))+~P107(f866(x77451,f2(a1)))
% 157.76/157.53 [7789]P150(x77892,x77893,x77891)+E(x77891,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f872(x77891,x77893,x77892)))+P107(f866(f866(f243(a1),f871(x77891,x77893,x77892)),f2(a1)))
% 157.76/157.53 [7790]P149(x77902,x77903,x77901)+E(x77901,f2(a1))+P107(f866(f866(f243(a1),f2(a1)),f878(x77901,x77903,x77902)))+P107(f866(f866(f243(a1),f877(x77901,x77903,x77902)),f2(a1)))
% 157.76/157.53 [7791]~P86(x77911)+~P107(f866(f866(f243(x77911),x77913),f2(x77911)))+~P107(f866(f866(f243(x77911),x77912),f2(x77911)))+P107(f866(f866(f243(x77911),f866(f866(f86(x77911),x77912),x77913)),f2(x77911)))
% 157.76/157.53 [7792]~P142(x77921)+~P107(f866(f866(f336(x77921),x77923),f116(x77921)))+~P107(f866(f866(f336(x77921),x77922),f116(x77921)))+P107(f866(f866(f336(x77921),f866(f866(f23(x77921),x77922),x77923)),f116(x77921)))
% 157.76/157.53 [7793]~P142(x77931)+~P107(f866(f866(f336(x77931),x77933),f116(x77931)))+~P107(f866(f866(f336(x77931),x77932),f116(x77931)))+P107(f866(f866(f336(x77931),f866(f866(f87(x77931),x77932),x77933)),f116(x77931)))
% 157.76/157.53 [7794]~P148(x77941)+~P107(f866(f866(f336(x77941),x77943),f193(x77941)))+~P107(f866(f866(f336(x77941),x77942),f193(x77941)))+P107(f866(f866(f336(x77941),f866(f866(f87(x77941),x77942),x77943)),f193(x77941)))
% 157.76/157.53 [7795]~P142(x77951)+~P107(f866(f866(f336(x77951),x77953),f116(x77951)))+~P107(f866(f866(f336(x77951),x77952),f116(x77951)))+P107(f866(f866(f336(x77951),f866(f866(f86(x77951),x77952),x77953)),f116(x77951)))
% 157.76/157.53 [7796]~P148(x77961)+~P107(f866(f866(f336(x77961),x77963),f193(x77961)))+~P107(f866(f866(f336(x77961),x77962),f193(x77961)))+P107(f866(f866(f336(x77961),f866(f866(f86(x77961),x77962),x77963)),f193(x77961)))
% 157.76/157.53 [7797]~P86(x77971)+~P107(f866(f866(f243(x77971),x77973),f2(x77971)))+~P107(f866(f866(f244(x77971),x77972),f2(x77971)))+P107(f866(f866(f244(x77971),f866(f866(f86(x77971),x77972),x77973)),f2(x77971)))
% 157.76/157.53 [7798]~P86(x77981)+~P107(f866(f866(f243(x77981),x77982),f2(x77981)))+~P107(f866(f866(f244(x77981),x77983),f2(x77981)))+P107(f866(f866(f244(x77981),f866(f866(f86(x77981),x77982),x77983)),f2(x77981)))
% 157.76/157.53 [7799]~P86(x77991)+~P107(f866(f866(f244(x77991),x77993),f2(x77991)))+~P107(f866(f866(f244(x77991),x77992),f2(x77991)))+P107(f866(f866(f244(x77991),f866(f866(f86(x77991),x77992),x77993)),f2(x77991)))
% 157.76/157.53 [7826]P150(x78263,x78262,x78261)+E(x78261,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x78261),f873(x78261,x78262,x78263))),f872(x78261,x78262,x78263)),x78262)+P107(f866(f866(f244(a1),x78261),f2(a1)))
% 157.76/157.53 [7827]P149(x78273,x78272,x78271)+E(x78271,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x78271),f879(x78271,x78272,x78273))),f878(x78271,x78272,x78273)),x78272)+P107(f866(f866(f244(a1),x78271),f2(a1)))
% 157.76/157.53 [7908]P149(x79081,x79082,x79083)+~P107(f866(x79081,x79082))+P107(f866(f866(f243(a1),f2(a1)),f878(x79083,x79082,x79081)))+P107(f866(f866(f243(a1),f877(x79083,x79082,x79081)),f2(a1)))
% 157.76/157.53 [7937]P150(x79371,x79372,x79373)+P107(f866(f866(f243(a1),f2(a1)),f872(x79373,x79372,x79371)))+~P107(f866(x79371,f2(a1)))+P107(f866(f866(f243(a1),f871(x79373,x79372,x79371)),f2(a1)))
% 157.76/157.53 [7946]P149(x79463,x79462,x79461)+~P107(f866(x79463,x79462))+E(f866(f866(f86(a1),f866(f866(f87(a1),x79461),f879(x79461,x79462,x79463))),f878(x79461,x79462,x79463)),x79462)+P107(f866(f866(f244(a1),x79461),f2(a1)))
% 157.76/157.53 [7952]P150(x79522,x79523,x79521)+E(x79521,f2(a1))+~P107(f866(x79522,f873(x79521,x79523,x79522)))+P107(f866(f866(f243(a1),f871(x79521,x79523,x79522)),f2(a1)))
% 157.76/157.53 [7953]P149(x79532,x79533,x79531)+E(x79531,f2(a1))+~P107(f866(x79532,f878(x79531,x79533,x79532)))+P107(f866(f866(f243(a1),f877(x79531,x79533,x79532)),f2(a1)))
% 157.76/157.53 [7958]P150(x79583,x79582,x79581)+E(f866(f866(f86(a1),f866(f866(f87(a1),x79581),f873(x79581,x79582,x79583))),f872(x79581,x79582,x79583)),x79582)+~P107(f866(x79583,f2(a1)))+P107(f866(f866(f244(a1),x79581),f2(a1)))
% 157.76/157.53 [8016]P149(x80161,x80162,x80163)+~P107(f866(x80161,x80162))+~P107(f866(x80161,f878(x80163,x80162,x80161)))+P107(f866(f866(f243(a1),f877(x80163,x80162,x80161)),f2(a1)))
% 157.76/157.53 [8020]P150(x80201,x80202,x80203)+~P107(f866(x80201,f873(x80203,x80202,x80201)))+~P107(f866(x80201,f2(a1)))+P107(f866(f866(f243(a1),f871(x80203,x80202,x80201)),f2(a1)))
% 157.76/157.53 [8085]~P120(x80851)+~P107(f866(f866(f243(x80851),f866(f866(f87(x80851),x80853),x80852)),f2(x80851)))+P107(f866(f866(f243(x80851),x80852),f2(x80851)))+P107(f866(f866(f243(x80851),x80853),f2(x80851)))
% 157.76/157.53 [8086]~P67(x80861)+~P107(f866(f866(f243(x80861),f866(f866(f297(x80861),x80863),x80862)),f2(x80861)))+P107(f866(f866(f243(x80861),x80862),f2(x80861)))+P107(f866(f866(f243(x80861),x80863),f2(x80861)))
% 157.76/157.53 [8087]~P67(x80871)+~P107(f866(f866(f244(x80871),f866(f866(f297(x80871),x80873),x80872)),f2(x80871)))+P107(f866(f866(f244(x80871),x80872),f2(x80871)))+P107(f866(f866(f244(x80871),x80873),f2(x80871)))
% 157.76/157.53 [8199]P150(x81993,x81992,x81991)+E(x81991,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x81991),f873(x81991,x81992,x81993))),f872(x81991,x81992,x81993)),x81992)+P107(f866(f866(f244(a1),x81991),f871(x81991,x81992,x81993)))
% 157.76/157.53 [8200]P149(x82003,x82002,x82001)+E(x82001,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82001),f879(x82001,x82002,x82003))),f878(x82001,x82002,x82003)),x82002)+P107(f866(f866(f244(a1),x82001),f877(x82001,x82002,x82003)))
% 157.76/157.53 [8213]P150(x82133,x82132,x82131)+E(x82131,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82131),f876(x82131,x82132,x82133))),f871(x82131,x82132,x82133)),x82132)+P107(f866(f866(f243(a1),f2(a1)),f872(x82131,x82132,x82133)))
% 157.76/157.53 [8214]P149(x82143,x82142,x82141)+E(x82141,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82141),f880(x82141,x82142,x82143))),f877(x82141,x82142,x82143)),x82142)+P107(f866(f866(f243(a1),f2(a1)),f878(x82141,x82142,x82143)))
% 157.76/157.53 [8256]P149(x82563,x82562,x82561)+~P107(f866(x82563,x82562))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82561),f879(x82561,x82562,x82563))),f878(x82561,x82562,x82563)),x82562)+P107(f866(f866(f244(a1),x82561),f877(x82561,x82562,x82563)))
% 157.76/157.53 [8265]P150(x82653,x82652,x82651)+E(f866(f866(f86(a1),f866(f866(f87(a1),x82651),f873(x82651,x82652,x82653))),f872(x82651,x82652,x82653)),x82652)+P107(f866(f866(f244(a1),x82651),f871(x82651,x82652,x82653)))+~P107(f866(x82653,f2(a1)))
% 157.76/157.53 [8271]P149(x82713,x82712,x82711)+~P107(f866(x82713,x82712))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82711),f880(x82711,x82712,x82713))),f877(x82711,x82712,x82713)),x82712)+P107(f866(f866(f243(a1),f2(a1)),f878(x82711,x82712,x82713)))
% 157.76/157.53 [8277]P150(x82773,x82772,x82771)+E(f866(f866(f86(a1),f866(f866(f87(a1),x82771),f876(x82771,x82772,x82773))),f871(x82771,x82772,x82773)),x82772)+P107(f866(f866(f243(a1),f2(a1)),f872(x82771,x82772,x82773)))+~P107(f866(x82773,f2(a1)))
% 157.76/157.53 [8288]P150(x82883,x82882,x82881)+E(x82881,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82881),f873(x82881,x82882,x82883))),f872(x82881,x82882,x82883)),x82882)+~P107(f866(x82883,f876(x82881,x82882,x82883)))
% 157.76/157.53 [8289]P149(x82893,x82892,x82891)+E(x82891,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82891),f879(x82891,x82892,x82893))),f878(x82891,x82892,x82893)),x82892)+~P107(f866(x82893,f877(x82891,x82892,x82893)))
% 157.76/157.53 [8290]P150(x82903,x82902,x82901)+E(x82901,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82901),f876(x82901,x82902,x82903))),f871(x82901,x82902,x82903)),x82902)+~P107(f866(x82903,f873(x82901,x82902,x82903)))
% 157.76/157.53 [8291]P149(x82913,x82912,x82911)+E(x82911,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x82911),f880(x82911,x82912,x82913))),f877(x82911,x82912,x82913)),x82912)+~P107(f866(x82913,f878(x82911,x82912,x82913)))
% 157.76/157.53 [8349]P149(x83493,x83492,x83491)+~P107(f866(x83493,x83492))+E(f866(f866(f86(a1),f866(f866(f87(a1),x83491),f879(x83491,x83492,x83493))),f878(x83491,x83492,x83493)),x83492)+~P107(f866(x83493,f877(x83491,x83492,x83493)))
% 157.76/157.53 [8350]P149(x83503,x83502,x83501)+~P107(f866(x83503,x83502))+E(f866(f866(f86(a1),f866(f866(f87(a1),x83501),f880(x83501,x83502,x83503))),f877(x83501,x83502,x83503)),x83502)+~P107(f866(x83503,f878(x83501,x83502,x83503)))
% 157.76/157.53 [8360]P150(x83603,x83602,x83601)+E(f866(f866(f86(a1),f866(f866(f87(a1),x83601),f873(x83601,x83602,x83603))),f872(x83601,x83602,x83603)),x83602)+~P107(f866(x83603,f876(x83601,x83602,x83603)))+~P107(f866(x83603,f2(a1)))
% 157.76/157.53 [8361]P150(x83613,x83612,x83611)+E(f866(f866(f86(a1),f866(f866(f87(a1),x83611),f876(x83611,x83612,x83613))),f871(x83611,x83612,x83613)),x83612)+~P107(f866(x83613,f873(x83611,x83612,x83613)))+~P107(f866(x83613,f2(a1)))
% 157.76/157.53 [8456]P150(x84563,x84562,x84561)+E(x84561,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84561),f873(x84561,x84562,x84563))),f872(x84561,x84562,x84563)),x84562)+P107(f866(f866(f243(a1),f871(x84561,x84562,x84563)),f2(a1)))
% 157.76/157.53 [8457]P149(x84573,x84572,x84571)+E(x84571,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84571),f879(x84571,x84572,x84573))),f878(x84571,x84572,x84573)),x84572)+P107(f866(f866(f243(a1),f877(x84571,x84572,x84573)),f2(a1)))
% 157.76/157.53 [8496]P149(x84963,x84962,x84961)+~P107(f866(x84963,x84962))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84961),f879(x84961,x84962,x84963))),f878(x84961,x84962,x84963)),x84962)+P107(f866(f866(f243(a1),f877(x84961,x84962,x84963)),f2(a1)))
% 157.76/157.53 [8501]P150(x85013,x85012,x85011)+E(f866(f866(f86(a1),f866(f866(f87(a1),x85011),f873(x85011,x85012,x85013))),f872(x85011,x85012,x85013)),x85012)+~P107(f866(x85013,f2(a1)))+P107(f866(f866(f243(a1),f871(x85011,x85012,x85013)),f2(a1)))
% 157.76/157.53 [8635]P150(x86353,x86352,x86351)+E(x86351,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x86351),f876(x86351,x86352,x86353))),f871(x86351,x86352,x86353)),x86352)+E(f866(f866(f86(a1),f866(f866(f87(a1),x86351),f873(x86351,x86352,x86353))),f872(x86351,x86352,x86353)),x86352)
% 157.76/157.53 [8636]P149(x86363,x86362,x86361)+E(x86361,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x86361),f880(x86361,x86362,x86363))),f877(x86361,x86362,x86363)),x86362)+E(f866(f866(f86(a1),f866(f866(f87(a1),x86361),f879(x86361,x86362,x86363))),f878(x86361,x86362,x86363)),x86362)
% 157.76/157.53 [8656]P149(x86563,x86562,x86561)+~P107(f866(x86563,x86562))+E(f866(f866(f86(a1),f866(f866(f87(a1),x86561),f880(x86561,x86562,x86563))),f877(x86561,x86562,x86563)),x86562)+E(f866(f866(f86(a1),f866(f866(f87(a1),x86561),f879(x86561,x86562,x86563))),f878(x86561,x86562,x86563)),x86562)
% 157.76/157.53 [8667]P150(x86673,x86672,x86671)+E(f866(f866(f86(a1),f866(f866(f87(a1),x86671),f876(x86671,x86672,x86673))),f871(x86671,x86672,x86673)),x86672)+E(f866(f866(f86(a1),f866(f866(f87(a1),x86671),f873(x86671,x86672,x86673))),f872(x86671,x86672,x86673)),x86672)+~P107(f866(x86673,f2(a1)))
% 157.76/157.53 [9336]~P120(x93361)+~E(x93363,f2(x93361))+~E(x93362,f2(x93361))+P107(f866(f866(f243(x93361),f866(f866(f86(x93361),f866(f866(f87(x93361),x93362),x93362)),f866(f866(f87(x93361),x93363),x93363))),f2(x93361)))
% 157.76/157.53 [10388]~P128(x103881)+~E(x103883,f2(x103881))+~E(x103882,f2(x103881))+P107(f866(f866(f243(x103881),f866(f866(f86(x103881),f866(f866(f252(x103881),x103882),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103881),x103883),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))),f2(x103881)))
% 157.76/157.53 [5056]~E(x50563,x50561)+~P125(x50562)+E(x50561,f2(x50562))+E(f866(f866(f297(x50562),x50563),x50561),f84(x50562))
% 157.76/157.53 [5109]~P85(x51091)+~E(x51093,f195(x51091))+~E(x51092,f195(x51091))+E(f866(f866(f117(x51091),x51092),x51093),f195(x51091))
% 157.76/157.53 [5110]~P84(x51101)+~E(x51103,f250(x51101))+~E(x51102,f250(x51101))+E(f866(f866(f108(x51101),x51102),x51103),f250(x51101))
% 157.76/157.53 [5203]~P125(x52033)+E(x52031,x52032)+E(x52032,f2(x52033))+~E(f866(f866(f297(x52033),x52031),x52032),f84(x52033))
% 157.76/157.53 [5220]~P134(x52202)+E(x52201,f2(x52202))+E(x52203,f2(x52202))+~E(f866(f866(f87(x52202),x52203),x52201),f2(x52202))
% 157.76/157.53 [5222]~P135(x52222)+E(x52221,f2(x52222))+E(x52223,f2(x52222))+~E(f866(f866(f87(x52222),x52223),x52221),f2(x52222))
% 157.76/157.53 [5599]~P123(x55993)+E(x55991,x55992)+E(x55991,f866(f85(x55993),x55992))+~E(f866(f866(f87(x55993),x55991),x55991),f866(f866(f87(x55993),x55992),x55992))
% 157.76/157.53 [5637]~P98(x56371)+E(f866(f85(x56371),x56372),x56373)+~E(f866(f866(f117(x56371),x56372),x56373),f250(x56371))+~E(f866(f866(f108(x56371),x56372),x56373),f195(x56371))
% 157.76/157.53 [5716]~P128(x57163)+E(x57161,x57162)+P107(f866(f866(f244(x57163),x57162),x57161))+P107(f866(f866(f244(x57163),x57161),x57162))
% 157.76/157.53 [5717]~P110(x57173)+E(x57171,x57172)+P107(f866(f866(f244(x57173),x57172),x57171))+P107(f866(f866(f244(x57173),x57171),x57172))
% 157.76/157.53 [5718]~E(x57182,x57183)+~P110(x57181)+P107(f866(f866(f244(x57181),x57182),x57183))+P107(f866(f866(f243(x57181),x57182),x57183))
% 157.76/157.53 [5986]~P111(x59863)+E(x59861,x59862)+~P107(f866(f866(f243(x59863),x59862),x59861))+P107(f866(f866(f244(x59863),x59862),x59861))
% 157.76/157.53 [5988]~P110(x59883)+E(x59881,x59882)+~P107(f866(f866(f243(x59883),x59881),x59882))+P107(f866(f866(f244(x59883),x59881),x59882))
% 157.76/157.53 [5994]~P111(x59943)+E(x59941,x59942)+~P107(f866(f866(f243(x59943),x59941),x59942))+P107(f866(f866(f244(x59943),x59941),x59942))
% 157.76/157.53 [6101]P149(x61011,x61012,x61013)+~P107(f866(x61011,x61012))+P107(f866(f866(f244(a1),x61013),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x61013))
% 157.76/157.53 [6152]P150(x61521,x61522,x61523)+~P107(f866(x61521,f2(a1)))+P107(f866(f866(f244(a1),x61523),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x61523))
% 157.76/157.53 [6157]~P83(x61571)+E(f866(f866(f117(x61571),x61572),f10(x61571,x61573)),x61572)+~P107(f866(f66(x61571),x61573))+~P107(f866(f866(f336(x61571),x61572),x61573))
% 157.76/157.53 [6158]~P83(x61581)+E(f866(f866(f108(x61581),x61582),f13(x61581,x61583)),x61582)+~P107(f866(f66(x61581),x61583))+~P107(f866(f866(f336(x61581),x61582),x61583))
% 157.76/157.53 [6195]~P83(x61951)+E(f866(f866(f117(x61951),x61952),f13(x61951,x61953)),f13(x61951,x61953))+~P107(f866(f66(x61951),x61953))+~P107(f866(f866(f336(x61951),x61952),x61953))
% 157.76/157.53 [6196]~P83(x61961)+E(f866(f866(f108(x61961),x61962),f10(x61961,x61963)),f10(x61961,x61963))+~P107(f866(f66(x61961),x61963))+~P107(f866(f866(f336(x61961),x61962),x61963))
% 157.76/157.53 [6197]~P110(x61971)+E(f866(f866(f241(x61971),x61972),f15(x61971,x61973)),f15(x61971,x61973))+~P107(f866(f66(x61971),x61973))+~P107(f866(f866(f336(x61971),x61972),x61973))
% 157.76/157.53 [6198]~P110(x61981)+E(f866(f866(f242(x61981),x61982),f14(x61981,x61983)),f14(x61981,x61983))+~P107(f866(f66(x61981),x61983))+~P107(f866(f866(f336(x61981),x61982),x61983))
% 157.76/157.53 [6236]E(x62361,x62362)+~P111(x62363)+~P107(f866(f866(f243(x62363),x62362),x62361))+~P107(f866(f866(f243(x62363),x62361),x62362))
% 157.76/157.53 [6379]~P108(x63791)+P107(f866(f866(f244(x63791),x63793),x63792))+~P107(f866(f866(f243(x63791),x63793),x63792))+P107(f866(f866(f243(x63791),x63792),x63793))
% 157.76/157.53 [6405]~P110(x64051)+~P107(f866(f66(x64051),x64053))+P107(f866(f866(f243(x64051),x64052),f14(x64051,x64053)))+~P107(f866(f866(f336(x64051),x64052),x64053))
% 157.76/157.53 [6450]~P110(x64501)+E(f866(f866(f241(x64501),x64502),f12(x64501,f242(x64501),x64503)),x64502)+~P107(f866(f66(x64501),x64503))+~P107(f866(f866(f336(x64501),x64502),x64503))
% 157.76/157.53 [6451]~P110(x64511)+E(f866(f866(f242(x64511),x64512),f11(x64511,f241(x64511),x64513)),x64512)+~P107(f866(f66(x64511),x64513))+~P107(f866(f866(f336(x64511),x64512),x64513))
% 157.76/157.53 [6593]E(x65931,x65932)+~E(f866(f866(f23(a930),x65931),x65933),f866(f866(f23(a930),x65932),x65933))+~P107(f866(f866(f243(a930),x65933),x65931))+~P107(f866(f866(f243(a930),x65933),x65932))
% 157.76/157.53 [6619]~P110(x66191)+~P107(f866(f66(x66191),x66192))+~P107(f866(f866(f336(x66191),x66193),x66192))+P107(f866(f866(f243(x66191),f15(x66191,x66192)),x66193))
% 157.76/157.53 [6685]P150(x66852,x66853,x66851)+E(x66851,f2(a1))+P107(f866(f866(f244(a1),x66851),f871(x66851,x66853,x66852)))+P107(f866(f866(f244(a1),f2(a1)),x66851))
% 157.76/157.53 [6686]P149(x66862,x66863,x66861)+E(x66861,f2(a1))+P107(f866(f866(f244(a1),x66861),f877(x66861,x66863,x66862)))+P107(f866(f866(f244(a1),f2(a1)),x66861))
% 157.76/157.53 [6687]~P110(x66871)+E(f866(f866(f241(x66871),x66872),f11(x66871,f241(x66871),x66873)),f11(x66871,f241(x66871),x66873))+~P107(f866(f66(x66871),x66873))+~P107(f866(f866(f336(x66871),x66872),x66873))
% 157.76/157.53 [6688]~P110(x66881)+E(f866(f866(f242(x66881),x66882),f12(x66881,f242(x66881),x66883)),f12(x66881,f242(x66881),x66883))+~P107(f866(f66(x66881),x66883))+~P107(f866(f866(f336(x66881),x66882),x66883))
% 157.76/157.53 [6695]~P107(f866(x66951,x66952))+P107(f866(x66951,f484(x66952,x66951,x66953)))+P107(f866(x66951,f2(a930)))+~P107(f866(f866(f244(a930),x66952),x66953))
% 157.76/157.53 [6751]~P107(f866(x67511,x67512))+~P107(f866(f66(x67513),x67512))+P107(f866(x67511,f748(x67511,x67512,x67513)))+P107(f866(x67511,f195(f937(x67513,a925))))
% 157.76/157.53 [6764]~P128(x67641)+~P96(x67641)+P107(f866(f866(f243(x67641),f866(f110(x67641),x67642)),f866(f110(x67641),x67643)))+~P107(f866(f866(f243(a1),x67642),x67643))
% 157.76/157.53 [6765]~P128(x67651)+~P96(x67651)+P107(f866(f866(f244(x67651),f866(f110(x67651),x67652)),f866(f110(x67651),x67653)))+~P107(f866(f866(f244(a1),x67652),x67653))
% 157.76/157.53 [6769]~P107(f866(x67691,x67693))+~P107(f866(f66(x67692),x67693))+P107(f866(f66(x67692),f748(x67691,x67693,x67692)))+P107(f866(x67691,f195(f937(x67692,a925))))
% 157.76/157.53 [6788]P57(a930,x67881,x67882)+~P57(a930,x67881,x67883)+~P57(a930,x67881,f866(f866(f23(a930),x67883),x67882))+~P107(f866(f866(f243(a930),x67882),x67883))
% 157.76/157.53 [6789]P57(a930,x67891,x67892)+~P57(a930,x67891,x67893)+~P57(a930,x67891,f866(f866(f23(a930),x67892),x67893))+~P107(f866(f866(f243(a930),x67893),x67892))
% 157.76/157.53 [6804]P149(x68041,x68042,x68043)+~P107(f866(x68041,x68042))+P107(f866(f866(f244(a1),x68043),f877(x68043,x68042,x68041)))+P107(f866(f866(f244(a1),f2(a1)),x68043))
% 157.76/157.53 [6840]P150(x68401,x68402,x68403)+P107(f866(f866(f244(a1),x68403),f871(x68403,x68402,x68401)))+~P107(f866(x68401,f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x68403))
% 157.76/157.53 [6870]~P109(x68701)+~P97(x68701)+E(f866(f866(f241(x68701),f866(f110(x68701),x68702)),f866(f110(x68701),x68703)),f866(f110(x68701),x68703))+P107(f866(f866(f243(x68701),f866(f110(x68701),x68702)),f866(f110(x68701),x68703)))
% 157.76/157.53 [6871]~P109(x68711)+~P97(x68711)+E(f866(f866(f242(x68711),f866(f110(x68711),x68712)),f866(f110(x68711),x68713)),f866(f110(x68711),x68712))+P107(f866(f866(f243(x68711),f866(f110(x68711),x68712)),f866(f110(x68711),x68713)))
% 157.76/157.53 [6927]P150(x69272,x69273,x69271)+E(x69271,f2(a1))+~P107(f866(x69272,f876(x69271,x69273,x69272)))+P107(f866(f866(f244(a1),f2(a1)),x69271))
% 157.76/157.53 [6928]P149(x69282,x69283,x69281)+E(x69281,f2(a1))+~P107(f866(x69282,f877(x69281,x69283,x69282)))+P107(f866(f866(f244(a1),f2(a1)),x69281))
% 157.76/157.53 [6932]P107(f866(x69321,x69322))+~P107(f866(f66(x69323),x69322))+P107(f866(x69321,f767(x69321,x69322,x69323)))+~P107(f866(x69321,f195(f937(x69323,a925))))
% 157.76/157.53 [6954]P107(f866(x69541,x69542))+P107(f866(f66(x69543),f767(x69541,x69542,x69543)))+~P107(f866(f66(x69543),x69542))+~P107(f866(x69541,f195(f937(x69543,a925))))
% 157.76/157.53 [7015]P149(x70151,x70152,x70153)+~P107(f866(x70151,x70152))+~P107(f866(x70151,f877(x70153,x70152,x70151)))+P107(f866(f866(f244(a1),f2(a1)),x70153))
% 157.76/157.53 [7045]P150(x70451,x70452,x70453)+~P107(f866(x70451,f876(x70453,x70452,x70451)))+~P107(f866(x70451,f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x70453))
% 157.76/157.53 [7152]~P96(x71523)+~P128(x71523)+~P107(f866(f866(f243(x71523),f866(f110(x71523),x71521)),f866(f110(x71523),x71522)))+P107(f866(f866(f243(a1),x71521),x71522))
% 157.76/157.53 [7153]~P96(x71533)+~P128(x71533)+~P107(f866(f866(f244(x71533),f866(f110(x71533),x71531)),f866(f110(x71533),x71532)))+P107(f866(f866(f244(a1),x71531),x71532))
% 157.76/157.53 [7180]~P110(x71801)+~P13(x71801,x71803)+P13(x71801,f866(f866(f158(x71801),x71802),x71803))+~P107(f866(f866(f243(x71801),x71802),f718(x71803,x71802,x71801)))
% 157.76/157.53 [7181]~P110(x71811)+~P13(x71811,x71813)+P13(x71811,f866(f866(f158(x71811),x71812),x71813))+~P107(f866(f866(f243(x71811),x71812),f721(x71813,x71812,x71811)))
% 157.76/157.53 [7182]~P110(x71821)+~P13(x71821,x71823)+P13(x71821,f866(f866(f158(x71821),x71822),x71823))+~P107(f866(f866(f243(x71821),x71822),f760(x71822,x71823,x71821)))
% 157.76/157.53 [7265]P150(x72652,x72653,x72651)+E(x72651,f2(a1))+P107(f866(f866(f244(a1),x72651),f2(a1)))+P107(f866(f866(f244(a1),f872(x72651,x72653,x72652)),x72651))
% 157.76/157.53 [7266]P149(x72662,x72663,x72661)+E(x72661,f2(a1))+P107(f866(f866(f244(a1),x72661),f2(a1)))+P107(f866(f866(f244(a1),f878(x72661,x72663,x72662)),x72661))
% 157.76/157.53 [7302]P150(x73022,x73023,x73021)+E(x73021,f2(a1))+P107(f866(f866(f243(a1),f871(x73021,x73023,x73022)),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x73021))
% 157.76/157.53 [7303]P149(x73032,x73033,x73031)+E(x73031,f2(a1))+P107(f866(f866(f243(a1),f877(x73031,x73033,x73032)),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x73031))
% 157.76/157.53 [7328]~P110(x73281)+~P13(x73281,x73283)+E(f866(f866(f155(x73281,x73281,f5(x73281)),x73282),f177(x73281,x73282,x73283)),x73283)+~P107(f866(f866(f336(x73281),x73282),f866(f179(x73281),x73283)))
% 157.76/157.53 [7375]P149(x73751,x73752,x73753)+~P107(f866(x73751,x73752))+P107(f866(f866(f244(a1),x73753),f2(a1)))+P107(f866(f866(f244(a1),f878(x73753,x73752,x73751)),x73753))
% 157.76/157.53 [7381]~P109(x73811)+~P97(x73811)+E(f866(f866(f241(x73811),f866(f110(x73811),x73812)),f866(f110(x73811),x73813)),f866(f110(x73811),x73812))+~P107(f866(f866(f243(x73811),f866(f110(x73811),x73812)),f866(f110(x73811),x73813)))
% 157.76/157.53 [7382]~P109(x73821)+~P97(x73821)+E(f866(f866(f242(x73821),f866(f110(x73821),x73822)),f866(f110(x73821),x73823)),f866(f110(x73821),x73823))+~P107(f866(f866(f243(x73821),f866(f110(x73821),x73822)),f866(f110(x73821),x73823)))
% 157.76/157.53 [7396]P150(x73961,x73962,x73963)+~P107(f866(x73961,f2(a1)))+P107(f866(f866(f244(a1),x73963),f2(a1)))+P107(f866(f866(f244(a1),f872(x73963,x73962,x73961)),x73963))
% 157.76/157.53 [7404]P149(x74041,x74042,x74043)+~P107(f866(x74041,x74042))+P107(f866(f866(f243(a1),f877(x74043,x74042,x74041)),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x74043))
% 157.76/157.53 [7428]P150(x74281,x74282,x74283)+~P107(f866(x74281,f2(a1)))+P107(f866(f866(f243(a1),f871(x74283,x74282,x74281)),f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x74283))
% 157.76/157.53 [7455]~P107(f866(x74551,x74552))+P107(f866(x74551,f2(a930)))+~P107(f866(f866(f244(a930),x74552),x74553))+P107(f866(f866(f244(a930),f484(x74552,x74551,x74553)),x74553))
% 157.76/157.53 [7472]~P110(x74721)+~P13(x74721,x74723)+P13(x74721,f866(f866(f158(x74721),x74722),x74723))+P107(f866(f866(f336(x74721),f718(x74723,x74722,x74721)),f866(f179(x74721),x74723)))
% 157.76/157.53 [7473]~P110(x74731)+~P13(x74731,x74733)+P13(x74731,f866(f866(f158(x74731),x74732),x74733))+P107(f866(f866(f336(x74731),f721(x74733,x74732,x74731)),f866(f179(x74731),x74733)))
% 157.76/157.53 [7474]~P110(x74741)+~P13(x74741,x74743)+P13(x74741,f866(f866(f158(x74741),x74742),x74743))+P107(f866(f866(f336(x74741),f760(x74742,x74743,x74741)),f866(f179(x74741),x74743)))
% 157.76/157.53 [7589]~P110(x75891)+~P5(x75891)+~P107(f866(f866(f244(x75891),x75893),f42(x75891,x75892)))+P107(f866(f866(f336(x75891),f592(x75892,x75893,x75891)),x75892))
% 157.76/157.53 [7743]~P110(x77431)+~P5(x77431)+~P107(f866(f866(f244(x77431),f43(x77431,x77433)),x77432))+P107(f866(f866(f336(x77431),f622(x77432,x77433,x77431)),x77433))
% 157.76/157.53 [7744]~P110(x77441)+~P5(x77441)+~P107(f866(f866(f244(x77441),f43(x77441,x77443)),x77442))+P107(f866(f866(f244(x77441),f622(x77442,x77443,x77441)),x77442))
% 157.76/157.53 [7756]P150(x77562,x77563,x77561)+E(x77561,f2(a1))+P107(f866(f866(f244(a1),x77561),f871(x77561,x77563,x77562)))+P107(f866(f866(f244(a1),f872(x77561,x77563,x77562)),x77561))
% 157.76/157.53 [7757]P149(x77572,x77573,x77571)+E(x77571,f2(a1))+P107(f866(f866(f244(a1),x77571),f877(x77571,x77573,x77572)))+P107(f866(f866(f244(a1),f878(x77571,x77573,x77572)),x77571))
% 157.76/157.53 [7847]P150(x78473,x78472,x78471)+E(x78471,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x78471),f876(x78471,x78472,x78473))),f871(x78471,x78472,x78473)),x78472)+P107(f866(f866(f244(a1),f2(a1)),x78471))
% 157.76/157.53 [7848]P149(x78483,x78482,x78481)+E(x78481,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x78481),f880(x78481,x78482,x78483))),f877(x78481,x78482,x78483)),x78482)+P107(f866(f866(f244(a1),f2(a1)),x78481))
% 157.76/157.53 [7850]~P120(x78501)+~P107(f866(f866(f243(x78501),x78503),f2(x78501)))+P107(f866(f866(f243(x78501),f866(f866(f87(x78501),x78502),x78503)),f2(x78501)))+~P107(f866(f866(f243(x78501),f2(x78501)),x78502))
% 157.76/157.53 [7851]~P120(x78511)+~P107(f866(f866(f243(x78511),x78512),f2(x78511)))+P107(f866(f866(f243(x78511),f866(f866(f87(x78511),x78512),x78513)),f2(x78511)))+~P107(f866(f866(f243(x78511),f2(x78511)),x78513))
% 157.76/157.53 [7853]~P137(x78531)+~P107(f866(f866(f243(x78531),x78533),f2(x78531)))+P107(f866(f866(f243(x78531),f866(f866(f87(x78531),x78532),x78533)),f2(x78531)))+~P107(f866(f866(f243(x78531),f2(x78531)),x78532))
% 157.76/157.53 [7855]~P137(x78551)+~P107(f866(f866(f243(x78551),x78552),f2(x78551)))+P107(f866(f866(f243(x78551),f866(f866(f87(x78551),x78552),x78553)),f2(x78551)))+~P107(f866(f866(f243(x78551),f2(x78551)),x78553))
% 157.76/157.53 [7856]~P67(x78561)+~P107(f866(f866(f243(x78561),x78563),f2(x78561)))+P107(f866(f866(f243(x78561),f866(f866(f297(x78561),x78562),x78563)),f2(x78561)))+~P107(f866(f866(f243(x78561),f2(x78561)),x78562))
% 157.76/157.53 [7857]~P67(x78571)+~P107(f866(f866(f243(x78571),x78572),f2(x78571)))+P107(f866(f866(f243(x78571),f866(f866(f297(x78571),x78572),x78573)),f2(x78571)))+~P107(f866(f866(f243(x78571),f2(x78571)),x78573))
% 157.76/157.53 [7858]~P68(x78581)+~P107(f866(f866(f243(x78581),x78582),f2(x78581)))+P107(f866(f866(f243(x78581),f866(f866(f297(x78581),x78582),x78583)),f2(x78581)))+~P107(f866(f866(f244(x78581),f2(x78581)),x78583))
% 157.76/157.53 [7859]~P68(x78591)+~P107(f866(f866(f244(x78591),x78593),f2(x78591)))+P107(f866(f866(f243(x78591),f866(f866(f297(x78591),x78592),x78593)),f2(x78591)))+~P107(f866(f866(f243(x78591),f2(x78591)),x78592))
% 157.76/157.53 [7861]~P132(x78611)+~P107(f866(f866(f244(x78611),x78613),f2(x78611)))+P107(f866(f866(f244(x78611),f866(f866(f87(x78611),x78612),x78613)),f2(x78611)))+~P107(f866(f866(f244(x78611),f2(x78611)),x78612))
% 157.76/157.53 [7862]~P132(x78621)+~P107(f866(f866(f244(x78621),x78622),f2(x78621)))+P107(f866(f866(f244(x78621),f866(f866(f87(x78621),x78622),x78623)),f2(x78621)))+~P107(f866(f866(f244(x78621),f2(x78621)),x78623))
% 157.76/157.53 [7863]~P67(x78631)+~P107(f866(f866(f244(x78631),x78633),f2(x78631)))+P107(f866(f866(f244(x78631),f866(f866(f297(x78631),x78632),x78633)),f2(x78631)))+~P107(f866(f866(f244(x78631),f2(x78631)),x78632))
% 157.76/157.53 [7864]~P67(x78641)+~P107(f866(f866(f244(x78641),x78642),f2(x78641)))+P107(f866(f866(f244(x78641),f866(f866(f297(x78641),x78642),x78643)),f2(x78641)))+~P107(f866(f866(f244(x78641),f2(x78641)),x78643))
% 157.76/157.53 [7865]~P68(x78651)+~P107(f866(f866(f244(x78651),x78653),f2(x78651)))+P107(f866(f866(f244(x78651),f866(f866(f297(x78651),x78652),x78653)),f2(x78651)))+~P107(f866(f866(f244(x78651),f2(x78651)),x78652))
% 157.76/157.53 [7866]~P68(x78661)+~P107(f866(f866(f244(x78661),x78662),f2(x78661)))+P107(f866(f866(f244(x78661),f866(f866(f297(x78661),x78662),x78663)),f2(x78661)))+~P107(f866(f866(f244(x78661),f2(x78661)),x78663))
% 157.76/157.53 [7881]P149(x78811,x78812,x78813)+~P107(f866(x78811,x78812))+P107(f866(f866(f244(a1),x78813),f877(x78813,x78812,x78811)))+P107(f866(f866(f244(a1),f878(x78813,x78812,x78811)),x78813))
% 157.76/157.53 [7894]P150(x78941,x78942,x78943)+P107(f866(f866(f244(a1),x78943),f871(x78943,x78942,x78941)))+~P107(f866(x78941,f2(a1)))+P107(f866(f866(f244(a1),f872(x78943,x78942,x78941)),x78943))
% 157.76/157.53 [7944]P150(x79442,x79443,x79441)+E(x79441,f2(a1))+~P107(f866(x79442,f876(x79441,x79443,x79442)))+P107(f866(f866(f244(a1),f872(x79441,x79443,x79442)),x79441))
% 157.76/157.53 [7945]P149(x79452,x79453,x79451)+E(x79451,f2(a1))+~P107(f866(x79452,f877(x79451,x79453,x79452)))+P107(f866(f866(f244(a1),f878(x79451,x79453,x79452)),x79451))
% 157.76/157.53 [7955]P149(x79553,x79552,x79551)+~P107(f866(x79553,x79552))+E(f866(f866(f86(a1),f866(f866(f87(a1),x79551),f880(x79551,x79552,x79553))),f877(x79551,x79552,x79553)),x79552)+P107(f866(f866(f244(a1),f2(a1)),x79551))
% 157.76/157.53 [7971]P150(x79713,x79712,x79711)+E(f866(f866(f86(a1),f866(f866(f87(a1),x79711),f876(x79711,x79712,x79713))),f871(x79711,x79712,x79713)),x79712)+~P107(f866(x79713,f2(a1)))+P107(f866(f866(f244(a1),f2(a1)),x79711))
% 157.76/157.53 [8000]~P107(f866(x80001,x80003))+~P107(f866(f66(x80002),x80003))+P107(f866(f866(f336(x80002),f736(x80001,x80003,x80002)),f748(x80001,x80003,x80002)))+P107(f866(x80001,f195(f937(x80002,a925))))
% 157.76/157.53 [8011]P149(x80111,x80112,x80113)+~P107(f866(x80111,x80112))+~P107(f866(x80111,f877(x80113,x80112,x80111)))+P107(f866(f866(f244(a1),f878(x80113,x80112,x80111)),x80113))
% 157.76/157.53 [8017]P150(x80171,x80172,x80173)+~P107(f866(x80171,f876(x80173,x80172,x80171)))+~P107(f866(x80171,f2(a1)))+P107(f866(f866(f244(a1),f872(x80173,x80172,x80171)),x80173))
% 157.76/157.53 [8116]~P120(x81161)+~P107(f866(f866(f243(x81161),f866(f866(f87(x81161),x81163),x81162)),f2(x81161)))+P107(f866(f866(f243(x81161),x81162),f2(x81161)))+P107(f866(f866(f243(x81161),f2(x81161)),x81162))
% 157.76/157.53 [8117]~P120(x81171)+~P107(f866(f866(f243(x81171),f866(f866(f87(x81171),x81172),x81173)),f2(x81171)))+P107(f866(f866(f243(x81171),x81172),f2(x81171)))+P107(f866(f866(f243(x81171),f2(x81171)),x81172))
% 157.76/157.53 [8118]~P67(x81181)+~P107(f866(f866(f243(x81181),f866(f866(f297(x81181),x81183),x81182)),f2(x81181)))+P107(f866(f866(f243(x81181),x81182),f2(x81181)))+P107(f866(f866(f243(x81181),f2(x81181)),x81182))
% 157.76/157.53 [8119]~P67(x81191)+~P107(f866(f866(f243(x81191),f866(f866(f297(x81191),x81192),x81193)),f2(x81191)))+P107(f866(f866(f243(x81191),x81192),f2(x81191)))+P107(f866(f866(f243(x81191),f2(x81191)),x81192))
% 157.76/157.53 [8120]~P67(x81201)+~P107(f866(f866(f244(x81201),f866(f866(f297(x81201),x81203),x81202)),f2(x81201)))+P107(f866(f866(f244(x81201),x81202),f2(x81201)))+P107(f866(f866(f244(x81201),f2(x81201)),x81202))
% 157.76/157.53 [8121]~P67(x81211)+~P107(f866(f866(f244(x81211),f866(f866(f297(x81211),x81212),x81213)),f2(x81211)))+P107(f866(f866(f244(x81211),x81212),f2(x81211)))+P107(f866(f866(f244(x81211),f2(x81211)),x81212))
% 157.76/157.53 [8144]~P120(x81441)+~P107(f866(f866(f243(x81441),f866(f866(f87(x81441),x81442),x81443)),f2(x81441)))+P107(f866(f866(f243(x81441),f2(x81441)),x81442))+P107(f866(f866(f243(x81441),f2(x81441)),x81443))
% 157.76/157.53 [8145]~P67(x81451)+~P107(f866(f866(f243(x81451),f866(f866(f297(x81451),x81452),x81453)),f2(x81451)))+P107(f866(f866(f243(x81451),f2(x81451)),x81452))+P107(f866(f866(f243(x81451),f2(x81451)),x81453))
% 157.76/157.53 [8146]~P67(x81461)+~P107(f866(f866(f244(x81461),f866(f866(f297(x81461),x81462),x81463)),f2(x81461)))+P107(f866(f866(f244(x81461),f2(x81461)),x81462))+P107(f866(f866(f244(x81461),f2(x81461)),x81463))
% 157.76/157.53 [8168]P150(x81682,x81683,x81681)+E(x81681,f2(a1))+P107(f866(f866(f243(a1),f871(x81681,x81683,x81682)),f2(a1)))+P107(f866(f866(f244(a1),f872(x81681,x81683,x81682)),x81681))
% 157.76/157.53 [8169]P149(x81692,x81693,x81691)+E(x81691,f2(a1))+P107(f866(f866(f243(a1),f877(x81691,x81693,x81692)),f2(a1)))+P107(f866(f866(f244(a1),f878(x81691,x81693,x81692)),x81691))
% 157.76/157.53 [8176]~P113(x81761)+~P107(f866(f866(f244(x81761),x81762),f84(x81761)))+P107(f866(f866(f244(x81761),f866(f866(f252(x81761),x81762),f866(a119,x81763))),f84(x81761)))+~P107(f866(f866(f244(x81761),f2(x81761)),x81762))
% 157.76/157.53 [8230]~P110(x82301)+~E(x82303,f120(x82301))+~P13(x82301,f866(f175(x82301),x82303))+E(f866(f149(x82301,x82301,f866(f7(x82301,x82301,x82301),f242(x82301)),x82302),f866(f175(x82301),x82303)),x82302)
% 157.76/157.53 [8233]P149(x82331,x82332,x82333)+~P107(f866(x82331,x82332))+P107(f866(f866(f243(a1),f877(x82333,x82332,x82331)),f2(a1)))+P107(f866(f866(f244(a1),f878(x82333,x82332,x82331)),x82333))
% 157.76/157.53 [8240]P150(x82401,x82402,x82403)+~P107(f866(x82401,f2(a1)))+P107(f866(f866(f243(a1),f871(x82403,x82402,x82401)),f2(a1)))+P107(f866(f866(f244(a1),f872(x82403,x82402,x82401)),x82403))
% 157.76/157.53 [8451]P150(x84513,x84512,x84511)+E(x84511,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84511),f876(x84511,x84512,x84513))),f871(x84511,x84512,x84513)),x84512)+P107(f866(f866(f244(a1),f872(x84511,x84512,x84513)),x84511))
% 157.76/157.53 [8452]P149(x84523,x84522,x84521)+E(x84521,f2(a1))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84521),f880(x84521,x84522,x84523))),f877(x84521,x84522,x84523)),x84522)+P107(f866(f866(f244(a1),f878(x84521,x84522,x84523)),x84521))
% 157.76/157.53 [8487]P149(x84873,x84872,x84871)+~P107(f866(x84873,x84872))+E(f866(f866(f86(a1),f866(f866(f87(a1),x84871),f880(x84871,x84872,x84873))),f877(x84871,x84872,x84873)),x84872)+P107(f866(f866(f244(a1),f878(x84871,x84872,x84873)),x84871))
% 157.76/157.53 [8488]~P71(x84881)+~P72(x84881)+~P40(x84883)+E(f866(f866(f9(a930,x84881),f866(f866(f8(a1,x84881,a930),x84882),f107(a1))),f866(f317(a1,a930,a111),x84883)),f866(f866(f9(a1,x84881),x84882),x84883))
% 157.76/157.53 [8489]~P71(x84891)+~P72(x84891)+~P40(x84893)+E(f866(f866(f6(a930,x84891),f866(f866(f8(a1,x84891,a930),x84892),f107(a1))),f866(f317(a1,a930,a111),x84893)),f866(f866(f6(a1,x84891),x84892),x84893))
% 157.76/157.53 [8498]P150(x84983,x84982,x84981)+E(f866(f866(f86(a1),f866(f866(f87(a1),x84981),f876(x84981,x84982,x84983))),f871(x84981,x84982,x84983)),x84982)+~P107(f866(x84983,f2(a1)))+P107(f866(f866(f244(a1),f872(x84981,x84982,x84983)),x84981))
% 157.76/157.53 [8521]~E(x85212,f2(a930))+~E(f866(f259(a930,a930),x85213),f2(a930))+~E(x85211,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x85213)),x85212)),f866(f264(a930,a930),x85213)))+P107(f866(f53(x85211,x85212),x85213))
% 157.76/157.53 [8577]P107(f866(x85771,x85772))+~P107(f866(f866(f336(x85773),f773(x85771,x85772,x85773)),f767(x85771,x85772,x85773)))+~P107(f866(f66(x85773),x85772))+~P107(f866(x85771,f195(f937(x85773,a925))))
% 157.76/157.53 [9207]P107(f866(x92071,x92072))+~P107(f866(f66(x92073),x92072))+~P107(f866(x92071,f866(f866(f316(x92073),f773(x92071,x92072,x92073)),f767(x92071,x92072,x92073))))+~P107(f866(x92071,f195(f937(x92073,a925))))
% 157.76/157.53 [9438]P107(f866(f866(f243(a1),x94381),f2(a1)))+~P107(f866(f866(f244(a1),f866(f866(f86(a1),f866(f866(f87(a1),x94383),x94381)),x94382)),f2(a1)))+~P107(f866(f866(f243(a1),f2(a1)),x94382))+~P107(f866(f866(f244(a1),f2(a1)),x94383))
% 157.76/157.53 [6056]~P83(x60562)+E(x60561,f195(f937(x60562,a925)))+~P107(f866(f66(x60562),x60561))+E(f13(x60562,f866(f866(f316(x60562),x60563),x60561)),f866(f866(f117(x60562),x60563),f13(x60562,x60561)))
% 157.76/157.53 [6057]~P83(x60572)+E(x60571,f195(f937(x60572,a925)))+~P107(f866(f66(x60572),x60571))+E(f10(x60572,f866(f866(f316(x60572),x60573),x60571)),f866(f866(f108(x60572),x60573),f10(x60572,x60571)))
% 157.76/157.53 [6058]~P110(x60582)+E(x60581,f195(f937(x60582,a925)))+~P107(f866(f66(x60582),x60581))+E(f14(x60582,f866(f866(f316(x60582),x60583),x60581)),f866(f866(f242(x60582),x60583),f14(x60582,x60581)))
% 157.76/157.53 [6059]~P110(x60592)+E(x60591,f195(f937(x60592,a925)))+~P107(f866(f66(x60592),x60591))+E(f15(x60592,f866(f866(f316(x60592),x60593),x60591)),f866(f866(f241(x60592),x60593),f15(x60592,x60591)))
% 157.76/157.53 [6376]~P120(x63761)+~E(x63763,f2(x63761))+~E(x63762,f2(x63761))+E(f866(f866(f86(x63761),f866(f866(f87(x63761),x63762),x63762)),f866(f866(f87(x63761),x63763),x63763)),f2(x63761))
% 157.76/157.53 [6443]~P99(x64432)+E(x64431,f195(f937(x64432,a925)))+~P107(f866(f66(x64432),x64431))+E(f866(f68(x64432,f87(x64432)),f866(f866(f316(x64432),x64433),x64431)),f866(f866(f87(x64432),x64433),f866(f68(x64432,f87(x64432)),x64431)))
% 157.76/157.53 [6568]~P110(x65682)+E(x65681,f195(f937(x65682,a925)))+~P107(f866(f66(x65682),x65681))+E(f11(x65682,f241(x65682),f866(f866(f316(x65682),x65683),x65681)),f866(f866(f241(x65682),x65683),f11(x65682,f241(x65682),x65681)))
% 157.76/157.53 [6569]~P110(x65692)+E(x65691,f195(f937(x65692,a925)))+~P107(f866(f66(x65692),x65691))+E(f12(x65692,f242(x65692),f866(f866(f316(x65692),x65693),x65691)),f866(f866(f242(x65692),x65693),f12(x65692,f242(x65692),x65691)))
% 157.76/157.53 [7080]~P69(x70801)+~P107(f866(f66(x70801),x70803))+E(f866(f68(x70801,f87(x70801)),f866(f866(f316(x70801),x70802),x70803)),f866(f866(f69(x70801,x70801,f87(x70801)),x70802),x70803))+P107(f866(f866(f336(x70801),x70802),x70803))
% 157.76/157.53 [7159]~E(f866(f866(f86(a1),x71592),f866(f866(f87(a1),x71593),x71591)),x71593)+~P107(f866(f866(f244(a1),f2(a1)),x71593))+P107(f866(f866(f243(a1),f84(a1)),x71591))+~P107(f866(f866(f244(a1),x71592),x71593))
% 157.76/157.53 [7187]~E(f866(f866(f86(a1),x71872),f866(f866(f87(a1),x71873),x71871)),x71873)+P107(f866(f866(f243(a1),x71871),f84(a1)))+~P107(f866(f866(f243(a1),f2(a1)),x71872))+~P107(f866(f866(f244(a1),f2(a1)),x71873))
% 157.76/157.53 [7203]E(x72031,f2(a930))+~P107(f866(f53(x72033,x72031),x72032))+~P107(f866(f866(f244(a930),f2(a930)),x72031))+P107(f866(f866(f244(a930),f866(f264(a930,a930),x72032)),x72031))
% 157.76/157.53 [7233]~P141(x72331)+~P107(f866(f866(f243(x72331),x72332),f2(x72331)))+~P107(f866(f866(f243(x72331),x72333),f2(x72331)))+E(f866(f866(f87(x72331),f866(f81(x72331),x72332)),f866(f81(x72331),x72333)),f866(f81(x72331),f866(f866(f87(x72331),x72332),x72333)))
% 157.76/157.53 [7279]~P141(x72791)+~P107(f866(f866(f243(x72791),x72792),f2(x72791)))+E(f866(f866(f87(x72791),f866(f81(x72791),x72792)),f866(f81(x72791),x72793)),f866(f81(x72791),f866(f866(f87(x72791),x72792),x72793)))+~P107(f866(f866(f243(x72791),f2(x72791)),x72793))
% 157.76/157.53 [7280]~P141(x72801)+~P107(f866(f866(f243(x72801),x72803),f2(x72801)))+E(f866(f866(f87(x72801),f866(f81(x72801),x72802)),f866(f81(x72801),x72803)),f866(f81(x72801),f866(f866(f87(x72801),x72802),x72803)))+~P107(f866(f866(f243(x72801),f2(x72801)),x72802))
% 157.76/157.53 [7336]~P141(x73361)+E(f866(f866(f87(x73361),f866(f81(x73361),x73362)),f866(f81(x73361),x73363)),f866(f81(x73361),f866(f866(f87(x73361),x73362),x73363)))+~P107(f866(f866(f243(x73361),f2(x73361)),x73362))+~P107(f866(f866(f243(x73361),f2(x73361)),x73363))
% 157.76/157.53 [7352]~P120(x73521)+~P107(f866(f866(f243(x73521),x73523),f2(x73521)))+~P107(f866(f866(f243(x73521),x73522),f2(x73521)))+P107(f866(f866(f243(x73521),f2(x73521)),f866(f866(f87(x73521),x73522),x73523)))
% 157.76/157.53 [7354]~P138(x73541)+~P107(f866(f866(f243(x73541),x73543),f2(x73541)))+~P107(f866(f866(f243(x73541),x73542),f2(x73541)))+P107(f866(f866(f243(x73541),f2(x73541)),f866(f866(f87(x73541),x73542),x73543)))
% 157.76/157.53 [7355]~P67(x73551)+~P107(f866(f866(f243(x73551),x73553),f2(x73551)))+~P107(f866(f866(f243(x73551),x73552),f2(x73551)))+P107(f866(f866(f243(x73551),f2(x73551)),f866(f866(f297(x73551),x73552),x73553)))
% 157.76/157.53 [7356]~P68(x73561)+~P107(f866(f866(f244(x73561),x73563),f2(x73561)))+~P107(f866(f866(f243(x73561),x73562),f2(x73561)))+P107(f866(f866(f243(x73561),f2(x73561)),f866(f866(f297(x73561),x73562),x73563)))
% 157.76/157.53 [7357]~P120(x73571)+~P107(f866(f866(f244(x73571),x73573),f2(x73571)))+~P107(f866(f866(f244(x73571),x73572),f2(x73571)))+P107(f866(f866(f244(x73571),f2(x73571)),f866(f866(f87(x73571),x73572),x73573)))
% 157.76/157.53 [7358]~P67(x73581)+~P107(f866(f866(f244(x73581),x73583),f2(x73581)))+~P107(f866(f866(f244(x73581),x73582),f2(x73581)))+P107(f866(f866(f244(x73581),f2(x73581)),f866(f866(f297(x73581),x73582),x73583)))
% 157.76/157.53 [7359]~P68(x73591)+~P107(f866(f866(f244(x73591),x73593),f2(x73591)))+~P107(f866(f866(f244(x73591),x73592),f2(x73591)))+P107(f866(f866(f244(x73591),f2(x73591)),f866(f866(f297(x73591),x73592),x73593)))
% 157.76/157.53 [7360]~P113(x73601)+~P107(f866(f866(f244(a930),f2(a930)),x73603))+~P107(f866(f866(f244(x73601),f84(x73601)),x73602))+P107(f866(f866(f244(x73601),f84(x73601)),f866(f866(f252(x73601),x73602),x73603)))
% 157.76/157.53 [7456]~P120(x74561)+~P107(f866(f866(f243(x74561),f2(x74561)),x74563))+~P107(f866(f866(f243(x74561),f2(x74561)),x74562))+P107(f866(f866(f243(x74561),f2(x74561)),f866(f866(f87(x74561),x74562),x74563)))
% 157.76/157.53 [7457]~P137(x74571)+~P107(f866(f866(f243(x74571),f2(x74571)),x74573))+~P107(f866(f866(f243(x74571),f2(x74571)),x74572))+P107(f866(f866(f243(x74571),f2(x74571)),f866(f866(f87(x74571),x74572),x74573)))
% 157.76/157.53 [7458]~P138(x74581)+~P107(f866(f866(f243(x74581),f2(x74581)),x74583))+~P107(f866(f866(f243(x74581),f2(x74581)),x74582))+P107(f866(f866(f243(x74581),f2(x74581)),f866(f866(f87(x74581),x74582),x74583)))
% 157.76/157.53 [7460]~P67(x74601)+~P107(f866(f866(f243(x74601),f2(x74601)),x74603))+~P107(f866(f866(f243(x74601),f2(x74601)),x74602))+P107(f866(f866(f243(x74601),f2(x74601)),f866(f866(f297(x74601),x74602),x74603)))
% 157.76/157.53 [7461]~P68(x74611)+~P107(f866(f866(f244(x74611),f2(x74611)),x74613))+~P107(f866(f866(f243(x74611),f2(x74611)),x74612))+P107(f866(f866(f243(x74611),f2(x74611)),f866(f866(f297(x74611),x74612),x74613)))
% 157.76/157.53 [7462]~P113(x74621)+~P107(f866(f866(f244(x74621),f84(x74621)),x74623))+~P107(f866(f866(f244(x74621),f84(x74621)),x74622))+P107(f866(f866(f244(x74621),f84(x74621)),f866(f866(f87(x74621),x74622),x74623)))
% 157.76/157.53 [7463]~P132(x74631)+~P107(f866(f866(f244(x74631),f2(x74631)),x74633))+~P107(f866(f866(f244(x74631),f2(x74631)),x74632))+P107(f866(f866(f244(x74631),f2(x74631)),f866(f866(f87(x74631),x74632),x74633)))
% 157.76/157.53 [7466]~P86(x74661)+~P107(f866(f866(f244(x74661),f2(x74661)),x74663))+~P107(f866(f866(f244(x74661),f2(x74661)),x74662))+P107(f866(f866(f244(x74661),f2(x74661)),f866(f866(f86(x74661),x74662),x74663)))
% 157.76/157.53 [7467]~P67(x74671)+~P107(f866(f866(f244(x74671),f2(x74671)),x74673))+~P107(f866(f866(f244(x74671),f2(x74671)),x74672))+P107(f866(f866(f244(x74671),f2(x74671)),f866(f866(f297(x74671),x74672),x74673)))
% 157.76/157.53 [7468]~P68(x74681)+~P107(f866(f866(f244(x74681),f2(x74681)),x74683))+~P107(f866(f866(f244(x74681),f2(x74681)),x74682))+P107(f866(f866(f244(x74681),f2(x74681)),f866(f866(f297(x74681),x74682),x74683)))
% 157.76/157.53 [7549]~P83(x75491)+~P107(f866(f66(x75491),x75493))+E(f13(x75491,f866(f866(f316(x75491),x75492),x75493)),x75492)+~E(f866(f866(f23(f937(x75491,a925)),x75493),f866(f866(f316(x75491),x75492),f195(f937(x75491,a925)))),f195(f937(x75491,a925)))
% 157.76/157.53 [7550]~P83(x75501)+~P107(f866(f66(x75501),x75503))+E(f10(x75501,f866(f866(f316(x75501),x75502),x75503)),x75502)+~E(f866(f866(f23(f937(x75501,a925)),x75503),f866(f866(f316(x75501),x75502),f195(f937(x75501,a925)))),f195(f937(x75501,a925)))
% 157.76/157.53 [7551]~P110(x75511)+~P107(f866(f66(x75511),x75513))+E(f14(x75511,f866(f866(f316(x75511),x75512),x75513)),x75512)+~E(f866(f866(f23(f937(x75511,a925)),x75513),f866(f866(f316(x75511),x75512),f195(f937(x75511,a925)))),f195(f937(x75511,a925)))
% 157.76/157.53 [7552]~P110(x75521)+~P107(f866(f66(x75521),x75523))+E(f15(x75521,f866(f866(f316(x75521),x75522),x75523)),x75522)+~E(f866(f866(f23(f937(x75521,a925)),x75523),f866(f866(f316(x75521),x75522),f195(f937(x75521,a925)))),f195(f937(x75521,a925)))
% 157.76/157.53 [7554]~P120(x75541)+P107(f866(f866(f243(x75541),x75542),f2(x75541)))+P107(f866(f866(f243(x75541),f2(x75541)),x75543))+~P107(f866(f866(f243(x75541),f2(x75541)),f866(f866(f87(x75541),x75543),x75542)))
% 157.76/157.53 [7555]~P120(x75551)+P107(f866(f866(f243(x75551),x75552),f2(x75551)))+P107(f866(f866(f243(x75551),f2(x75551)),x75553))+~P107(f866(f866(f243(x75551),f2(x75551)),f866(f866(f87(x75551),x75552),x75553)))
% 157.76/157.53 [7556]~P67(x75561)+P107(f866(f866(f243(x75561),x75562),f2(x75561)))+P107(f866(f866(f243(x75561),f2(x75561)),x75563))+~P107(f866(f866(f243(x75561),f2(x75561)),f866(f866(f297(x75561),x75563),x75562)))
% 157.76/157.53 [7557]~P67(x75571)+P107(f866(f866(f243(x75571),x75572),f2(x75571)))+P107(f866(f866(f243(x75571),f2(x75571)),x75573))+~P107(f866(f866(f243(x75571),f2(x75571)),f866(f866(f297(x75571),x75572),x75573)))
% 157.76/157.53 [7558]~P120(x75581)+P107(f866(f866(f243(x75581),x75582),f2(x75581)))+P107(f866(f866(f243(x75581),f2(x75581)),x75582))+~P107(f866(f866(f243(x75581),f2(x75581)),f866(f866(f87(x75581),x75583),x75582)))
% 157.76/157.53 [7559]~P120(x75591)+P107(f866(f866(f243(x75591),x75592),f2(x75591)))+P107(f866(f866(f243(x75591),f2(x75591)),x75592))+~P107(f866(f866(f243(x75591),f2(x75591)),f866(f866(f87(x75591),x75592),x75593)))
% 157.76/157.53 [7560]~P67(x75601)+P107(f866(f866(f243(x75601),x75602),f2(x75601)))+P107(f866(f866(f243(x75601),f2(x75601)),x75602))+~P107(f866(f866(f243(x75601),f2(x75601)),f866(f866(f297(x75601),x75603),x75602)))
% 157.76/157.53 [7561]~P67(x75611)+P107(f866(f866(f243(x75611),x75612),f2(x75611)))+P107(f866(f866(f243(x75611),f2(x75611)),x75612))+~P107(f866(f866(f243(x75611),f2(x75611)),f866(f866(f297(x75611),x75612),x75613)))
% 157.76/157.53 [7562]~P67(x75621)+P107(f866(f866(f244(x75621),x75622),f2(x75621)))+P107(f866(f866(f244(x75621),f2(x75621)),x75623))+~P107(f866(f866(f244(x75621),f2(x75621)),f866(f866(f297(x75621),x75623),x75622)))
% 157.76/157.53 [7563]~P67(x75631)+P107(f866(f866(f244(x75631),x75632),f2(x75631)))+P107(f866(f866(f244(x75631),f2(x75631)),x75633))+~P107(f866(f866(f244(x75631),f2(x75631)),f866(f866(f297(x75631),x75632),x75633)))
% 157.76/157.53 [7564]~P67(x75641)+P107(f866(f866(f244(x75641),x75642),f2(x75641)))+P107(f866(f866(f244(x75641),f2(x75641)),x75642))+~P107(f866(f866(f244(x75641),f2(x75641)),f866(f866(f297(x75641),x75643),x75642)))
% 157.76/157.53 [7565]~P67(x75651)+P107(f866(f866(f244(x75651),x75652),f2(x75651)))+P107(f866(f866(f244(x75651),f2(x75651)),x75652))+~P107(f866(f866(f244(x75651),f2(x75651)),f866(f866(f297(x75651),x75652),x75653)))
% 157.76/157.53 [7649]~E(f866(f866(f108(f937(x76491,a925)),f866(f179(x76491),x76492)),f866(f179(x76491),x76493)),f195(f937(x76491,a925)))+~P107(f866(f144(x76491),x76493))+~P107(f866(f144(x76491),x76492))+P107(f866(f144(x76491),f866(f866(f141(x76491),x76492),x76493)))
% 157.76/157.53 [7650]~P110(x76501)+~P107(f866(f66(x76501),x76503))+E(f11(x76501,f241(x76501),f866(f866(f316(x76501),x76502),x76503)),x76502)+~E(f866(f866(f23(f937(x76501,a925)),x76503),f866(f866(f316(x76501),x76502),f195(f937(x76501,a925)))),f195(f937(x76501,a925)))
% 157.76/157.53 [7651]~P110(x76511)+~P107(f866(f66(x76511),x76513))+E(f12(x76511,f242(x76511),f866(f866(f316(x76511),x76512),x76513)),x76512)+~E(f866(f866(f23(f937(x76511,a925)),x76513),f866(f866(f316(x76511),x76512),f195(f937(x76511,a925)))),f195(f937(x76511,a925)))
% 157.76/157.53 [7665]~P89(x76651)+~P107(f866(f866(f243(x76651),x76652),x76653))+~P107(f866(f866(f243(x76651),f866(f85(x76651),x76652)),x76653))+P107(f866(f866(f243(x76651),f866(f81(x76651),x76652)),x76653))
% 157.76/157.53 [7666]~P128(x76661)+~P107(f866(f866(f244(x76661),x76662),x76663))+~P107(f866(f866(f244(x76661),f866(f85(x76661),x76662)),x76663))+P107(f866(f866(f244(x76661),f866(f81(x76661),x76662)),x76663))
% 157.76/157.53 [7733]~P132(x77331)+P107(f866(f866(f244(x77331),f2(x77331)),x77332))+~P107(f866(f866(f244(x77331),f2(x77331)),x77333))+~P107(f866(f866(f244(x77331),f2(x77331)),f866(f866(f87(x77331),x77333),x77332)))
% 157.76/157.53 [7734]~P132(x77341)+P107(f866(f866(f244(x77341),f2(x77341)),x77342))+~P107(f866(f866(f244(x77341),f2(x77341)),x77343))+~P107(f866(f866(f244(x77341),f2(x77341)),f866(f866(f87(x77341),x77342),x77343)))
% 157.76/157.53 [8031]E(x80311,x80312)+~P107(f866(f66(x80313),x80311))+~P107(f866(f866(f243(a930),f866(f40(x80313),x80311)),f866(f40(x80313),x80312)))+~P107(f866(f866(f243(f937(x80313,a925)),x80312),x80311))
% 157.76/157.53 [8173]~P107(f866(f866(f244(a1),x81731),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x81732))+~P107(f866(f866(f243(a1),x81732),x81733))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x81731),x81732)),f866(f866(f41(a1),x81731),x81733)))
% 157.76/157.53 [8183]~P107(f866(f866(f243(a1),f2(a1)),x81831))+~P107(f866(f866(f244(a1),f2(a1)),x81833))+~P107(f866(f866(f243(a1),x81833),x81832))+P107(f866(f866(f243(a1),f866(f866(f41(a1),x81831),x81832)),f866(f866(f41(a1),x81831),x81833)))
% 157.76/157.53 [8318]E(f866(x83181,f471(x83182,x83181,x83183)),x83182)+~P107(f866(f866(f243(a1),x83182),f866(x83181,x83183)))+P107(f866(f866(f244(a930),f472(x83182,x83181,x83183)),x83183))+~P107(f866(f866(f243(a1),f866(x83181,f2(a930))),x83182))
% 157.76/157.53 [8319]E(f866(x83191,f479(x83192,x83191,x83193)),x83192)+~P107(f866(f866(f243(a1),x83192),f866(x83191,x83193)))+P107(f866(f866(f244(a930),f480(x83192,x83191,x83193)),x83193))+~P107(f866(f866(f243(a1),f866(x83191,f2(a930))),x83192))
% 157.76/157.53 [8414]~P107(f866(f66(x84141),x84143))+~P107(f866(f866(f244(a930),f866(f40(x84141),x84142)),f866(f40(x84141),x84143)))+~P107(f866(f866(f243(f937(x84141,a925)),x84142),x84143))+P107(f866(f866(f244(f937(x84141,a925)),x84142),x84143))
% 157.76/157.53 [8441]E(f866(f866(f86(a1),f432(x84413,x84411,x84412)),f433(x84413,x84411,x84412)),x84411)+E(f866(f866(f23(a1),x84411),x84412),x84411)+~P107(f866(f866(f244(a1),f2(a1)),x84412))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x84411),f84(a1))),x84413))
% 157.76/157.53 [8442]E(f866(f866(f23(a1),f440(x84423,x84421,x84422)),f441(x84423,x84421,x84422)),x84421)+E(f866(f866(f86(a1),x84421),x84422),x84421)+~P107(f866(f866(f244(a1),f2(a1)),x84422))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x84421),f84(a1))),x84423))
% 157.76/157.53 [8493]~P107(f866(f866(f243(a930),x84933),x84931))+P107(f866(f866(f243(a930),x84931),x84932))+~P107(f866(f866(f243(a930),x84933),x84932))+~P107(f866(f866(f243(a930),f866(f866(f23(a930),x84931),x84933)),f866(f866(f23(a930),x84932),x84933)))
% 157.76/157.53 [8494]~P107(f866(f866(f243(a930),x84943),x84941))+P107(f866(f866(f244(a930),x84941),x84942))+~P107(f866(f866(f243(a930),x84943),x84942))+~P107(f866(f866(f244(a930),f866(f866(f23(a930),x84941),x84943)),f866(f866(f23(a930),x84942),x84943)))
% 157.76/157.53 [8513]~P110(x85132)+E(x85131,f120(x85132))+~P13(x85132,f866(f175(x85132),x85131))+E(f866(f149(x85132,x85132,f866(f7(x85132,x85132,x85132),f242(x85132)),x85133),f866(f175(x85132),x85131)),f866(f866(f242(x85132),f866(f866(f171(x85132),x85131),f2(a930))),x85133))
% 157.76/157.53 [8582]E(f866(f866(f23(a1),x85821),x85822),x85821)+~P107(f866(f866(f244(a1),f2(a1)),x85822))+P107(f866(f866(f336(a1),f432(x85823,x85821,x85822)),x85823))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x85821),f84(a1))),x85823))
% 157.76/157.53 [8583]E(f866(f866(f86(a1),x85831),x85832),x85831)+~P107(f866(f866(f244(a1),f2(a1)),x85832))+P107(f866(f866(f336(a1),f440(x85833,x85831,x85832)),x85833))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x85831),f84(a1))),x85833))
% 157.76/157.53 [8654]~P107(f866(f866(f243(a1),x86541),f866(x86542,x86543)))+P107(f866(f866(f244(a930),f472(x86541,x86542,x86543)),x86543))+P107(f866(f866(f243(a930),f471(x86541,x86542,x86543)),x86543))+~P107(f866(f866(f243(a1),f866(x86542,f2(a930))),x86541))
% 157.76/157.53 [8655]~P107(f866(f866(f243(a1),x86551),f866(x86552,x86553)))+P107(f866(f866(f244(a930),f480(x86551,x86552,x86553)),x86553))+P107(f866(f866(f243(a930),f479(x86551,x86552,x86553)),x86553))+~P107(f866(f866(f243(a1),f866(x86552,f2(a930))),x86551))
% 157.76/157.53 [8727]E(f866(f866(f23(a1),x87271),x87272),x87271)+~P107(f866(f866(f244(a1),f2(a1)),x87272))+P107(f866(f866(f336(a1),f433(x87273,x87271,x87272)),f310(a1,f84(a1),x87272)))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x87271),f84(a1))),x87273))
% 157.76/157.53 [8728]E(f866(f866(f86(a1),x87281),x87282),x87281)+~P107(f866(f866(f244(a1),f2(a1)),x87282))+P107(f866(f866(f336(a1),f441(x87283,x87281,x87282)),f310(a1,f84(a1),x87282)))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x87281),f84(a1))),x87283))
% 157.76/157.53 [8862]~P113(x88621)+~P107(f866(f866(f244(x88621),x88622),f84(x88621)))+~P107(f866(f866(f244(x88621),f2(x88621)),x88622))+P107(f866(f866(f244(x88621),f866(f866(f87(x88621),x88622),f866(f866(f252(x88621),x88622),x88623))),f866(f866(f252(x88621),x88622),x88623)))
% 157.76/157.53 [8955]~P107(f866(x89551,x89552))+P107(f866(x89551,f2(a930)))+~P107(f866(f866(f244(a930),x89552),x89553))+~P107(f866(x89551,f50(a930,f866(a119,f484(x89552,x89551,x89553)),x89553)))
% 157.76/157.53 [9109]E(f505(x91091,x91092,x91093),f2(a930))+P107(f866(f866(x91091,x91093),x91092))+P107(f866(f866(x91091,f505(x91091,x91092,x91093)),f50(a930,f504(x91091,x91092,x91093),f505(x91091,x91092,x91093))))+~P107(f866(f322(f936(a930,a930),a228),f866(f866(f260(a930,a930),x91093),x91092)))
% 157.76/157.53 [9147]~P25(x91471,x91471,x91472,x91473)+E(f866(f317(x91471,x91471,x91472),x91473),x91473)+~P107(f866(f66(x91471),x91473))+~P107(f866(f866(f243(f937(x91471,a925)),f866(f317(x91471,x91471,x91472),x91473)),x91473))
% 157.76/157.53 [9365]P107(f866(f866(x93651,x93652),x93653))+P107(f866(f866(f244(a1),f782(x93651,x93653,x93652)),f783(x93651,x93653,x93652)))+P107(f866(f866(x93651,f782(x93651,x93653,x93652)),f866(f866(f86(a1),f783(x93651,x93653,x93652)),f84(a1))))+~P107(f866(f322(f936(a1,a1),a140),f866(f866(f260(a1,a1),x93652),x93653)))
% 157.76/157.53 [9382]P107(f866(f866(x93821,x93822),x93823))+~P107(f866(f866(f244(a1),f503(x93821,x93823,x93822)),f2(a1)))+P107(f866(f866(x93821,f866(f85(a1),f502(x93821,x93823,x93822))),f866(f85(a1),f503(x93821,x93823,x93822))))+~P107(f866(f322(f936(a1,a1),a230),f866(f866(f260(a1,a1),x93822),x93823)))
% 157.76/157.53 [9568]P107(f866(f866(x95681,x95682),x95683))+P107(f866(f866(x95681,f866(f866(f86(a1),f684(x95681,x95683,x95682)),f84(a1))),f686(x95681,x95683,x95682)))+~P107(f866(f866(f243(a1),f684(x95681,x95683,x95682)),f686(x95681,x95683,x95682)))+~P107(f866(f322(f936(a1,a1),a189),f866(f866(f260(a1,a1),x95682),x95683)))
% 157.76/157.53 [10002]~P64(x100022)+~P64(x100021)+~P107(f866(f61(f936(x100021,x100022)),x100023))+P107(f866(f61(x100021),f866(f866(f8(f937(x100022,a925),a925,x100021),f61(x100022)),f866(f866(f8(f937(x100022,f936(x100021,x100022)),f937(x100022,a925),x100021),f866(f8(f936(x100021,x100022),a925,x100022),x100023)),f260(x100021,x100022)))))
% 157.76/157.53 [10003]~P64(x100032)+~P64(x100031)+~P107(f866(f62(f936(x100031,x100032)),x100033))+P107(f866(f62(x100031),f866(f866(f8(f937(x100032,a925),a925,x100031),f62(x100032)),f866(f866(f8(f937(x100032,f936(x100031,x100032)),f937(x100032,a925),x100031),f866(f8(f936(x100031,x100032),a925,x100032),x100033)),f260(x100031,x100032)))))
% 157.76/157.53 [10097]~P64(x100972)+~P64(x100971)+P107(f866(f61(f936(x100971,x100972)),x100973))+~P107(f866(f61(x100971),f866(f866(f8(f937(x100972,a925),a925,x100971),f61(x100972)),f866(f866(f8(f937(x100972,f936(x100971,x100972)),f937(x100972,a925),x100971),f866(f8(f936(x100971,x100972),a925,x100972),x100973)),f260(x100971,x100972)))))
% 157.76/157.53 [10098]~P64(x100982)+~P64(x100981)+P107(f866(f62(f936(x100981,x100982)),x100983))+~P107(f866(f62(x100981),f866(f866(f8(f937(x100982,a925),a925,x100981),f62(x100982)),f866(f866(f8(f937(x100982,f936(x100981,x100982)),f937(x100982,a925),x100981),f866(f8(f936(x100981,x100982),a925,x100982),x100983)),f260(x100981,x100982)))))
% 157.76/157.53 [10258]E(f866(x102581,f471(x102582,x102581,x102583)),x102582)+~P107(f866(f866(f243(a1),x102582),f866(x102581,x102583)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x102581,f866(f866(f86(a930),f472(x102582,x102581,x102583)),f84(a930)))),f866(x102581,f472(x102582,x102581,x102583))))),f84(a1)))+~P107(f866(f866(f243(a1),f866(x102581,f2(a930))),x102582))
% 157.76/157.53 [10259]E(f866(x102591,f479(x102592,x102591,x102593)),x102592)+~P107(f866(f866(f243(a1),x102592),f866(x102591,x102593)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x102591,f866(f866(f86(a930),f480(x102592,x102591,x102593)),f84(a930)))),f866(x102591,f480(x102592,x102591,x102593))))),f84(a1)))+~P107(f866(f866(f243(a1),f866(x102591,f2(a930))),x102592))
% 157.76/157.53 [10262]~P107(f866(f866(f243(a1),x102621),f866(x102622,x102623)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x102622,f866(f866(f86(a930),f472(x102621,x102622,x102623)),f84(a930)))),f866(x102622,f472(x102621,x102622,x102623))))),f84(a1)))+P107(f866(f866(f243(a930),f471(x102621,x102622,x102623)),x102623))+~P107(f866(f866(f243(a1),f866(x102622,f2(a930))),x102621))
% 157.76/157.53 [10263]~P107(f866(f866(f243(a1),x102631),f866(x102632,x102633)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x102632,f866(f866(f86(a930),f480(x102631,x102632,x102633)),f84(a930)))),f866(x102632,f480(x102631,x102632,x102633))))),f84(a1)))+P107(f866(f866(f243(a930),f479(x102631,x102632,x102633)),x102633))+~P107(f866(f866(f243(a1),f866(x102632,f2(a930))),x102631))
% 157.76/157.53 [10322]E(x103221,x103222)+~E(f866(f149(f931(x103223),f931(x103223),f141(x103223),f120(x103223)),x103221),f866(f149(f931(x103223),f931(x103223),f141(x103223),f120(x103223)),x103222))+~E(f866(f196(f931(f931(x103223))),x103221),f866(f196(f931(f931(x103223))),x103222))+~P107(f866(f866(f265(f931(x103223),f931(x103223),a925),f866(f866(f7(f931(x103223),f937(f931(x103223),a930),f937(f931(x103223),a925)),f866(f866(f8(f937(a930,a925),f937(f937(f931(x103223),a930),f937(f931(x103223),a925)),f931(x103223)),f8(a930,a925,f931(x103223))),f866(f866(f8(a930,f937(a930,a925),f931(x103223)),a332),f196(f931(x103223))))),f196(f931(x103223)))),f711(x103222,x103221,x103223)))
% 157.76/157.53 [10323]E(x103231,x103232)+~E(f866(f149(f931(x103233),f931(x103233),f141(x103233),f120(x103233)),x103231),f866(f149(f931(x103233),f931(x103233),f141(x103233),f120(x103233)),x103232))+~E(f866(f196(f931(f931(x103233))),x103231),f866(f196(f931(f931(x103233))),x103232))+~P107(f866(f866(f265(f931(x103233),f931(x103233),a925),f866(f866(f7(f931(x103233),f937(f931(x103233),a930),f937(f931(x103233),a925)),f866(f866(f8(f937(a930,a925),f937(f937(f931(x103233),a930),f937(f931(x103233),a925)),f931(x103233)),f8(a930,a925,f931(x103233))),f866(f866(f8(a930,f937(a930,a925),f931(x103233)),a332),f196(f931(x103233))))),f196(f931(x103233)))),f712(x103231,x103232,x103233)))
% 157.76/157.53 [7068]~E(f84(a930),f2(a930))+~P107(f866(f66(x70681),x70683))+~P107(f866(f66(x70681),x70682))+E(f866(f866(f86(a930),f866(f40(x70681),x70682)),f866(f40(x70681),x70683)),f866(f40(x70681),f866(f866(f117(f937(x70681,a925)),x70682),x70683)))
% 157.76/157.53 [7475]~P103(x74751)+~P107(f866(f66(x74751),x74752))+~P107(f866(f866(f336(x74751),x74753),x74752))+P107(f866(f866(f243(x74751),f866(f68(x74751,f108(x74751)),x74752)),x74753))
% 157.76/157.53 [7476]~P110(x74761)+~P107(f866(f66(x74761),x74762))+~P107(f866(f866(f336(x74761),x74763),x74762))+P107(f866(f866(f243(x74761),f866(f68(x74761,f241(x74761)),x74762)),x74763))
% 157.76/157.53 [7727]~P107(f866(f66(x77271),x77273))+~P107(f866(f66(x77271),x77272))+~E(f866(f866(f108(f937(x77271,a925)),x77272),x77273),f195(f937(x77271,a925)))+E(f866(f866(f86(a930),f866(f40(x77271),x77272)),f866(f40(x77271),x77273)),f866(f40(x77271),f866(f866(f117(f937(x77271,a925)),x77272),x77273)))
% 157.76/157.53 [8499]~P37(x84991,x84993)+~P37(x84991,x84992)+~E(f866(f866(f108(f937(x84991,a925)),f866(f272(x84991,x84991),x84992)),f866(f292(x84991,x84991),x84993)),f195(f937(x84991,a925)))+P37(x84991,f866(f866(f117(f937(f936(x84991,x84991),a925)),x84992),x84993))
% 157.76/157.53 [8594]E(x85941,f866(f866(f41(a930),x85942),x85943))+~P107(f866(f866(f244(a930),f2(a930)),x85943))+~P107(f866(f866(f244(a930),x85942),f866(f866(f87(a930),x85943),f866(a119,x85941))))+~P107(f866(f866(f243(a930),f866(f866(f87(a930),x85943),x85941)),x85942))
% 157.76/157.53 [8725]~P107(f866(f66(x87251),x87252))+~P107(f866(f66(x87251),x87253))+E(f866(f866(f86(a930),f866(f40(x87251),x87252)),f866(f40(x87251),x87253)),f866(f40(x87251),f866(f866(f117(f937(x87251,a925)),x87252),x87253)))+P107(f866(f866(f336(x87251),f917(x87253,x87252,x87251)),f866(f866(f108(f937(x87251,a925)),x87252),x87253)))
% 157.76/157.53 [9121]~P120(x91212)+~E(x91211,f2(x91212))+~E(x91213,f2(x91212))+~P107(f866(f866(f244(x91212),f2(x91212)),f866(f866(f86(x91212),f866(f866(f87(x91212),x91213),x91213)),f866(f866(f87(x91212),x91211),x91211))))
% 157.76/157.53 [9647]~P37(x96471,x96473)+~P37(x96471,x96472)+P37(x96471,f866(f866(f117(f937(f936(x96471,x96471),a925)),x96472),x96473))+~P107(f866(f866(f243(f937(f936(x96471,x96471),a925)),f866(f866(f296(x96471,x96471,x96471),x96472),x96473)),x96472))
% 157.76/157.53 [9775]~P107(f866(x97751,x97753))+~P107(f866(f66(x97752),x97753))+P107(f866(x97751,f195(f937(x97752,a925))))+~P107(f866(x97751,f866(f866(f23(f937(x97752,a925)),f748(x97751,x97753,x97752)),f866(f866(f316(x97752),f736(x97751,x97753,x97752)),f195(f937(x97752,a925))))))
% 157.76/157.53 [8902]~P107(f866(f866(f244(a1),f2(a1)),x89023))+P107(f866(f866(f243(a1),f2(a1)),x89021))+~P107(f866(f866(f244(a1),x89022),x89023))+~P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),f866(f866(f87(a1),x89023),x89021)),x89022)))
% 157.76/157.53 [8926]~P83(x89261)+~P107(f866(f66(x89261),x89262))+E(f866(f866(f23(f937(x89261,a925)),x89262),f866(f866(f316(x89261),x89263),f195(f937(x89261,a925)))),f195(f937(x89261,a925)))+E(f866(f866(f117(x89261),x89263),f13(x89261,f866(f866(f23(f937(x89261,a925)),x89262),f866(f866(f316(x89261),x89263),f195(f937(x89261,a925)))))),f13(x89261,f866(f866(f316(x89261),x89263),x89262)))
% 157.76/157.53 [8927]~P83(x89271)+~P107(f866(f66(x89271),x89272))+E(f866(f866(f23(f937(x89271,a925)),x89272),f866(f866(f316(x89271),x89273),f195(f937(x89271,a925)))),f195(f937(x89271,a925)))+E(f866(f866(f108(x89271),x89273),f10(x89271,f866(f866(f23(f937(x89271,a925)),x89272),f866(f866(f316(x89271),x89273),f195(f937(x89271,a925)))))),f10(x89271,f866(f866(f316(x89271),x89273),x89272)))
% 157.76/157.53 [8928]~P110(x89281)+~P107(f866(f66(x89281),x89282))+E(f866(f866(f23(f937(x89281,a925)),x89282),f866(f866(f316(x89281),x89283),f195(f937(x89281,a925)))),f195(f937(x89281,a925)))+E(f866(f866(f242(x89281),x89283),f14(x89281,f866(f866(f23(f937(x89281,a925)),x89282),f866(f866(f316(x89281),x89283),f195(f937(x89281,a925)))))),f14(x89281,f866(f866(f316(x89281),x89283),x89282)))
% 157.76/157.53 [8929]~P110(x89291)+~P107(f866(f66(x89291),x89292))+E(f866(f866(f23(f937(x89291,a925)),x89292),f866(f866(f316(x89291),x89293),f195(f937(x89291,a925)))),f195(f937(x89291,a925)))+E(f866(f866(f241(x89291),x89293),f15(x89291,f866(f866(f23(f937(x89291,a925)),x89292),f866(f866(f316(x89291),x89293),f195(f937(x89291,a925)))))),f15(x89291,f866(f866(f316(x89291),x89293),x89292)))
% 157.76/157.53 [9001]~P110(x90011)+~P107(f866(f66(x90011),x90012))+E(f866(f866(f23(f937(x90011,a925)),x90012),f866(f866(f316(x90011),x90013),f195(f937(x90011,a925)))),f195(f937(x90011,a925)))+E(f866(f866(f241(x90011),x90013),f11(x90011,f241(x90011),f866(f866(f23(f937(x90011,a925)),x90012),f866(f866(f316(x90011),x90013),f195(f937(x90011,a925)))))),f11(x90011,f241(x90011),f866(f866(f316(x90011),x90013),x90012)))
% 157.76/157.53 [9002]~P110(x90021)+~P107(f866(f66(x90021),x90022))+E(f866(f866(f23(f937(x90021,a925)),x90022),f866(f866(f316(x90021),x90023),f195(f937(x90021,a925)))),f195(f937(x90021,a925)))+E(f866(f866(f242(x90021),x90023),f12(x90021,f242(x90021),f866(f866(f23(f937(x90021,a925)),x90022),f866(f866(f316(x90021),x90023),f195(f937(x90021,a925)))))),f12(x90021,f242(x90021),f866(f866(f316(x90021),x90023),x90022)))
% 157.76/157.53 [9587]E(x95871,x95872)+~E(f866(f149(f931(x95873),f931(x95873),f141(x95873),f120(x95873)),x95871),f866(f149(f931(x95873),f931(x95873),f141(x95873),f120(x95873)),x95872))+~E(f866(f196(f931(f931(x95873))),x95871),f866(f196(f931(f931(x95873))),x95872))+P107(f866(f866(f336(f936(f931(x95873),f931(x95873))),f711(x95872,x95871,x95873)),f866(f179(f936(f931(x95873),f931(x95873))),f866(f866(f188(f931(x95873),f931(x95873)),x95871),x95872))))
% 157.76/157.53 [9588]E(x95881,x95882)+~E(f866(f149(f931(x95883),f931(x95883),f141(x95883),f120(x95883)),x95881),f866(f149(f931(x95883),f931(x95883),f141(x95883),f120(x95883)),x95882))+~E(f866(f196(f931(f931(x95883))),x95881),f866(f196(f931(f931(x95883))),x95882))+P107(f866(f866(f336(f936(f931(x95883),f931(x95883))),f712(x95881,x95882,x95883)),f866(f179(f936(f931(x95883),f931(x95883))),f866(f866(f188(f931(x95883),f931(x95883)),x95882),x95881))))
% 157.76/157.53 [10431]~P101(x104312)+E(x104311,f195(f937(x104312,a925)))+~P107(f866(f66(x104312),x104311))+E(f10(x104312,f866(f270(x104312),f866(f866(f8(f937(x104312,a925),a925,x104312),f93(x104312)),f866(f866(f7(x104312,f937(x104312,a925),f937(x104312,a925)),f866(f866(f8(f937(x104312,f937(a925,a925)),f937(f937(x104312,a925),f937(x104312,a925)),x104312),f18(x104312,a925,a925)),f866(f866(f8(f937(x104312,a925),f937(x104312,f937(a925,a925)),x104312),f866(f8(a925,f937(a925,a925),x104312),a333)),f866(f866(f7(x104312,f937(x104312,x104312),f937(x104312,a925)),f866(f866(f8(f937(x104312,a925),f937(f937(x104312,x104312),f937(x104312,a925)),x104312),f8(x104312,a925,x104312)),a332)),f866(f117(x104312),x104313))))),f866(f866(f7(x104312,f937(x104312,a925),a925),f336(x104312)),x104311))))),f866(f866(f117(x104312),x104313),f10(x104312,x104311)))
% 157.76/157.53 [10432]~P78(x104322)+E(x104321,f195(f937(x104322,a925)))+~P107(f866(f66(x104322),x104321))+E(f14(x104322,f866(f270(x104322),f866(f866(f8(f937(x104322,a925),a925,x104322),f93(x104322)),f866(f866(f7(x104322,f937(x104322,a925),f937(x104322,a925)),f866(f866(f8(f937(x104322,f937(a925,a925)),f937(f937(x104322,a925),f937(x104322,a925)),x104322),f18(x104322,a925,a925)),f866(f866(f8(f937(x104322,a925),f937(x104322,f937(a925,a925)),x104322),f866(f8(a925,f937(a925,a925),x104322),a333)),f866(f866(f7(x104322,f937(x104322,x104322),f937(x104322,a925)),f866(f866(f8(f937(x104322,a925),f937(f937(x104322,x104322),f937(x104322,a925)),x104322),f8(x104322,a925,x104322)),a332)),f866(f86(x104322),x104323))))),f866(f866(f7(x104322,f937(x104322,a925),a925),f336(x104322)),x104321))))),f866(f866(f86(x104322),x104323),f14(x104322,x104321)))
% 157.76/157.53 [10433]~P78(x104332)+E(x104331,f195(f937(x104332,a925)))+~P107(f866(f66(x104332),x104331))+E(f15(x104332,f866(f270(x104332),f866(f866(f8(f937(x104332,a925),a925,x104332),f93(x104332)),f866(f866(f7(x104332,f937(x104332,a925),f937(x104332,a925)),f866(f866(f8(f937(x104332,f937(a925,a925)),f937(f937(x104332,a925),f937(x104332,a925)),x104332),f18(x104332,a925,a925)),f866(f866(f8(f937(x104332,a925),f937(x104332,f937(a925,a925)),x104332),f866(f8(a925,f937(a925,a925),x104332),a333)),f866(f866(f7(x104332,f937(x104332,x104332),f937(x104332,a925)),f866(f866(f8(f937(x104332,a925),f937(f937(x104332,x104332),f937(x104332,a925)),x104332),f8(x104332,a925,x104332)),a332)),f866(f86(x104332),x104333))))),f866(f866(f7(x104332,f937(x104332,a925),a925),f336(x104332)),x104331))))),f866(f866(f86(x104332),x104333),f15(x104332,x104331)))
% 157.76/157.53 [10434]~P101(x104342)+E(x104341,f195(f937(x104342,a925)))+~P107(f866(f66(x104342),x104341))+E(f13(x104342,f866(f270(x104342),f866(f866(f8(f937(x104342,a925),a925,x104342),f93(x104342)),f866(f866(f7(x104342,f937(x104342,a925),f937(x104342,a925)),f866(f866(f8(f937(x104342,f937(a925,a925)),f937(f937(x104342,a925),f937(x104342,a925)),x104342),f18(x104342,a925,a925)),f866(f866(f8(f937(x104342,a925),f937(x104342,f937(a925,a925)),x104342),f866(f8(a925,f937(a925,a925),x104342),a333)),f866(f866(f7(x104342,f937(x104342,x104342),f937(x104342,a925)),f866(f866(f8(f937(x104342,a925),f937(f937(x104342,x104342),f937(x104342,a925)),x104342),f8(x104342,a925,x104342)),a332)),f866(f108(x104342),x104343))))),f866(f866(f7(x104342,f937(x104342,a925),a925),f336(x104342)),x104341))))),f866(f866(f108(x104342),x104343),f13(x104342,x104341)))
% 157.76/157.53 [10435]~P110(x104352)+E(x104351,f195(f937(x104352,a925)))+~P107(f866(f66(x104352),x104351))+E(f12(x104352,f242(x104352),f866(f270(x104352),f866(f866(f8(f937(x104352,a925),a925,x104352),f93(x104352)),f866(f866(f7(x104352,f937(x104352,a925),f937(x104352,a925)),f866(f866(f8(f937(x104352,f937(a925,a925)),f937(f937(x104352,a925),f937(x104352,a925)),x104352),f18(x104352,a925,a925)),f866(f866(f8(f937(x104352,a925),f937(x104352,f937(a925,a925)),x104352),f866(f8(a925,f937(a925,a925),x104352),a333)),f866(f866(f7(x104352,f937(x104352,x104352),f937(x104352,a925)),f866(f866(f8(f937(x104352,a925),f937(f937(x104352,x104352),f937(x104352,a925)),x104352),f8(x104352,a925,x104352)),a332)),f866(f241(x104352),x104353))))),f866(f866(f7(x104352,f937(x104352,a925),a925),f336(x104352)),x104351))))),f866(f866(f241(x104352),x104353),f12(x104352,f242(x104352),x104351)))
% 157.76/157.53 [10436]~P110(x104362)+E(x104361,f195(f937(x104362,a925)))+~P107(f866(f66(x104362),x104361))+E(f11(x104362,f241(x104362),f866(f270(x104362),f866(f866(f8(f937(x104362,a925),a925,x104362),f93(x104362)),f866(f866(f7(x104362,f937(x104362,a925),f937(x104362,a925)),f866(f866(f8(f937(x104362,f937(a925,a925)),f937(f937(x104362,a925),f937(x104362,a925)),x104362),f18(x104362,a925,a925)),f866(f866(f8(f937(x104362,a925),f937(x104362,f937(a925,a925)),x104362),f866(f8(a925,f937(a925,a925),x104362),a333)),f866(f866(f7(x104362,f937(x104362,x104362),f937(x104362,a925)),f866(f866(f8(f937(x104362,a925),f937(f937(x104362,x104362),f937(x104362,a925)),x104362),f8(x104362,a925,x104362)),a332)),f866(f242(x104362),x104363))))),f866(f866(f7(x104362,f937(x104362,a925),a925),f336(x104362)),x104361))))),f866(f866(f242(x104362),x104363),f11(x104362,f241(x104362),x104361)))
% 157.76/157.53 [10162]~P128(x101621)+~E(x101623,f2(x101621))+~E(x101622,f2(x101621))+E(f866(f866(f86(x101621),f866(f866(f252(x101621),x101622),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x101621),x101623),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f2(x101621))
% 157.76/157.53 [10303]~P113(x103031)+~P107(f866(f866(f243(x103031),f2(x103031)),x103033))+P107(f866(f866(f243(x103031),x103032),x103033))+~P107(f866(f866(f243(x103031),f866(f866(f252(x103031),x103032),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103031),x103033),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))))
% 157.76/157.53 [10360]~P128(x103602)+~E(x103601,f2(x103602))+~E(x103603,f2(x103602))+~P107(f866(f866(f244(x103602),f2(x103602)),f866(f866(f86(x103602),f866(f866(f252(x103602),x103603),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104))))),f866(f866(f252(x103602),x103601),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))))
% 157.76/157.53 [6952]~P7(x69523,x69522)+~P107(f866(x69521,x69524))+~P107(f866(f866(f336(x69523),x69524),f278(x69523,x69522)))+P107(f866(x69521,f828(x69521,x69522,x69523)))
% 157.76/157.53 [8837]P26(x88371,x88372,f832(x88373,x88372,x88374,x88371),x88374,x88373)+~E(f866(f40(x88371),x88374),f866(f40(x88372),x88373))+~P107(f866(f66(x88372),x88373))+~P107(f866(f66(x88371),x88374))
% 157.76/157.53 [9550]E(x95501,x95502)+~E(f664(x95501,x95502,x95504,x95503),f665(x95501,x95502,x95504,x95503))+P107(f866(f866(f336(f936(f931(x95503),f931(x95503))),f866(f866(f260(f931(x95503),f931(x95503)),x95502),x95501)),f154(x95503,x95504)))+P107(f866(f866(f336(f936(f931(x95503),f931(x95503))),f866(f866(f260(f931(x95503),f931(x95503)),x95501),x95502)),f154(x95503,x95504)))
% 157.76/157.53 [5094]~P65(x50942)+~E(x50944,f2(x50942))+~E(x50941,f2(x50942))+E(x50941,f866(f866(f297(x50942),x50943),x50944))
% 157.76/157.53 [5095]~P65(x50951)+~E(x50953,f2(x50951))+~E(x50954,f2(x50951))+E(f866(f866(f297(x50951),x50952),x50953),x50954)
% 157.76/157.53 [5211]~P65(x52112)+E(x52111,f2(x52112))+~E(x52113,f2(x52112))+~E(x52111,f866(f866(f297(x52112),x52114),x52113))
% 157.76/157.53 [5212]~P65(x52122)+E(x52121,f2(x52122))+~E(x52123,f2(x52122))+~E(f866(f866(f297(x52122),x52124),x52123),x52121)
% 157.76/157.53 [5392]~P125(x53922)+E(x53921,f2(x53922))+~E(f866(f866(f297(x53922),x53923),x53921),x53924)+E(x53923,f866(f866(f87(x53922),x53924),x53921))
% 157.76/157.53 [5394]~P125(x53942)+E(x53941,f2(x53942))+~E(f866(f866(f87(x53942),x53943),x53941),x53944)+E(x53943,f866(f866(f297(x53942),x53944),x53941))
% 157.76/157.53 [5395]~P65(x53952)+E(x53951,f2(x53952))+~E(f866(f866(f297(x53952),x53953),x53951),x53954)+E(x53953,f866(f866(f87(x53952),x53954),x53951))
% 157.76/157.53 [5396]~P65(x53962)+E(x53961,f2(x53962))+~E(f866(f866(f87(x53962),x53963),x53961),x53964)+E(x53963,f866(f866(f297(x53962),x53964),x53961))
% 157.76/157.53 [5397]~P125(x53972)+E(x53971,f2(x53972))+~E(x53973,f866(f866(f297(x53972),x53974),x53971))+E(f866(f866(f87(x53972),x53973),x53971),x53974)
% 157.76/157.53 [5399]~P125(x53992)+E(x53991,f2(x53992))+~E(x53993,f866(f866(f87(x53992),x53994),x53991))+E(f866(f866(f297(x53992),x53993),x53991),x53994)
% 157.76/157.53 [5400]~P65(x54002)+E(x54001,f2(x54002))+~E(x54003,f866(f866(f297(x54002),x54004),x54001))+E(f866(f866(f87(x54002),x54003),x54001),x54004)
% 157.76/157.53 [5401]~P65(x54012)+E(x54011,f2(x54012))+~E(x54013,f866(f866(f87(x54012),x54014),x54011))+E(f866(f866(f297(x54012),x54013),x54011),x54014)
% 157.76/157.53 [5425]~P65(x54252)+~E(x54251,f2(x54252))+~E(f866(f866(f87(x54252),x54251),x54254),x54253)+E(x54251,f866(f866(f297(x54252),x54253),x54254))
% 157.76/157.53 [5426]~P65(x54261)+~E(x54264,f2(x54261))+~E(x54262,f866(f866(f87(x54261),x54264),x54263))+E(f866(f866(f297(x54261),x54262),x54263),x54264)
% 157.76/157.53 [5502]~E(x55023,x55024)+~E(x55022,x55023)+~P111(x55021)+E(f310(x55021,x55022,x55023),f866(f866(f316(x55021),x55024),f195(f937(x55021,a925))))
% 157.76/157.53 [5706]~E(f121(x57062,x57061),x57063)+~E(f151(x57062,x57061),x57064)+E(x57061,f120(x57062))+E(f866(f866(f141(x57062),x57063),f866(f866(f158(x57062),x57064),f120(x57062))),x57061)
% 157.76/157.53 [6342]~P113(x63423)+E(x63421,x63422)+~E(f866(f866(f252(x63423),x63424),x63421),f866(f866(f252(x63423),x63424),x63422))+~P107(f866(f866(f244(x63423),f84(x63423)),x63424))
% 157.76/157.53 [6343]E(x63431,x63432)+~E(f866(f866(f316(x63433),x63434),x63431),f866(f866(f316(x63433),x63434),x63432))+P107(f866(f866(f336(x63433),x63434),x63432))+P107(f866(f866(f336(x63433),x63434),x63431))
% 157.76/157.53 [6385]E(f866(x63851,x63852),f84(a930))+~E(f866(f866(f9(x63853,a930),x63851),x63854),f84(a930))+~P107(f866(f66(x63853),x63854))+~P107(f866(f866(f336(x63853),x63852),x63854))
% 157.76/157.53 [6386]E(f866(x63861,x63862),f2(a930))+~E(f866(f866(f6(x63863,a930),x63861),x63864),f2(a930))+~P107(f866(f66(x63863),x63864))+~P107(f866(f866(f336(x63863),x63862),x63864))
% 157.76/157.53 [6604]~P111(x66041)+~P107(f866(f866(f243(x66041),x66044),x66043))+P107(f866(f866(f243(x66041),x66042),x66043))+~P107(f866(f866(f243(x66041),x66042),x66044))
% 157.76/157.53 [6605]~P108(x66051)+~P107(f866(f866(f243(x66051),x66052),x66054))+P107(f866(f866(f243(x66051),x66052),x66053))+~P107(f866(f866(f243(x66051),x66054),x66053))
% 157.76/157.53 [6606]~P111(x66061)+~P107(f866(f866(f244(x66061),x66064),x66063))+P107(f866(f866(f244(x66061),x66062),x66063))+~P107(f866(f866(f243(x66061),x66062),x66064))
% 157.76/157.53 [6607]~P111(x66071)+~P107(f866(f866(f244(x66071),x66072),x66074))+P107(f866(f866(f244(x66071),x66072),x66073))+~P107(f866(f866(f243(x66071),x66074),x66073))
% 157.76/157.53 [6608]~P111(x66081)+~P107(f866(f866(f244(x66081),x66084),x66083))+P107(f866(f866(f244(x66081),x66082),x66083))+~P107(f866(f866(f244(x66081),x66082),x66084))
% 157.76/157.53 [6609]~P108(x66091)+~P107(f866(f866(f244(x66091),x66092),x66094))+P107(f866(f866(f244(x66091),x66092),x66093))+~P107(f866(f866(f243(x66091),x66094),x66093))
% 157.76/157.53 [6610]~P108(x66101)+~P107(f866(f866(f244(x66101),x66104),x66103))+P107(f866(f866(f244(x66101),x66102),x66103))+~P107(f866(f866(f243(x66101),x66102),x66104))
% 157.76/157.53 [6611]~P108(x66111)+~P107(f866(f866(f244(x66111),x66112),x66114))+P107(f866(f866(f244(x66111),x66112),x66113))+~P107(f866(f866(f244(x66111),x66114),x66113))
% 157.76/157.53 [6690]~P123(x66902)+P57(x66902,x66903,x66904)+E(x66901,f2(x66902))+~P57(x66902,f866(f866(f87(x66902),x66903),x66901),f866(f866(f87(x66902),x66904),x66901))
% 157.76/157.53 [6691]~P123(x66912)+P57(x66912,x66913,x66914)+E(x66911,f2(x66912))+~P57(x66912,f866(f866(f87(x66912),x66911),x66913),f866(f866(f87(x66912),x66911),x66914))
% 157.76/157.53 [6696]~P35(x66964,x66963,x66962)+E(x66961,f774(x66962,x66963,x66964))+~P107(f866(x66963,x66961))+~P107(f866(f866(f336(x66964),x66961),f866(f179(x66964),x66962)))
% 157.76/157.53 [6697]~P35(x66974,x66973,x66972)+E(x66971,f777(x66972,x66973,x66974))+~P107(f866(x66973,x66971))+~P107(f866(f866(f336(x66974),x66971),f866(f179(x66974),x66972)))
% 157.76/157.53 [6846]~P5(x68461)+~P107(f866(f866(f243(x68461),x68462),f43(x68461,x68464)))+P107(f866(f866(f243(x68461),x68462),x68463))+~P107(f866(f866(f336(x68461),x68463),x68464))
% 157.76/157.53 [6990]~P110(x69901)+~P13(x69901,f866(f866(f158(x69901),x69902),x69904))+~P107(f866(f866(f336(x69901),x69903),f866(f179(x69901),x69904)))+P107(f866(f866(f243(x69901),x69902),x69903))
% 157.76/157.53 [7078]~P5(x70781)+~P107(f866(f866(f243(x70781),f42(x70781,x70784)),x70783))+P107(f866(f866(f243(x70781),x70782),x70783))+~P107(f866(f866(f336(x70781),x70782),x70784))
% 157.76/157.53 [7478]~P110(x74781)+E(f866(f866(f117(f937(x74781,a925)),f866(f309(x74781,x74782),x74783)),f866(f309(x74781,x74783),x74784)),f866(f309(x74781,x74782),x74784))+~P107(f866(f866(f243(x74781),x74783),x74784))+~P107(f866(f866(f243(x74781),x74782),x74783))
% 157.76/157.53 [7525]P35(x75251,x75252,x75253)+~E(f779(x75253,x75252,x75251,x75254),x75254)+~P107(f866(x75252,x75254))+~P107(f866(f866(f336(x75251),x75254),f866(f179(x75251),x75253)))
% 157.76/157.53 [7526]P35(x75261,x75262,x75263)+~E(f788(x75263,x75262,x75261,x75264),x75264)+~P107(f866(x75262,x75264))+~P107(f866(f866(f336(x75261),x75264),f866(f179(x75261),x75263)))
% 157.76/157.53 [7599]~P110(x75991)+E(f866(f866(f117(f937(x75991,a925)),f866(f309(x75991,x75992),x75993)),f310(x75991,x75993,x75994)),f310(x75991,x75992,x75994))+~P107(f866(f866(f243(x75991),x75993),x75994))+~P107(f866(f866(f243(x75991),x75992),x75993))
% 157.76/157.53 [7660]~P110(x76601)+E(f866(f866(f117(f937(x76601,a925)),f313(x76601,x76602,x76603)),f866(f309(x76601,x76603),x76604)),f313(x76601,x76602,x76604))+~P107(f866(f866(f243(x76601),x76603),x76604))+~P107(f866(f866(f244(x76601),x76602),x76603))
% 157.76/157.53 [7677]~P110(x76771)+E(f866(f866(f117(f937(x76771,a925)),f310(x76771,x76772,x76773)),f313(x76771,x76773,x76774)),f866(f309(x76771,x76772),x76774))+~P107(f866(f866(f243(x76771),x76772),x76773))+~P107(f866(f866(f244(x76771),x76773),x76774))
% 157.76/157.53 [7708]~P110(x77081)+E(f866(f866(f117(f937(x77081,a925)),f313(x77081,x77082,x77083)),f310(x77081,x77083,x77084)),f312(x77081,x77082,x77084))+~P107(f866(f866(f243(x77081),x77083),x77084))+~P107(f866(f866(f244(x77081),x77082),x77083))
% 157.76/157.53 [7709]~P110(x77091)+E(f866(f866(f117(f937(x77091,a925)),f310(x77091,x77092,x77093)),f312(x77091,x77093,x77094)),f310(x77091,x77092,x77094))+~P107(f866(f866(f243(x77091),x77093),x77094))+~P107(f866(f866(f243(x77091),x77092),x77093))
% 157.76/157.53 [7710]~P110(x77101)+E(f866(f866(f117(f937(x77101,a925)),f312(x77101,x77102,x77103)),f313(x77101,x77103,x77104)),f313(x77101,x77102,x77104))+~P107(f866(f866(f243(x77101),x77102),x77103))+~P107(f866(f866(f244(x77101),x77103),x77104))
% 157.76/157.53 [7711]~P110(x77111)+E(f866(f866(f117(f937(x77111,a925)),f312(x77111,x77112,x77113)),f312(x77111,x77113,x77114)),f312(x77111,x77112,x77114))+~P107(f866(f866(f243(x77111),x77113),x77114))+~P107(f866(f866(f243(x77111),x77112),x77113))
% 157.76/157.53 [8483]P25(x84831,x84832,f890(x84833,x84832,x84834,x84831),x84834)+~P107(f866(f66(x84832),x84833))+~P107(f866(f66(x84831),x84834))+~P107(f866(f866(f243(a930),f866(f40(x84831),x84834)),f866(f40(x84832),x84833)))
% 157.76/157.53 [8504]P35(x85041,x85042,x85043)+~P107(f866(x85042,x85044))+P107(f866(x85042,f779(x85043,x85042,x85041,x85044)))+~P107(f866(f866(f336(x85041),x85044),f866(f179(x85041),x85043)))
% 157.76/157.53 [8505]P35(x85051,x85052,x85053)+~P107(f866(x85052,x85054))+P107(f866(x85052,f788(x85053,x85052,x85051,x85054)))+~P107(f866(f866(f336(x85051),x85054),f866(f179(x85051),x85053)))
% 157.76/157.53 [8560]~P71(x85601)+~E(f866(x85603,f483(x85603,x85604,x85602,x85601)),f84(x85601))+E(f866(f866(f866(f70(x85601,x85602,f87(x85601)),x85603),f84(x85601)),x85604),f84(x85601))+~P107(f866(f66(x85602),x85604))
% 157.76/157.53 [8826]~P113(x88261)+~P107(f866(f866(f243(x88261),f2(x88261)),x88263))+P107(f866(f866(f243(x88261),x88262),x88263))+~P107(f866(f866(f243(x88261),f866(f866(f252(x88261),x88262),f866(a119,x88264))),f866(f866(f252(x88261),x88263),f866(a119,x88264))))
% 157.76/157.53 [9148]P35(x91481,x91482,x91483)+~P107(f866(x91482,x91484))+~P107(f866(f866(f336(x91481),x91484),f866(f179(x91481),x91483)))+P107(f866(f866(f336(x91481),f779(x91483,x91482,x91481,x91484)),f866(f179(x91481),x91483)))
% 157.76/157.53 [9149]P35(x91491,x91492,x91493)+~P107(f866(x91492,x91494))+~P107(f866(f866(f336(x91491),x91494),f866(f179(x91491),x91493)))+P107(f866(f866(f336(x91491),f788(x91493,x91492,x91491,x91494)),f866(f179(x91491),x91493)))
% 157.76/157.53 [9227]~P71(x92271)+E(f866(f866(f866(f70(x92271,x92272,f87(x92271)),x92273),f84(x92271)),x92274),f84(x92271))+~P107(f866(f66(x92272),x92274))+P107(f866(f866(f336(x92272),f483(x92273,x92274,x92272,x92271)),x92274))
% 157.76/157.53 [9718]~P107(f866(f866(f243(a1),x97184),f2(a1)))+P107(f866(f866(f243(a1),f866(f866(f86(a1),f866(f866(f87(a1),x97181),f50(a1,x97182,x97183))),x97184)),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x97183))+~P107(f866(f866(f244(a1),x97181),x97184))
% 157.76/157.53 [10155]~P107(f866(f66(x101551),x101552))+~P107(f866(f866(f336(x101551),x101554),x101552))+~P107(f866(f866(f336(x101551),x101553),x101552))+P107(f866(f866(f244(a930),f866(f40(x101551),f866(f866(f23(f937(x101551,a925)),f866(f866(f23(f937(x101551,a925)),x101552),f866(f866(f316(x101551),x101553),f195(f937(x101551,a925))))),f866(f866(f316(x101551),x101554),f195(f937(x101551,a925)))))),f866(f40(x101551),x101552)))
% 157.76/157.53 [7134]~P147(x71343)+~P124(x71343)+P107(f866(x71341,f863(x71342,x71341,x71343)))+~P107(f866(x71341,f866(f866(f87(x71343),x71342),x71344)))
% 157.76/157.53 [7191]~P103(x71911)+~P107(f866(f866(f243(x71911),x71912),x71914))+~P107(f866(f866(f243(x71911),x71912),x71913))+P107(f866(f866(f243(x71911),x71912),f866(f866(f108(x71911),x71913),x71914)))
% 157.76/157.53 [7194]~P110(x71941)+~P107(f866(f866(f243(x71941),x71942),x71944))+~P107(f866(f866(f243(x71941),x71942),x71943))+P107(f866(f866(f243(x71941),x71942),f866(f866(f241(x71941),x71943),x71944)))
% 157.76/157.53 [7195]~P110(x71951)+~P107(f866(f866(f244(x71951),x71952),x71954))+~P107(f866(f866(f244(x71951),x71952),x71953))+P107(f866(f866(f244(x71951),x71952),f866(f866(f241(x71951),x71953),x71954)))
% 157.76/157.53 [7215]~P66(x72152)+E(x72151,f2(x72152))+E(f866(f866(f297(x72152),f866(f866(f252(x72152),x72151),x72153)),f866(f866(f252(x72152),x72151),x72154)),f866(f866(f252(x72152),x72151),f866(f866(f23(a930),x72153),x72154)))+~P107(f866(f866(f243(a930),x72154),x72153))
% 157.76/157.53 [7259]~P110(x72591)+~P13(x72591,f866(f866(f158(x72591),x72593),x72594))+P13(x72591,f866(f866(f158(x72591),x72592),f866(f866(f158(x72591),x72593),x72594)))+~P107(f866(f866(f243(x72591),x72592),x72593))
% 157.76/157.53 [7295]~P86(x72951)+~P107(f866(f866(f243(x72951),f2(x72951)),x72954))+~P107(f866(f866(f243(x72951),x72952),x72953))+P107(f866(f866(f243(x72951),x72952),f866(f866(f86(x72951),x72953),x72954)))
% 157.76/157.53 [7296]~P86(x72961)+~P107(f866(f866(f243(x72961),f2(x72961)),x72963))+~P107(f866(f866(f243(x72961),x72962),x72964))+P107(f866(f866(f243(x72961),x72962),f866(f866(f86(x72961),x72963),x72964)))
% 157.76/157.53 [7297]~P113(x72971)+~P107(f866(f866(f244(x72971),f2(x72971)),x72973))+~P107(f866(f866(f244(x72971),x72972),x72974))+P107(f866(f866(f244(x72971),x72972),f866(f866(f86(x72971),x72973),x72974)))
% 157.76/157.53 [7298]~P86(x72981)+~P107(f866(f866(f243(x72981),x72982),x72984))+~P107(f866(f866(f244(x72981),f2(x72981)),x72983))+P107(f866(f866(f244(x72981),x72982),f866(f866(f86(x72981),x72983),x72984)))
% 157.76/157.53 [7299]~P86(x72991)+~P107(f866(f866(f243(x72991),f2(x72991)),x72993))+~P107(f866(f866(f244(x72991),x72992),x72994))+P107(f866(f866(f244(x72991),x72992),f866(f866(f86(x72991),x72993),x72994)))
% 157.76/157.53 [7340]~P110(x73401)+P107(f866(f866(f243(x73401),x73402),x73403))+P107(f866(f866(f243(x73401),x73402),x73404))+~P107(f866(f866(f243(x73401),x73402),f866(f866(f242(x73401),x73404),x73403)))
% 157.76/157.53 [7341]~P110(x73411)+P107(f866(f866(f244(x73411),x73412),x73413))+P107(f866(f866(f244(x73411),x73412),x73414))+~P107(f866(f866(f244(x73411),x73412),f866(f866(f242(x73411),x73414),x73413)))
% 157.76/157.53 [7632]~P111(x76322)+~P64(x76321)+~P107(f866(f866(f244(f937(x76321,x76322)),x76323),x76324))+P107(f866(f866(f243(f937(x76321,x76322)),x76323),x76324))
% 157.76/157.53 [7970]~P147(x79701)+~P124(x79701)+P57(x79701,x79702,f866(f866(f86(x79701),f863(x79702,x79703,x79701)),f2(x79701)))+~P107(f866(x79703,f866(f866(f87(x79701),x79702),x79704)))
% 157.76/157.53 [7993]~P68(x79931)+~P107(f866(f866(f244(x79931),x79934),f2(x79931)))+~P107(f866(f866(f243(x79931),x79933),f866(f866(f297(x79931),x79932),x79934)))+P107(f866(f866(f243(x79931),x79932),f866(f866(f87(x79931),x79933),x79934)))
% 157.76/157.53 [7994]~P68(x79941)+~P107(f866(f866(f244(x79941),x79944),f2(x79941)))+~P107(f866(f866(f243(x79941),x79943),f866(f866(f87(x79941),x79942),x79944)))+P107(f866(f866(f243(x79941),x79942),f866(f866(f297(x79941),x79943),x79944)))
% 157.76/157.53 [7995]~P68(x79951)+~P107(f866(f866(f244(x79951),x79954),f2(x79951)))+~P107(f866(f866(f244(x79951),x79953),f866(f866(f297(x79951),x79952),x79954)))+P107(f866(f866(f244(x79951),x79952),f866(f866(f87(x79951),x79953),x79954)))
% 157.76/157.53 [7996]~P68(x79961)+~P107(f866(f866(f244(x79961),x79964),f2(x79961)))+~P107(f866(f866(f244(x79961),x79963),f866(f866(f87(x79961),x79962),x79964)))+P107(f866(f866(f244(x79961),x79962),f866(f866(f297(x79961),x79963),x79964)))
% 157.76/157.53 [8099]~P120(x80991)+~P107(f866(f866(f244(x80991),x80992),f2(x80991)))+~P107(f866(f866(f243(x80991),x80994),x80993))+P107(f866(f866(f243(x80991),f866(f866(f87(x80991),x80992),x80993)),f866(f866(f87(x80991),x80992),x80994)))
% 157.76/157.53 [8100]~P138(x81001)+~P107(f866(f866(f243(x81001),x81002),f2(x81001)))+~P107(f866(f866(f243(x81001),x81004),x81003))+P107(f866(f866(f243(x81001),f866(f866(f87(x81001),x81002),x81003)),f866(f866(f87(x81001),x81002),x81004)))
% 157.76/157.53 [8101]~P138(x81011)+~P107(f866(f866(f243(x81011),x81013),f2(x81011)))+~P107(f866(f866(f243(x81011),x81014),x81012))+P107(f866(f866(f243(x81011),f866(f866(f87(x81011),x81012),x81013)),f866(f866(f87(x81011),x81014),x81013)))
% 157.76/157.53 [8102]~P67(x81021)+~P107(f866(f866(f243(x81021),x81023),f2(x81021)))+~P107(f866(f866(f243(x81021),x81024),x81022))+P107(f866(f866(f243(x81021),f866(f866(f297(x81021),x81022),x81023)),f866(f866(f297(x81021),x81024),x81023)))
% 157.76/157.53 [8106]~P120(x81061)+~P107(f866(f866(f244(x81061),x81063),f2(x81061)))+~P107(f866(f866(f244(x81061),x81064),x81062))+P107(f866(f866(f244(x81061),f866(f866(f87(x81061),x81062),x81063)),f866(f866(f87(x81061),x81064),x81063)))
% 157.76/157.53 [8107]~P120(x81071)+~P107(f866(f866(f244(x81071),x81072),f2(x81071)))+~P107(f866(f866(f244(x81071),x81074),x81073))+P107(f866(f866(f244(x81071),f866(f866(f87(x81071),x81072),x81073)),f866(f866(f87(x81071),x81072),x81074)))
% 157.76/157.53 [8108]~P68(x81081)+~P107(f866(f866(f244(x81081),x81083),f2(x81081)))+~P107(f866(f866(f244(x81081),x81084),x81082))+P107(f866(f866(f244(x81081),f866(f866(f297(x81081),x81082),x81083)),f866(f866(f297(x81081),x81084),x81083)))
% 157.76/157.53 [8109]~P113(x81091)+~P107(f866(f866(f244(x81091),f84(x81091)),x81092))+~P107(f866(f866(f243(a930),x81093),x81094))+P107(f866(f866(f243(x81091),f866(f866(f252(x81091),x81092),x81093)),f866(f866(f252(x81091),x81092),x81094)))
% 157.76/157.53 [8110]~P113(x81101)+~P107(f866(f866(f243(x81101),f84(x81101)),x81102))+~P107(f866(f866(f243(a930),x81103),x81104))+P107(f866(f866(f243(x81101),f866(f866(f252(x81101),x81102),x81103)),f866(f866(f252(x81101),x81102),x81104)))
% 157.76/157.53 [8112]~P113(x81121)+~P107(f866(f866(f244(x81121),f84(x81121)),x81122))+~P107(f866(f866(f244(a930),x81123),x81124))+P107(f866(f866(f244(x81121),f866(f866(f252(x81121),x81122),x81123)),f866(f866(f252(x81121),x81122),x81124)))
% 157.76/157.53 [8139]P107(f866(f866(f244(a930),f2(a930)),f866(x81391,x81392)))+~P107(f866(f66(x81393),x81394))+~P107(f866(f866(f336(x81393),x81392),x81394))+~P107(f866(f866(f244(a930),f2(a930)),f866(f866(f9(x81393,a930),x81391),x81394)))
% 157.76/157.53 [8147]~P120(x81471)+~P107(f866(f866(f244(x81471),f2(x81471)),x81472))+~P107(f866(f866(f243(x81471),x81473),x81474))+P107(f866(f866(f243(x81471),f866(f866(f87(x81471),x81472),x81473)),f866(f866(f87(x81471),x81472),x81474)))
% 157.76/157.53 [8148]~P140(x81481)+~P107(f866(f866(f243(x81481),x81483),x81484))+~P107(f866(f866(f243(x81481),f2(x81481)),x81482))+P107(f866(f866(f243(x81481),f866(f866(f87(x81481),x81482),x81483)),f866(f866(f87(x81481),x81482),x81484)))
% 157.76/157.53 [8149]~P139(x81491)+~P107(f866(f866(f243(x81491),x81493),x81494))+~P107(f866(f866(f243(x81491),f2(x81491)),x81492))+P107(f866(f866(f243(x81491),f866(f866(f87(x81491),x81492),x81493)),f866(f866(f87(x81491),x81492),x81494)))
% 157.76/157.53 [8150]~P140(x81501)+~P107(f866(f866(f243(x81501),x81502),x81504))+~P107(f866(f866(f243(x81501),f2(x81501)),x81503))+P107(f866(f866(f243(x81501),f866(f866(f87(x81501),x81502),x81503)),f866(f866(f87(x81501),x81504),x81503)))
% 157.76/157.53 [8151]~P113(x81511)+~P107(f866(f866(f243(x81511),x81512),x81514))+~P107(f866(f866(f243(x81511),f2(x81511)),x81512))+P107(f866(f866(f243(x81511),f866(f866(f252(x81511),x81512),x81513)),f866(f866(f252(x81511),x81514),x81513)))
% 157.76/157.53 [8152]~P67(x81521)+~P107(f866(f866(f243(x81521),x81522),x81524))+~P107(f866(f866(f243(x81521),f2(x81521)),x81523))+P107(f866(f866(f243(x81521),f866(f866(f297(x81521),x81522),x81523)),f866(f866(f297(x81521),x81524),x81523)))
% 157.76/157.53 [8154]~P122(x81541)+~P107(f866(f866(f244(x81541),x81543),x81544))+~P107(f866(f866(f244(x81541),f2(x81541)),x81542))+P107(f866(f866(f244(x81541),f866(f866(f87(x81541),x81542),x81543)),f866(f866(f87(x81541),x81542),x81544)))
% 157.76/157.53 [8155]~P132(x81551)+~P107(f866(f866(f244(x81551),x81553),x81554))+~P107(f866(f866(f244(x81551),f2(x81551)),x81552))+P107(f866(f866(f244(x81551),f866(f866(f87(x81551),x81552),x81553)),f866(f866(f87(x81551),x81552),x81554)))
% 157.76/157.53 [8156]~P120(x81561)+~P107(f866(f866(f244(x81561),x81562),x81564))+~P107(f866(f866(f244(x81561),f2(x81561)),x81563))+P107(f866(f866(f244(x81561),f866(f866(f87(x81561),x81562),x81563)),f866(f866(f87(x81561),x81564),x81563)))
% 157.76/157.53 [8157]~P132(x81571)+~P107(f866(f866(f244(x81571),x81572),x81574))+~P107(f866(f866(f244(x81571),f2(x81571)),x81573))+P107(f866(f866(f244(x81571),f866(f866(f87(x81571),x81572),x81573)),f866(f866(f87(x81571),x81574),x81573)))
% 157.76/157.53 [8158]~P120(x81581)+~P107(f866(f866(f244(x81581),x81583),x81584))+~P107(f866(f866(f244(x81581),f2(x81581)),x81582))+P107(f866(f866(f244(x81581),f866(f866(f87(x81581),x81582),x81583)),f866(f866(f87(x81581),x81582),x81584)))
% 157.76/157.53 [8159]~P68(x81591)+~P107(f866(f866(f244(x81591),x81592),x81594))+~P107(f866(f866(f244(x81591),f2(x81591)),x81593))+P107(f866(f866(f244(x81591),f866(f866(f297(x81591),x81592),x81593)),f866(f866(f297(x81591),x81594),x81593)))
% 157.76/157.53 [8202]~P109(x82022)+P107(f866(f866(f244(f937(x82021,x82022)),x82024),x82023))+~P107(f866(f866(f243(f937(x82021,x82022)),x82024),x82023))+P107(f866(f866(f243(f937(x82021,x82022)),x82023),x82024))
% 157.76/157.53 [8242]P107(f866(f866(f336(x82421),x82422),x82423))+P107(f866(f866(f336(x82421),x82422),x82424))+~P107(f866(f866(f243(f937(x82421,a925)),x82424),x82423))+P107(f866(f866(f244(f937(x82421,a925)),x82424),f866(f866(f316(x82421),x82422),x82423)))
% 157.76/157.53 [8396]P107(f866(f866(f336(x83961),x83962),x83963))+P107(f866(f866(f336(x83961),x83962),x83964))+~P107(f866(f866(f244(f937(x83961,a925)),x83964),f866(f866(f316(x83961),x83962),x83963)))+P107(f866(f866(f243(f937(x83961,a925)),x83964),x83963))
% 157.76/157.53 [8461]~P120(x84611)+P107(f866(f866(f244(x84611),x84613),x84612))+P107(f866(f866(f244(x84611),x84612),x84613))+~P107(f866(f866(f244(x84611),f866(f866(f87(x84611),x84614),x84612)),f866(f866(f87(x84611),x84614),x84613)))
% 157.76/157.53 [8462]~P120(x84621)+P107(f866(f866(f244(x84621),x84623),x84622))+P107(f866(f866(f244(x84621),x84622),x84623))+~P107(f866(f866(f244(x84621),f866(f866(f87(x84621),x84622),x84624)),f866(f866(f87(x84621),x84623),x84624)))
% 157.76/157.53 [8473]~P120(x84731)+P107(f866(f866(f244(x84731),x84734),f2(x84731)))+P107(f866(f866(f244(x84731),x84732),x84733))+~P107(f866(f866(f244(x84731),f866(f866(f87(x84731),x84732),x84734)),f866(f866(f87(x84731),x84733),x84734)))
% 157.76/157.53 [8474]~P120(x84741)+P107(f866(f866(f244(x84741),x84744),f2(x84741)))+P107(f866(f866(f244(x84741),x84742),x84743))+~P107(f866(f866(f244(x84741),f866(f866(f87(x84741),x84744),x84742)),f866(f866(f87(x84741),x84744),x84743)))
% 157.76/157.53 [8477]~P120(x84771)+P107(f866(f866(f244(x84771),x84772),x84773))+P107(f866(f866(f244(x84771),f2(x84771)),x84774))+~P107(f866(f866(f244(x84771),f866(f866(f87(x84771),x84774),x84773)),f866(f866(f87(x84771),x84774),x84772)))
% 157.76/157.53 [8478]~P120(x84781)+P107(f866(f866(f244(x84781),x84782),x84783))+P107(f866(f866(f244(x84781),f2(x84781)),x84784))+~P107(f866(f866(f244(x84781),f866(f866(f87(x84781),x84783),x84784)),f866(f866(f87(x84781),x84782),x84784)))
% 157.76/157.53 [8491]~P120(x84911)+P107(f866(f866(f244(x84911),x84912),f2(x84911)))+P107(f866(f866(f244(x84911),f2(x84911)),x84912))+~P107(f866(f866(f244(x84911),f866(f866(f87(x84911),x84913),x84912)),f866(f866(f87(x84911),x84914),x84912)))
% 157.76/157.53 [8492]~P120(x84921)+P107(f866(f866(f244(x84921),x84922),f2(x84921)))+P107(f866(f866(f244(x84921),f2(x84921)),x84922))+~P107(f866(f866(f244(x84921),f866(f866(f87(x84921),x84922),x84923)),f866(f866(f87(x84921),x84922),x84924)))
% 157.76/157.53 [8522]~P120(x85221)+~P107(f866(f866(f244(x85221),x85224),f2(x85221)))+P107(f866(f866(f243(x85221),x85222),x85223))+~P107(f866(f866(f243(x85221),f866(f866(f87(x85221),x85224),x85223)),f866(f866(f87(x85221),x85224),x85222)))
% 157.76/157.53 [8523]~P120(x85231)+~P107(f866(f866(f244(x85231),x85234),f2(x85231)))+P107(f866(f866(f244(x85231),x85232),x85233))+~P107(f866(f866(f244(x85231),f866(f866(f87(x85231),x85234),x85233)),f866(f866(f87(x85231),x85234),x85232)))
% 157.76/157.53 [8534]~P113(x85343)+~P107(f866(f866(f244(x85343),f84(x85343)),x85344))+P107(f866(f866(f243(a930),x85341),x85342))+~P107(f866(f866(f243(x85343),f866(f866(f252(x85343),x85344),x85341)),f866(f866(f252(x85343),x85344),x85342)))
% 157.76/157.53 [8536]~P113(x85363)+~P107(f866(f866(f244(x85363),f84(x85363)),x85364))+P107(f866(f866(f244(a930),x85361),x85362))+~P107(f866(f866(f244(x85363),f866(f866(f252(x85363),x85364),x85361)),f866(f866(f252(x85363),x85364),x85362)))
% 157.76/157.53 [8546]~P120(x85461)+P107(f866(f866(f243(x85461),x85462),x85463))+~P107(f866(f866(f244(x85461),f2(x85461)),x85464))+~P107(f866(f866(f243(x85461),f866(f866(f87(x85461),x85464),x85462)),f866(f866(f87(x85461),x85464),x85463)))
% 157.76/157.53 [8547]~P132(x85471)+P107(f866(f866(f243(x85471),x85472),x85473))+~P107(f866(f866(f244(x85471),f2(x85471)),x85474))+~P107(f866(f866(f243(x85471),f866(f866(f87(x85471),x85474),x85472)),f866(f866(f87(x85471),x85474),x85473)))
% 157.76/157.53 [8548]~P132(x85481)+P107(f866(f866(f243(x85481),x85482),x85483))+~P107(f866(f866(f244(x85481),f2(x85481)),x85484))+~P107(f866(f866(f243(x85481),f866(f866(f87(x85481),x85482),x85484)),f866(f866(f87(x85481),x85483),x85484)))
% 157.76/157.53 [8549]~P120(x85491)+P107(f866(f866(f244(x85491),x85492),x85493))+~P107(f866(f866(f244(x85491),f2(x85491)),x85494))+~P107(f866(f866(f244(x85491),f866(f866(f87(x85491),x85494),x85492)),f866(f866(f87(x85491),x85494),x85493)))
% 157.76/157.53 [8550]~P132(x85501)+P107(f866(f866(f244(x85501),x85502),x85503))+~P107(f866(f866(f243(x85501),f2(x85501)),x85504))+~P107(f866(f866(f244(x85501),f866(f866(f87(x85501),x85504),x85502)),f866(f866(f87(x85501),x85504),x85503)))
% 157.76/157.53 [8551]~P131(x85511)+P107(f866(f866(f244(x85511),x85512),x85513))+~P107(f866(f866(f243(x85511),f2(x85511)),x85514))+~P107(f866(f866(f244(x85511),f866(f866(f87(x85511),x85514),x85512)),f866(f866(f87(x85511),x85514),x85513)))
% 157.76/157.53 [8552]~P113(x85521)+~P107(f866(f866(f243(x85521),f2(x85521)),x85523))+P107(f866(f866(f244(x85521),x85522),x85523))+~P107(f866(f866(f244(x85521),f866(f866(f252(x85521),x85522),x85524)),f866(f866(f252(x85521),x85523),x85524)))
% 157.76/157.53 [8553]~P132(x85531)+P107(f866(f866(f244(x85531),x85532),x85533))+~P107(f866(f866(f243(x85531),f2(x85531)),x85534))+~P107(f866(f866(f244(x85531),f866(f866(f87(x85531),x85532),x85534)),f866(f866(f87(x85531),x85533),x85534)))
% 157.76/157.53 [8554]~P131(x85541)+P107(f866(f866(f244(x85541),x85542),x85543))+~P107(f866(f866(f243(x85541),f2(x85541)),x85544))+~P107(f866(f866(f244(x85541),f866(f866(f87(x85541),x85542),x85544)),f866(f866(f87(x85541),x85543),x85544)))
% 157.76/157.53 [8597]P107(f866(f866(f336(x85971),x85972),x85973))+~P107(f866(f866(f243(f937(x85971,a925)),x85973),x85974))+~P107(f866(f866(f244(f937(x85971,a925)),x85973),x85974))+P107(f866(f866(f244(f937(x85971,a925)),x85973),f866(f866(f316(x85971),x85972),x85974)))
% 157.76/157.53 [8976]E(f866(f866(f23(a1),f455(x89761,x89762,x89763,x89764)),f456(x89761,x89762,x89763,x89764)),x89764)+~P107(f866(f866(f244(a1),f2(a1)),x89763))+~P107(f866(f866(f243(a1),x89761),x89764))+P107(f866(f866(f243(a1),x89761),f866(f866(f86(a1),x89764),x89763)))
% 157.76/157.53 [8977]E(f866(f866(f23(a1),f465(x89771,x89772,x89773,x89774)),f466(x89771,x89772,x89773,x89774)),x89774)+~P107(f866(f866(f244(a1),f2(a1)),x89773))+~P107(f866(f866(f244(a1),x89771),x89774))+P107(f866(f866(f244(a1),x89771),f866(f866(f86(a1),x89774),x89773)))
% 157.76/157.53 [9129]~E(f866(f866(f171(x91291),x91293),f685(x91294,x91293,x91291,x91292)),f866(f866(f171(x91291),x91294),f685(x91294,x91293,x91291,x91292)))+E(f866(f866(f182(x91291),x91292),x91293),f866(f866(f182(x91291),x91292),x91294))+~P107(f866(f866(f243(a930),x91292),f866(f196(f931(x91291)),x91293)))+~P107(f866(f866(f243(a930),x91292),f866(f196(f931(x91291)),x91294)))
% 157.76/157.53 [9195]~P107(f866(f866(f244(a1),f2(a1)),x91953))+~P107(f866(f866(f243(a1),x91951),x91954))+P107(f866(f866(f336(a1),f455(x91951,x91952,x91953,x91954)),x91952))+P107(f866(f866(f243(a1),x91951),f866(f866(f86(a1),x91954),x91953)))
% 157.76/157.53 [9196]~P107(f866(f866(f244(a1),f2(a1)),x91963))+~P107(f866(f866(f244(a1),x91961),x91964))+P107(f866(f866(f336(a1),f465(x91961,x91962,x91963,x91964)),x91962))+P107(f866(f866(f244(a1),x91961),f866(f866(f86(a1),x91964),x91963)))
% 157.76/157.53 [9236]~P103(x92361)+~P107(f866(f66(x92361),x92363))+~P107(f866(f866(f336(x92361),x92364),x92363))+P107(f866(f866(f243(x92361),f866(f866(f69(x92361,x92361,f108(x92361)),x92362),x92363)),f866(f866(f108(x92361),x92364),x92362)))
% 157.76/157.53 [9237]~P110(x92371)+~P107(f866(f66(x92371),x92373))+~P107(f866(f866(f336(x92371),x92374),x92373))+P107(f866(f866(f243(x92371),f866(f866(f69(x92371,x92371,f241(x92371)),x92372),x92373)),f866(f866(f241(x92371),x92374),x92372)))
% 157.76/157.53 [9281]E(f866(f866(f182(x92811),x92812),x92813),f866(f866(f182(x92811),x92812),x92814))+P107(f866(f866(f244(a930),f685(x92813,x92814,x92811,x92812)),x92812))+~P107(f866(f866(f243(a930),x92812),f866(f196(f931(x92811)),x92813)))+~P107(f866(f866(f243(a930),x92812),f866(f196(f931(x92811)),x92814)))
% 157.76/157.53 [9286]~P107(f866(f866(f244(a1),f2(a1)),x92863))+~P107(f866(f866(f243(a1),x92861),x92862))+P107(f866(f866(f336(a1),f456(x92861,x92864,x92863,x92862)),f310(a1,f84(a1),x92863)))+P107(f866(f866(f243(a1),x92861),f866(f866(f86(a1),x92862),x92863)))
% 157.76/157.53 [9287]~P107(f866(f866(f244(a1),f2(a1)),x92873))+~P107(f866(f866(f244(a1),x92871),x92872))+P107(f866(f866(f336(a1),f466(x92871,x92874,x92873,x92872)),f310(a1,f84(a1),x92873)))+P107(f866(f866(f244(a1),x92871),f866(f866(f86(a1),x92872),x92873)))
% 157.76/157.53 [9608]~P110(x96081)+~P107(f866(f66(x96081),x96084))+P107(f866(f866(f336(x96081),f636(x96082,x96083,x96084,x96081)),x96084))+P107(f866(f866(f243(x96081),f866(f866(f69(x96081,x96081,f242(x96081)),x96082),x96084)),f866(f866(f242(x96081),x96083),x96082)))
% 157.76/157.53 [9609]~P102(x96091)+~P107(f866(f66(x96091),x96094))+P107(f866(f866(f336(x96091),f641(x96092,x96093,x96094,x96091)),x96094))+P107(f866(f866(f243(x96091),f866(f866(f69(x96091,x96091,f117(x96091)),x96092),x96094)),f866(f866(f117(x96091),x96093),x96092)))
% 157.76/157.53 [9734]~P102(x97341)+~P107(f866(f66(x97341),x97343))+~P107(f866(f866(f243(x97341),f641(x97342,x97344,x97343,x97341)),x97344))+P107(f866(f866(f243(x97341),f866(f866(f69(x97341,x97341,f117(x97341)),x97342),x97343)),f866(f866(f117(x97341),x97344),x97342)))
% 157.76/157.53 [9735]~P110(x97351)+~P107(f866(f66(x97351),x97353))+~P107(f866(f866(f243(x97351),f636(x97352,x97354,x97353,x97351)),x97354))+P107(f866(f866(f243(x97351),f866(f866(f69(x97351,x97351,f242(x97351)),x97352),x97353)),f866(f866(f242(x97351),x97354),x97352)))
% 157.76/157.53 [9737]~P107(f866(f866(f243(a1),f2(a1)),x97374))+~P107(f866(f866(f244(a1),f2(a1)),x97373))+~P107(f866(f866(f244(a1),x97374),x97371))+P107(f866(f866(f244(a1),f866(f866(f86(a1),f866(f866(f87(a1),x97371),f50(a1,x97372,x97373))),x97374)),f866(f866(f87(a1),x97371),x97373)))
% 157.76/157.53 [10126]E(x101261,x101262)+P107(f866(f866(f336(f936(f931(x101263),f931(x101263))),f866(f866(f260(f931(x101263),f931(x101263)),x101262),x101261)),f154(x101263,x101264)))+P107(f866(f866(f336(f936(f931(x101263),f931(x101263))),f866(f866(f260(f931(x101263),f931(x101263)),x101261),x101262)),f154(x101263,x101264)))+~P107(f866(f866(f336(f936(x101263,x101263)),f866(f866(f260(x101263,x101263),f664(x101261,x101262,x101264,x101263)),f665(x101261,x101262,x101264,x101263))),x101264))
% 157.76/157.53 [10127]E(x101271,x101272)+P107(f866(f866(f336(f936(f931(x101273),f931(x101273))),f866(f866(f260(f931(x101273),f931(x101273)),x101272),x101271)),f154(x101273,x101274)))+P107(f866(f866(f336(f936(f931(x101273),f931(x101273))),f866(f866(f260(f931(x101273),f931(x101273)),x101271),x101272)),f154(x101273,x101274)))+~P107(f866(f866(f336(f936(x101273,x101273)),f866(f866(f260(x101273,x101273),f665(x101271,x101272,x101274,x101273)),f664(x101271,x101272,x101274,x101273))),x101274))
% 157.76/157.53 [7699]~P102(x76991)+~P107(f866(f866(f243(x76991),x76993),x76994))+~P107(f866(f866(f243(x76991),x76992),x76994))+P107(f866(f866(f243(x76991),f866(f866(f117(x76991),x76992),x76993)),x76994))
% 157.76/157.53 [7702]~P110(x77021)+~P107(f866(f866(f243(x77021),x77023),x77024))+~P107(f866(f866(f243(x77021),x77022),x77024))+P107(f866(f866(f243(x77021),f866(f866(f242(x77021),x77022),x77023)),x77024))
% 157.76/157.53 [7703]~P110(x77031)+~P107(f866(f866(f244(x77031),x77033),x77034))+~P107(f866(f866(f244(x77031),x77032),x77034))+P107(f866(f866(f244(x77031),f866(f866(f242(x77031),x77032),x77033)),x77034))
% 157.76/157.53 [8018]~E(x80181,x80183)+E(f146(a930,f866(f309(a930,x80181),x80182)),f866(f866(f158(a930),x80183),x80184))+~E(f146(a930,f866(f309(a930,f866(f866(f86(a930),x80181),f84(a930))),x80182)),x80184)+~P107(f866(f866(f244(a930),x80181),x80182))
% 157.76/157.53 [8026]~P110(x80261)+P107(f866(f866(f243(x80261),x80262),x80263))+P107(f866(f866(f243(x80261),x80264),x80263))+~P107(f866(f866(f243(x80261),f866(f866(f241(x80261),x80264),x80262)),x80263))
% 157.76/157.53 [8027]~P110(x80271)+P107(f866(f866(f244(x80271),x80272),x80273))+P107(f866(f866(f244(x80271),x80274),x80273))+~P107(f866(f866(f244(x80271),f866(f866(f241(x80271),x80274),x80272)),x80273))
% 157.76/157.53 [8300]~P67(x83001)+~P107(f866(f866(f244(x83001),f2(x83001)),x83003))+~P107(f866(f866(f243(x83001),x83002),f866(f866(f297(x83001),x83004),x83003)))+P107(f866(f866(f243(x83001),f866(f866(f87(x83001),x83002),x83003)),x83004))
% 157.76/157.53 [8301]~P68(x83011)+~P107(f866(f866(f244(x83011),f2(x83011)),x83013))+~P107(f866(f866(f243(x83011),x83012),f866(f866(f297(x83011),x83014),x83013)))+P107(f866(f866(f243(x83011),f866(f866(f87(x83011),x83012),x83013)),x83014))
% 157.76/157.53 [8302]~P67(x83021)+~P107(f866(f866(f244(x83021),f2(x83021)),x83023))+~P107(f866(f866(f243(x83021),x83022),f866(f866(f87(x83021),x83024),x83023)))+P107(f866(f866(f243(x83021),f866(f866(f297(x83021),x83022),x83023)),x83024))
% 157.76/157.53 [8304]~P68(x83041)+~P107(f866(f866(f244(x83041),f2(x83041)),x83043))+~P107(f866(f866(f243(x83041),x83042),f866(f866(f87(x83041),x83044),x83043)))+P107(f866(f866(f243(x83041),f866(f866(f297(x83041),x83042),x83043)),x83044))
% 157.76/157.53 [8305]~P67(x83051)+~P107(f866(f866(f244(x83051),f2(x83051)),x83053))+~P107(f866(f866(f244(x83051),x83052),f866(f866(f297(x83051),x83054),x83053)))+P107(f866(f866(f244(x83051),f866(f866(f87(x83051),x83052),x83053)),x83054))
% 157.76/157.53 [8306]~P68(x83061)+~P107(f866(f866(f244(x83061),f2(x83061)),x83063))+~P107(f866(f866(f244(x83061),x83062),f866(f866(f297(x83061),x83064),x83063)))+P107(f866(f866(f244(x83061),f866(f866(f87(x83061),x83062),x83063)),x83064))
% 157.76/157.53 [8307]~P67(x83071)+~P107(f866(f866(f244(x83071),f2(x83071)),x83073))+~P107(f866(f866(f244(x83071),x83072),f866(f866(f87(x83071),x83074),x83073)))+P107(f866(f866(f244(x83071),f866(f866(f297(x83071),x83072),x83073)),x83074))
% 157.76/157.53 [8309]~P68(x83091)+~P107(f866(f866(f244(x83091),f2(x83091)),x83093))+~P107(f866(f866(f244(x83091),x83092),f866(f866(f87(x83091),x83094),x83093)))+P107(f866(f866(f244(x83091),f866(f866(f297(x83091),x83092),x83093)),x83094))
% 157.76/157.53 [8431]~P67(x84311)+~P107(f866(f866(f244(x84311),f2(x84311)),x84314))+P107(f866(f866(f243(x84311),x84312),f866(f866(f87(x84311),x84313),x84314)))+~P107(f866(f866(f243(x84311),f866(f866(f297(x84311),x84312),x84314)),x84313))
% 157.76/157.53 [8432]~P67(x84321)+~P107(f866(f866(f244(x84321),f2(x84321)),x84324))+P107(f866(f866(f243(x84321),x84322),f866(f866(f297(x84321),x84323),x84324)))+~P107(f866(f866(f243(x84321),f866(f866(f87(x84321),x84322),x84324)),x84323))
% 157.76/157.53 [8434]~P68(x84341)+~P107(f866(f866(f244(x84341),f2(x84341)),x84344))+P107(f866(f866(f243(x84341),x84342),f866(f866(f87(x84341),x84343),x84344)))+~P107(f866(f866(f243(x84341),f866(f866(f297(x84341),x84342),x84344)),x84343))
% 157.76/157.53 [8435]~P68(x84351)+~P107(f866(f866(f244(x84351),f2(x84351)),x84354))+P107(f866(f866(f243(x84351),x84352),f866(f866(f297(x84351),x84353),x84354)))+~P107(f866(f866(f243(x84351),f866(f866(f87(x84351),x84352),x84354)),x84353))
% 157.76/157.53 [8436]~P67(x84361)+~P107(f866(f866(f244(x84361),f2(x84361)),x84364))+P107(f866(f866(f244(x84361),x84362),f866(f866(f87(x84361),x84363),x84364)))+~P107(f866(f866(f244(x84361),f866(f866(f297(x84361),x84362),x84364)),x84363))
% 157.76/157.53 [8437]~P67(x84371)+~P107(f866(f866(f244(x84371),f2(x84371)),x84374))+P107(f866(f866(f244(x84371),x84372),f866(f866(f297(x84371),x84373),x84374)))+~P107(f866(f866(f244(x84371),f866(f866(f87(x84371),x84372),x84374)),x84373))
% 157.76/157.53 [8439]~P68(x84391)+~P107(f866(f866(f244(x84391),f2(x84391)),x84394))+P107(f866(f866(f244(x84391),x84392),f866(f866(f87(x84391),x84393),x84394)))+~P107(f866(f866(f244(x84391),f866(f866(f297(x84391),x84392),x84394)),x84393))
% 157.76/157.53 [8440]~P68(x84401)+~P107(f866(f866(f244(x84401),f2(x84401)),x84404))+P107(f866(f866(f244(x84401),x84402),f866(f866(f297(x84401),x84403),x84404)))+~P107(f866(f866(f244(x84401),f866(f866(f87(x84401),x84402),x84404)),x84403))
% 157.76/157.53 [8600]~P68(x86001)+~P107(f866(f866(f244(x86001),x86003),f2(x86001)))+~P107(f866(f866(f243(x86001),f866(f866(f297(x86001),x86004),x86003)),x86002))+P107(f866(f866(f243(x86001),f866(f866(f87(x86001),x86002),x86003)),x86004))
% 157.76/157.53 [8601]~P68(x86011)+~P107(f866(f866(f244(x86011),x86013),f2(x86011)))+~P107(f866(f866(f243(x86011),f866(f866(f87(x86011),x86014),x86013)),x86012))+P107(f866(f866(f243(x86011),f866(f866(f297(x86011),x86012),x86013)),x86014))
% 157.76/157.53 [8602]~P68(x86021)+~P107(f866(f866(f244(x86021),x86023),f2(x86021)))+~P107(f866(f866(f244(x86021),f866(f866(f297(x86021),x86024),x86023)),x86022))+P107(f866(f866(f244(x86021),f866(f866(f87(x86021),x86022),x86023)),x86024))
% 157.76/157.53 [8603]~P68(x86031)+~P107(f866(f866(f244(x86031),x86033),f2(x86031)))+~P107(f866(f866(f244(x86031),f866(f866(f87(x86031),x86034),x86033)),x86032))+P107(f866(f866(f244(x86031),f866(f866(f297(x86031),x86032),x86033)),x86034))
% 157.76/157.53 [8615]~P107(f866(x86151,x86154))+~P107(f866(f866(f244(a930),x86152),f866(f866(f87(a930),x86153),f866(a119,x86154))))+P107(f866(x86151,f866(f866(f41(a930),x86152),x86153)))+~P107(f866(f866(f243(a930),f866(f866(f87(a930),x86153),x86154)),x86152))
% 157.76/157.53 [8824]~P102(x88241)+~P107(f866(f66(x88241),x88244))+~P107(f866(f866(f336(x88241),x88242),x88244))+P107(f866(f866(f243(x88241),f866(f866(f117(x88241),x88242),x88243)),f866(f866(f69(x88241,x88241,f117(x88241)),x88243),x88244)))
% 157.76/157.53 [8825]~P110(x88251)+~P107(f866(f66(x88251),x88254))+~P107(f866(f866(f336(x88251),x88252),x88254))+P107(f866(f866(f243(x88251),f866(f866(f242(x88251),x88252),x88253)),f866(f866(f69(x88251,x88251,f242(x88251)),x88253),x88254)))
% 157.76/157.53 [8978]~P107(f866(f66(x89781),x89782))+E(f866(f40(x89781),f866(f866(f23(f937(x89781,a925)),x89782),f866(f866(f316(x89781),x89783),x89784))),f866(f866(f23(a930),f866(f40(x89781),f866(f866(f23(f937(x89781,a925)),x89782),x89784))),f84(a930)))+P107(f866(f866(f336(x89781),x89783),x89784))+~P107(f866(f866(f336(x89781),x89783),x89782))
% 157.76/157.53 [9055]E(f866(f866(f86(a1),f457(x90551,x90552,x90553,x90554)),f450(x90551,x90552,x90553,x90554)),x90554)+~P107(f866(f866(f244(a1),f2(a1)),x90553))+~P107(f866(f866(f243(a1),x90554),x90551))+P107(f866(f866(f243(a1),f866(f866(f23(a1),x90554),x90553)),x90551))
% 157.76/157.53 [9056]E(f866(f866(f86(a1),f467(x90561,x90562,x90563,x90564)),f463(x90561,x90562,x90563,x90564)),x90564)+~P107(f866(f866(f244(a1),f2(a1)),x90563))+~P107(f866(f866(f244(a1),x90564),x90561))+P107(f866(f866(f244(a1),f866(f866(f23(a1),x90564),x90563)),x90561))
% 157.76/157.53 [9266]~P107(f866(f866(f244(a1),f2(a1)),x92663))+~P107(f866(f866(f243(a1),x92664),x92661))+P107(f866(f866(f336(a1),f457(x92661,x92662,x92663,x92664)),x92662))+P107(f866(f866(f243(a1),f866(f866(f23(a1),x92664),x92663)),x92661))
% 157.76/157.53 [9267]~P107(f866(f866(f244(a1),f2(a1)),x92673))+~P107(f866(f866(f244(a1),x92674),x92671))+P107(f866(f866(f336(a1),f467(x92671,x92672,x92673,x92674)),x92672))+P107(f866(f866(f244(a1),f866(f866(f23(a1),x92674),x92673)),x92671))
% 157.76/157.53 [9354]~P107(f866(f866(f244(a1),f2(a1)),x93542))+~P107(f866(f866(f243(a1),x93541),x93543))+P107(f866(f866(f336(a1),f450(x93543,x93544,x93542,x93541)),f310(a1,f84(a1),x93542)))+P107(f866(f866(f243(a1),f866(f866(f23(a1),x93541),x93542)),x93543))
% 157.76/157.53 [9355]~P107(f866(f866(f244(a1),f2(a1)),x93552))+~P107(f866(f866(f244(a1),x93551),x93553))+P107(f866(f866(f336(a1),f463(x93553,x93554,x93552,x93551)),f310(a1,f84(a1),x93552)))+P107(f866(f866(f244(a1),f866(f866(f23(a1),x93551),x93552)),x93553))
% 157.76/157.53 [9373]~P107(f866(f866(f243(a1),f2(a1)),x93734))+~P107(f866(f866(f244(a1),f2(a1)),x93733))+~P107(f866(f866(f244(a1),x93734),x93731))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),f866(f866(f87(a1),x93731),f50(a1,x93732,x93733))),x93734)))
% 157.76/157.53 [9402]E(x94021,x94022)+~P39(x94023,x94024)+~P107(f866(f866(f336(f936(x94023,x94023)),f866(f866(f260(x94023,x94023),x94022),x94021)),x94024))+~P107(f866(f866(f336(f936(x94023,x94023)),f866(f866(f260(x94023,x94023),x94021),x94022)),x94024))
% 157.76/157.53 [9434]~P103(x94341)+~P107(f866(f66(x94341),x94344))+~P107(f866(f866(f243(x94341),x94342),f640(x94343,x94342,x94344,x94341)))+P107(f866(f866(f243(x94341),f866(f866(f108(x94341),x94342),x94343)),f866(f866(f69(x94341,x94341,f108(x94341)),x94343),x94344)))
% 157.76/157.53 [9435]~P110(x94351)+~P107(f866(f66(x94351),x94354))+~P107(f866(f866(f243(x94351),x94352),f635(x94353,x94352,x94354,x94351)))+P107(f866(f866(f243(x94351),f866(f866(f241(x94351),x94352),x94353)),f866(f866(f69(x94351,x94351,f241(x94351)),x94353),x94354)))
% 157.76/157.53 [9449]~P107(f866(f866(f243(a1),x94494),f2(a1)))+~P107(f866(f866(f244(a1),f2(a1)),x94492))+~P107(f866(f866(f244(a1),x94491),x94494))+P107(f866(f866(f244(a1),f866(f866(f87(a1),x94491),x94492)),f866(f866(f86(a1),f866(f866(f87(a1),x94491),f50(a1,x94493,x94492))),x94494)))
% 157.76/157.53 [9474]P107(f866(f66(x94741),x94742))+~P107(f866(f66(x94741),x94743))+~P107(f866(f866(f336(f937(x94741,a925)),x94742),f866(f866(f65(x94741),x94743),x94744)))+~P107(f866(f866(f243(f937(f936(x94741,x94741),a925)),x94744),f866(f866(f262(x94741,x94741),x94743),f866(f16(f937(x94741,a925),x94741),x94743))))
% 157.76/157.53 [9499]~P110(x94991)+~P107(f866(f66(x94991),x94994))+P107(f866(f866(f336(x94991),f635(x94992,x94993,x94994,x94991)),x94994))+P107(f866(f866(f243(x94991),f866(f866(f241(x94991),x94993),x94992)),f866(f866(f69(x94991,x94991,f241(x94991)),x94992),x94994)))
% 157.76/157.53 [9500]~P103(x95001)+~P107(f866(f66(x95001),x95004))+P107(f866(f866(f336(x95001),f640(x95002,x95003,x95004,x95001)),x95004))+P107(f866(f866(f243(x95001),f866(f866(f108(x95001),x95003),x95002)),f866(f866(f69(x95001,x95001,f108(x95001)),x95002),x95004)))
% 157.76/157.53 [9901]~P107(f866(f66(x99012),x99014))+~P107(f866(f66(x99011),x99013))+~P107(f866(f866(f243(a930),f866(f40(x99012),x99014)),f866(f40(x99011),x99013)))+P107(f866(f866(f243(f937(x99011,a925)),f866(f317(x99012,x99011,f890(x99013,x99011,x99014,x99012)),x99014)),x99013))
% 157.76/157.53 [9549]~P107(f866(f866(f336(x95491),x95492),x95494))+P107(f866(f866(f336(x95491),x95492),x95493))+~P107(f866(f866(f244(f937(x95491,a925)),x95494),f866(f866(f316(x95491),x95492),x95493)))+P107(f866(f866(f244(f937(x95491,a925)),f866(f866(f23(f937(x95491,a925)),x95494),f866(f866(f316(x95491),x95492),f195(f937(x95491,a925))))),x95493))
% 157.76/157.53 [9715]~P107(f866(f866(f336(x97151),x97152),x97154))+P107(f866(f866(f336(x97151),x97152),x97153))+P107(f866(f866(f244(f937(x97151,a925)),x97154),f866(f866(f316(x97151),x97152),x97153)))+~P107(f866(f866(f244(f937(x97151,a925)),f866(f866(f23(f937(x97151,a925)),x97154),f866(f866(f316(x97151),x97152),f195(f937(x97151,a925))))),x97153))
% 157.76/157.53 [9740]P107(f866(f866(f336(x97401),x97402),x97403))+~P107(f866(f866(f243(f937(x97401,a925)),x97404),x97403))+P107(f866(f866(f244(f937(x97401,a925)),x97404),f866(f866(f316(x97401),x97402),x97403)))+~P107(f866(f866(f244(f937(x97401,a925)),f866(f866(f23(f937(x97401,a925)),x97404),f866(f866(f316(x97401),x97402),f195(f937(x97401,a925))))),x97403))
% 157.76/157.53 [9745]~P107(f866(f866(f336(x97451),x97453),x97452))+~P107(f866(f866(f244(f937(x97451,a925)),x97452),x97454))+P107(f866(f866(f244(f937(x97451,a925)),x97452),f866(f866(f316(x97451),x97453),x97454)))+~P107(f866(f866(f244(f937(x97451,a925)),f866(f866(f23(f937(x97451,a925)),x97452),f866(f866(f316(x97451),x97453),f195(f937(x97451,a925))))),x97454))
% 157.76/157.53 [9761]~P107(f866(f866(f243(f937(x97611,a925)),x97612),x97614))+~P107(f866(f866(f244(f937(x97611,a925)),x97612),x97614))+P107(f866(f866(f244(f937(x97611,a925)),x97612),f866(f866(f316(x97611),x97613),x97614)))+~P107(f866(f866(f244(f937(x97611,a925)),f866(f866(f23(f937(x97611,a925)),x97612),f866(f866(f316(x97611),x97613),f195(f937(x97611,a925))))),x97614))
% 157.76/157.53 [9806]~P111(x98062)+~P64(x98061)+~P107(f866(f866(f243(f937(x98061,x98062)),x98063),x98064))+P107(f866(f62(x98061),f866(f866(f18(x98061,x98062,a925),f866(f866(f8(x98062,f937(x98062,a925),x98061),f243(x98062)),x98063)),x98064)))
% 157.76/157.53 [9950]~P111(x99502)+~P64(x99501)+P107(f866(f866(f243(f937(x99501,x99502)),x99503),x99504))+~P107(f866(f62(x99501),f866(f866(f18(x99501,x99502,a925),f866(f866(f8(x99502,f937(x99502,a925),x99501),f243(x99502)),x99503)),x99504)))
% 157.76/157.53 [10117]E(f866(f866(f171(x101171),f866(f866(f171(f931(x101171)),f186(x101171,x101172)),x101173)),x101174),f866(f866(f171(x101171),f866(f866(f171(f931(x101171)),x101172),x101174)),x101173))+~P107(f866(f866(f244(a930),x101173),f866(f196(f931(f931(x101171))),f186(x101171,x101172))))+~P13(a930,f866(f175(a930),f866(f866(f161(f931(x101171),a930),f196(f931(x101171))),x101172)))+~P107(f866(f866(f244(a930),x101174),f866(f196(f931(f931(x101171))),f866(f143(f931(x101171),f866(f866(f8(a930,a925,f931(x101171)),f866(f244(a930),x101173)),f196(f931(x101171)))),x101172))))
% 157.76/157.53 [10139]~P107(f866(f866(f336(f936(a930,a930)),x101394),x101391))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x101394),x101392)),a38))+~P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101391),x101393)),a74))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101391),f866(f866(f316(f936(a930,a930)),x101392),x101393))),a74))
% 157.76/157.53 [10140]~P107(f866(f866(f336(f936(a930,a930)),x101404),x101401))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x101404),x101402)),a76))+~P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101401),x101403)),a77))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101401),f866(f866(f316(f936(a930,a930)),x101402),x101403))),a77))
% 157.76/157.53 [10029]~P111(x100292)+~P64(x100291)+~P107(f866(f866(f244(f937(x100291,x100292)),x100293),x100294))+P107(f866(f61(x100291),f866(f866(f8(a925,a925,x100291),a329),f866(f866(f18(x100291,x100292,a925),f866(f866(f8(x100292,f937(x100292,a925),x100291),a332),x100293)),x100294))))
% 157.76/157.53 [10151]~P107(f866(f866(f336(f936(a930,a930)),x101514),x101513))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x101511),x101514)),a38))+~P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101512),x101513)),a39))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f866(f866(f316(f936(a930,a930)),x101511),x101512)),x101513)),a39))
% 157.76/157.53 [10152]~P107(f866(f866(f336(f936(a930,a930)),x101524),x101523))+~P107(f866(f866(f336(f936(f936(a930,a930),f936(a930,a930))),f866(f866(f260(f936(a930,a930),f936(a930,a930)),x101521),x101524)),a76))+~P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),x101522),x101523)),a75))+P107(f866(f866(f336(f936(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925))),f866(f866(f260(f937(f936(a930,a930),a925),f937(f936(a930,a930),a925)),f866(f866(f316(f936(a930,a930)),x101521),x101522)),x101523)),a75))
% 157.76/157.53 [6295]~P7(x62954,x62951)+~P107(f866(f866(x62951,x62952),x62955))+P107(f866(f866(x62951,x62952),x62953))+~P107(f866(f866(x62951,x62955),x62953))
% 157.76/157.53 [6296]~P50(x62964,x62961)+~P107(f866(f866(x62961,x62962),x62965))+P107(f866(f866(x62961,x62962),x62963))+~P107(f866(f866(x62961,x62965),x62963))
% 157.76/157.53 [6297]~P15(x62974,x62971)+~P107(f866(f866(x62971,x62972),x62975))+P107(f866(f866(x62971,x62972),x62973))+~P107(f866(f866(x62971,x62975),x62973))
% 157.76/157.53 [8963]~P7(x89634,x89633)+~P107(f866(x89631,x89635))+P107(f866(x89632,f840(x89632,x89631,x89633,x89634)))+P107(f866(x89631,f838(x89632,x89631,x89633,x89634)))
% 157.76/157.53 [9203]~P7(x92034,x92033)+~P107(f866(x92032,x92035))+~P107(f866(x92031,f838(x92031,x92032,x92033,x92034)))+P107(f866(x92031,f840(x92031,x92032,x92033,x92034)))
% 157.76/157.53 [9386]~P7(x93864,x93863)+~P107(f866(x93861,x93865))+P107(f866(f866(f336(x93864),f840(x93862,x93861,x93863,x93864)),f278(x93864,x93863)))+P107(f866(x93861,f838(x93862,x93861,x93863,x93864)))
% 157.76/157.53 [9506]~P7(x95061,x95064)+~P107(f866(x95063,x95065))+~P107(f866(x95062,f838(x95062,x95063,x95064,x95061)))+P107(f866(f866(f336(x95061),f840(x95062,x95063,x95064,x95061)),f278(x95061,x95064)))
% 157.76/157.53 [9795]~P38(x97951,x97954)+P107(f866(f866(f336(f936(f931(x97951),f931(x97951))),f866(f866(f260(f931(x97951),f931(x97951)),x97952),x97953)),f154(x97951,x97954)))+~P107(f866(f866(f336(f936(f931(x97951),f931(x97951))),f866(f866(f260(f931(x97951),f931(x97951)),x97952),x97955)),f154(x97951,x97954)))+~P107(f866(f866(f336(f936(f931(x97951),f931(x97951))),f866(f866(f260(f931(x97951),f931(x97951)),x97955),x97953)),f154(x97951,x97954)))
% 157.76/157.53 [5531]~P3(x55315)+E(x55311,x55312)+~E(x55313,x55314)+~E(f866(f866(f23(x55315),x55313),x55314),f866(f866(f23(x55315),x55311),x55312))
% 157.76/157.53 [6406]~P17(x64065,x64061,x64063)+E(f866(f866(x64061,x64062),f866(x64063,x64064)),f866(x64063,x64064))+~P107(f866(f66(x64065),x64064))+~P107(f866(f866(f336(x64065),x64062),x64064))
% 157.76/157.53 [6579]~P114(x65791)+~P57(x65791,x65793,x65795)+~P57(x65791,x65792,x65794)+P57(x65791,f866(f866(f87(x65791),x65792),x65793),f866(f866(f87(x65791),x65794),x65795))
% 157.76/157.53 [6595]~P79(x65951)+~E(f866(f866(f23(x65951),x65954),x65955),f866(f866(f23(x65951),x65952),x65953))+~P107(f866(f866(f243(x65951),x65954),x65955))+P107(f866(f866(f243(x65951),x65952),x65953))
% 157.76/157.53 [6597]~P79(x65971)+~E(f866(f866(f23(x65971),x65974),x65975),f866(f866(f23(x65971),x65972),x65973))+~P107(f866(f866(f244(x65971),x65974),x65975))+P107(f866(f866(f244(x65971),x65972),x65973))
% 157.76/157.53 [6947]~P114(x69471)+~P57(x69471,f866(f866(f252(x69471),x69472),x69475),x69474)+P57(x69471,f866(f866(f252(x69471),x69472),x69473),x69474)+~P107(f866(f866(f243(a930),x69473),x69475))
% 157.76/157.53 [7567]~E(x75672,f866(f866(f158(x75671),x75674),x75675))+P107(f866(f866(f336(f931(x75671)),x75672),f168(x75671,x75673)))+~P107(f866(f866(f336(f931(x75671)),x75675),f168(x75671,x75673)))+~P107(f866(f866(f336(x75671),x75674),x75673))
% 157.76/157.53 [7965]~E(f866(f196(f931(x79651)),x79653),f866(f196(f931(x79652)),x79654))+~E(f866(f866(f161(f936(x79651,x79652),x79652),f264(x79651,x79652)),x79655),x79654)+~E(f866(f866(f161(f936(x79651,x79652),x79651),f259(x79651,x79652)),x79655),x79653)+E(f866(f866(f188(x79651,x79652),x79653),x79654),x79655)
% 157.76/157.53 [8296]~P111(x82961)+P107(f866(f866(f244(f937(x82961,a925)),f310(x82961,x82962,x82963)),f310(x82961,x82964,x82965)))+~P107(f866(f866(f243(x82961),x82964),x82965))+P107(f866(f866(f243(x82961),x82962),x82963))
% 157.76/157.53 [8389]~P111(x83891)+P107(f866(f866(f243(f937(x83891,a925)),f310(x83891,x83892,x83893)),f310(x83891,x83894,x83895)))+~P107(f866(f866(f243(x83891),x83893),x83895))+~P107(f866(f866(f243(x83891),x83894),x83892))
% 157.76/157.53 [8507]~P110(x85071)+P107(f866(f866(f243(x85071),x85072),x85073))+P107(f866(f866(f243(x85071),x85074),x85073))+~P107(f866(f866(f243(f937(x85071,a925)),f866(f309(x85071,x85073),x85072)),f866(f309(x85071,x85074),x85075)))
% 157.76/157.53 [8508]~P110(x85081)+P107(f866(f866(f243(x85081),x85082),x85083))+P107(f866(f866(f243(x85081),x85082),x85084))+~P107(f866(f866(f243(f937(x85081,a925)),f866(f309(x85081,x85083),x85082)),f866(f309(x85081,x85085),x85084)))
% 157.76/157.53 [8741]~P111(x87411)+~P107(f866(f866(f243(f937(x87411,a925)),f310(x87411,x87414,x87412)),f310(x87411,x87415,x87413)))+P107(f866(f866(f243(x87411),x87412),x87413))+~P107(f866(f866(f243(x87411),x87414),x87412))
% 157.76/157.53 [8742]~P111(x87421)+~P107(f866(f866(f244(f937(x87421,a925)),f310(x87421,x87424,x87422)),f310(x87421,x87425,x87423)))+P107(f866(f866(f243(x87421),x87422),x87423))+~P107(f866(f866(f243(x87421),x87424),x87422))
% 157.76/157.53 [8743]~P111(x87431)+~P107(f866(f866(f243(f937(x87431,a925)),f310(x87431,x87433,x87434)),f310(x87431,x87432,x87435)))+P107(f866(f866(f243(x87431),x87432),x87433))+~P107(f866(f866(f243(x87431),x87433),x87434))
% 157.76/157.53 [8744]~P111(x87441)+~P107(f866(f866(f244(f937(x87441,a925)),f310(x87441,x87443,x87444)),f310(x87441,x87442,x87445)))+P107(f866(f866(f243(x87441),x87442),x87443))+~P107(f866(f866(f243(x87441),x87443),x87444))
% 157.76/157.53 [6294]~P17(x62942,x62945,x62943)+E(x62941,f195(f937(x62942,a925)))+~P107(f866(f66(x62942),x62941))+E(f866(x62943,f866(f866(f316(x62942),x62944),x62941)),f866(f866(x62945,x62944),f866(x62943,x62941)))
% 157.76/157.53 [7066]~E(x70661,x70662)+~E(f866(f866(f108(f937(x70663,a925)),x70664),x70665),f195(f937(x70663,a925)))+~P107(f866(f866(f336(x70663),x70662),x70665))+~P107(f866(f866(f336(x70663),x70661),x70664))
% 157.76/157.53 [7146]~P18(x71462,x71465,x71461)+~P107(f866(f66(x71462),x71464))+E(f866(x71461,f866(f866(f316(x71462),x71463),x71464)),f866(f866(f69(x71462,x71462,x71465),x71463),x71464))+P107(f866(f866(f336(x71462),x71463),x71464))
% 157.76/157.53 [7211]~P71(x72112)+~P107(f866(f66(x72111),x72115))+E(f866(f866(f9(x72111,x72112),x72113),f866(f866(f316(x72111),x72114),x72115)),f866(f866(f87(x72112),f866(x72113,x72114)),f866(f866(f9(x72111,x72112),x72113),x72115)))+P107(f866(f866(f336(x72111),x72114),x72115))
% 157.76/157.53 [7213]~P72(x72132)+~P107(f866(f66(x72131),x72135))+E(f866(f866(f6(x72131,x72132),x72133),f866(f866(f316(x72131),x72134),x72135)),f866(f866(f86(x72132),f866(x72133,x72134)),f866(f866(f6(x72131,x72132),x72133),x72135)))+P107(f866(f866(f336(x72131),x72134),x72135))
% 157.76/157.53 [7712]~P18(x77122,x77125,x77121)+~P107(f866(f66(x77122),x77124))+E(f866(x77121,f866(f866(f316(x77122),x77123),x77124)),x77123)+~E(f866(f866(f23(f937(x77122,a925)),x77124),f866(f866(f316(x77122),x77123),f195(f937(x77122,a925)))),f195(f937(x77122,a925)))
% 157.76/157.53 [7781]~P62(x77811)+~P57(x77811,x77815,x77813)+~P57(x77811,x77814,x77812)+E(f866(f866(f41(x77811),f866(f866(f87(x77811),x77812),x77813)),f866(f866(f87(x77811),x77814),x77815)),f866(f866(f87(x77811),f866(f866(f41(x77811),x77812),x77814)),f866(f866(f41(x77811),x77813),x77815)))
% 157.76/157.53 [8069]~P102(x80691)+~P107(f866(f866(f243(x80691),x80693),x80695))+~P107(f866(f866(f243(x80691),x80692),x80694))+P107(f866(f866(f243(x80691),f866(f866(f117(x80691),x80692),x80693)),f866(f866(f117(x80691),x80694),x80695)))
% 157.76/157.53 [8070]~P88(x80701)+~P107(f866(f866(f243(x80701),x80703),x80705))+~P107(f866(f866(f243(x80701),x80702),x80704))+P107(f866(f866(f243(x80701),f866(f866(f86(x80701),x80702),x80703)),f866(f866(f86(x80701),x80704),x80705)))
% 157.76/157.53 [8071]~P103(x80711)+~P107(f866(f866(f243(x80711),x80713),x80715))+~P107(f866(f866(f243(x80711),x80712),x80714))+P107(f866(f866(f243(x80711),f866(f866(f108(x80711),x80712),x80713)),f866(f866(f108(x80711),x80714),x80715)))
% 157.76/157.53 [8072]~P110(x80721)+~P107(f866(f866(f243(x80721),x80723),x80725))+~P107(f866(f866(f243(x80721),x80722),x80724))+P107(f866(f866(f243(x80721),f866(f866(f241(x80721),x80722),x80723)),f866(f866(f241(x80721),x80724),x80725)))
% 157.76/157.53 [8073]~P110(x80731)+~P107(f866(f866(f243(x80731),x80733),x80735))+~P107(f866(f866(f243(x80731),x80732),x80734))+P107(f866(f866(f243(x80731),f866(f866(f242(x80731),x80732),x80733)),f866(f866(f242(x80731),x80734),x80735)))
% 157.76/157.53 [8074]~P90(x80741)+~P107(f866(f866(f243(x80741),x80743),x80745))+~P107(f866(f866(f244(x80741),x80742),x80744))+P107(f866(f866(f244(x80741),f866(f866(f86(x80741),x80742),x80743)),f866(f866(f86(x80741),x80744),x80745)))
% 157.76/157.53 [8075]~P90(x80751)+~P107(f866(f866(f243(x80751),x80752),x80754))+~P107(f866(f866(f244(x80751),x80753),x80755))+P107(f866(f866(f244(x80751),f866(f866(f86(x80751),x80752),x80753)),f866(f866(f86(x80751),x80754),x80755)))
% 157.76/157.53 [8076]~P90(x80761)+~P107(f866(f866(f244(x80761),x80763),x80765))+~P107(f866(f866(f244(x80761),x80762),x80764))+P107(f866(f866(f244(x80761),f866(f866(f86(x80761),x80762),x80763)),f866(f866(f86(x80761),x80764),x80765)))
% 157.76/157.53 [8212]~P144(x82125)+E(x82121,x82122)+E(x82123,x82124)+~E(f866(f866(f86(x82125),f866(f866(f87(x82125),x82123),x82121)),f866(f866(f87(x82125),x82124),x82122)),f866(f866(f86(x82125),f866(f866(f87(x82125),x82123),x82122)),f866(f866(f87(x82125),x82124),x82121)))
% 157.76/157.53 [8409]~P110(x84094)+~P107(f866(f144(x84091),x84093))+P107(f866(f866(f336(x84091),x84092),f866(f179(x84091),x84093)))+P107(f866(f144(x84091),f866(f866(f155(x84091,x84094,x84095),x84092),x84093)))
% 157.76/157.53 [8555]~P3(x85551)+E(f866(f866(f23(x85551),f866(f866(f6(a930,x85551),x85552),f866(f309(a930,x85553),x85554))),f866(f866(f6(a930,x85551),x85552),f866(f309(a930,x85553),x85555))),f866(f866(f6(a930,x85551),x85552),f866(f309(a930,x85555),x85554)))+~P107(f866(f866(f243(a930),x85555),x85554))+~P107(f866(f866(f243(a930),x85553),x85555))
% 157.76/157.53 [8556]~P72(x85561)+E(f866(f866(f86(x85561),f866(f866(f6(a930,x85561),x85562),f866(f309(a930,x85563),x85564))),f866(f866(f6(a930,x85561),x85562),f866(f309(a930,x85564),x85565))),f866(f866(f6(a930,x85561),x85562),f866(f309(a930,x85563),x85565)))+~P107(f866(f866(f243(a930),x85564),x85565))+~P107(f866(f866(f243(a930),x85563),x85564))
% 157.76/157.53 [8884]~P66(x88842)+E(x88841,f2(x88842))+E(x88843,f2(x88842))+E(f866(f866(f297(x88842),f866(f866(f23(x88842),f866(f866(f87(x88842),x88844),x88841)),f866(f866(f87(x88842),x88845),x88843))),f866(f866(f87(x88842),x88843),x88841)),f866(f866(f23(x88842),f866(f866(f297(x88842),x88844),x88843)),f866(f866(f297(x88842),x88845),x88841)))
% 157.76/157.53 [8885]~P66(x88852)+E(x88851,f2(x88852))+E(x88853,f2(x88852))+E(f866(f866(f297(x88852),f866(f866(f86(x88852),f866(f866(f87(x88852),x88854),x88851)),f866(f866(f87(x88852),x88855),x88853))),f866(f866(f87(x88852),x88853),x88851)),f866(f866(f86(x88852),f866(f866(f297(x88852),x88854),x88853)),f866(f866(f297(x88852),x88855),x88851)))
% 157.76/157.53 [8894]~E(x88942,f866(x88943,x88941))+E(x88941,f671(x88942,x88943,x88944,x88945))+~P25(x88945,x88944,x88943,f250(f937(x88945,a925)))+~P107(f866(f866(f336(x88944),x88942),f866(f317(x88945,x88944,x88943),f250(f937(x88945,a925)))))
% 157.76/157.53 [9113]~P128(x91131)+~P107(f866(f866(f244(x91131),f866(f81(x91131),x91132)),x91134))+P107(f866(f866(f244(x91131),f866(f866(f87(x91131),f866(f81(x91131),x91132)),f866(f81(x91131),x91133))),f866(f866(f87(x91131),x91134),x91135)))+~P107(f866(f866(f244(x91131),f866(f81(x91131),x91133)),x91135))
% 157.76/157.53 [9228]~P25(x92281,x92283,x92285,x92282)+~P107(f866(f66(x92283),x92284))+P107(f866(f866(f243(a930),f866(f40(x92281),x92282)),f866(f40(x92283),x92284)))+~P107(f866(f866(f243(f937(x92283,a925)),f866(f317(x92281,x92283,x92285),x92282)),x92284))
% 157.76/157.53 [9295]~P71(x92952)+~P25(x92951,x92951,x92954,x92955)+~P107(f866(f66(x92951),x92955))+E(f866(f866(f9(x92951,x92952),f866(f78(x92951,x92952,x92951,x92953),x92954)),x92955),f866(f866(f9(x92951,x92952),x92953),f866(f317(x92951,x92951,x92954),x92955)))
% 157.76/157.53 [9296]~P72(x92962)+~P25(x92961,x92961,x92964,x92965)+~P107(f866(f66(x92961),x92965))+E(f866(f866(f6(x92961,x92962),f866(f78(x92961,x92962,x92961,x92963),x92964)),x92965),f866(f866(f6(x92961,x92962),x92963),f866(f317(x92961,x92961,x92964),x92965)))
% 157.76/157.53 [9414]~P37(x94141,x94142)+~P107(f866(f866(f336(x94141),x94143),x94144))+~P107(f866(f866(f336(x94141),x94145),x94144))+~P107(f866(f866(f336(f936(x94141,x94141)),f866(f866(f260(x94141,x94141),x94145),f631(x94142,x94141,x94144))),x94142))
% 157.76/157.53 [9448]~P25(x94482,x94483,x94485,x94481)+E(x94481,f195(f937(x94482,a925)))+E(f866(f317(x94483,x94482,f473(x94484,x94483,x94482,x94481)),x94484),x94481)+~P107(f866(f866(f243(f937(x94483,a925)),f866(f317(x94482,x94483,x94485),x94481)),x94484))
% 157.76/157.53 [9931]~P110(x99315)+~P5(x99315)+P107(f866(f866(f336(x99311),f875(x99312,x99313,x99311,x99314,x99315)),x99313))+~P107(f866(f866(f244(x99315),x99314),f866(f866(f44(x99311,x99315),x99313),x99312)))
% 157.76/157.53 [9936]~P110(x99361)+~P5(x99361)+P107(f866(f866(f244(x99361),x99362),f866(x99363,f875(x99363,x99364,x99365,x99362,x99361))))+~P107(f866(f866(f244(x99361),x99362),f866(f866(f44(x99365,x99361),x99364),x99363)))
% 157.76/157.53 [10016]~P69(x100161)+~P107(f866(f71(x100161,x100161,f87(x100161),x100162,x100163),x100165))+P107(f866(f866(f336(x100161),x100162),x100163))+P107(f866(f71(x100161,x100161,f87(x100161),x100164,f866(f866(f316(x100161),x100162),x100163)),f866(f866(f87(x100161),x100164),x100165)))
% 157.76/157.53 [10220]~P71(x102202)+~P107(f866(f66(x102201),x102205))+E(f866(f866(f9(x102201,x102202),f866(f866(f7(x102201,x102202,x102202),f866(f866(f18(x102201,x102202,f937(x102202,x102202)),f866(f866(f8(a925,f937(x102202,f937(x102202,x102202)),x102201),f103(x102202)),f866(a332,x102203))),x102204)),f84(x102202))),x102205),f84(x102202))+P107(f866(f866(f336(x102201),x102203),x102205))
% 157.76/157.53 [10221]~P72(x102212)+~P107(f866(f66(x102211),x102215))+E(f866(f866(f6(x102211,x102212),f866(f866(f7(x102211,x102212,x102212),f866(f866(f18(x102211,x102212,f937(x102212,x102212)),f866(f866(f8(a925,f937(x102212,f937(x102212,x102212)),x102211),f103(x102212)),f866(a332,x102213))),x102214)),f2(x102212))),x102215),f2(x102212))+P107(f866(f866(f336(x102211),x102213),x102215))
% 157.76/157.53 [10222]~P71(x102222)+~P107(f866(f66(x102221),x102225))+E(f866(f866(f9(x102221,x102222),f866(f866(f7(x102221,x102222,x102222),f866(f866(f18(x102221,x102222,f937(x102222,x102222)),f866(f866(f8(a925,f937(x102222,f937(x102222,x102222)),x102221),f103(x102222)),f866(a332,x102223))),x102224)),f84(x102222))),x102225),f866(x102224,x102223))+~P107(f866(f866(f336(x102221),x102223),x102225))
% 157.76/157.53 [10223]~P72(x102232)+~P107(f866(f66(x102231),x102235))+E(f866(f866(f6(x102231,x102232),f866(f866(f7(x102231,x102232,x102232),f866(f866(f18(x102231,x102232,f937(x102232,x102232)),f866(f866(f8(a925,f937(x102232,f937(x102232,x102232)),x102231),f103(x102232)),f866(a332,x102233))),x102234)),f2(x102232))),x102235),f866(x102234,x102233))+~P107(f866(f866(f336(x102231),x102233),x102235))
% 157.76/157.53 [10276]~P71(x102762)+~P107(f866(f66(x102761),x102765))+E(f866(f866(f9(x102761,x102762),f866(f866(f7(x102761,x102762,x102762),f866(f866(f18(x102761,x102762,f937(x102762,x102762)),f866(f866(f8(a925,f937(x102762,f937(x102762,x102762)),x102761),f103(x102762)),f866(f866(f7(x102761,x102761,a925),a332),x102763))),x102764)),f84(x102762))),x102765),f84(x102762))+P107(f866(f866(f336(x102761),x102763),x102765))
% 157.76/157.53 [10277]~P72(x102772)+~P107(f866(f66(x102771),x102775))+E(f866(f866(f6(x102771,x102772),f866(f866(f7(x102771,x102772,x102772),f866(f866(f18(x102771,x102772,f937(x102772,x102772)),f866(f866(f8(a925,f937(x102772,f937(x102772,x102772)),x102771),f103(x102772)),f866(f866(f7(x102771,x102771,a925),a332),x102773))),x102774)),f2(x102772))),x102775),f2(x102772))+P107(f866(f866(f336(x102771),x102773),x102775))
% 157.76/157.53 [10279]~P71(x102792)+~P107(f866(f66(x102791),x102795))+E(f866(f866(f9(x102791,x102792),f866(f866(f7(x102791,x102792,x102792),f866(f866(f18(x102791,x102792,f937(x102792,x102792)),f866(f866(f8(a925,f937(x102792,f937(x102792,x102792)),x102791),f103(x102792)),f866(f866(f7(x102791,x102791,a925),a332),x102793))),x102794)),f84(x102792))),x102795),f866(x102794,x102793))+~P107(f866(f866(f336(x102791),x102793),x102795))
% 157.76/157.53 [10280]~P72(x102802)+~P107(f866(f66(x102801),x102805))+E(f866(f866(f6(x102801,x102802),f866(f866(f7(x102801,x102802,x102802),f866(f866(f18(x102801,x102802,f937(x102802,x102802)),f866(f866(f8(a925,f937(x102802,f937(x102802,x102802)),x102801),f103(x102802)),f866(f866(f7(x102801,x102801,a925),a332),x102803))),x102804)),f2(x102802))),x102805),f866(x102804,x102803))+~P107(f866(f866(f336(x102801),x102803),x102805))
% 157.76/157.53 [8068]~P3(x80682)+~P107(f866(f66(x80681),x80684))+E(f866(f866(f6(x80681,x80682),x80683),f866(f866(f23(f937(x80681,a925)),x80684),f866(f866(f316(x80681),x80685),f195(f937(x80681,a925))))),f866(f866(f6(x80681,x80682),x80683),x80684))+P107(f866(f866(f336(x80681),x80685),x80684))
% 157.76/157.53 [8563]~P136(x85632)+~P107(f866(f66(x85631),x85634))+E(f866(f866(f6(x85631,x85632),x85633),f866(f866(f23(f937(x85631,a925)),x85634),f866(f866(f316(x85631),x85635),f195(f937(x85631,a925))))),f866(f866(f23(x85632),f866(f866(f6(x85631,x85632),x85633),x85634)),f866(x85633,x85635)))+~P107(f866(f866(f336(x85631),x85635),x85634))
% 157.76/157.53 [8564]~P3(x85642)+~P107(f866(f66(x85641),x85644))+E(f866(f866(f6(x85641,x85642),x85643),f866(f866(f23(f937(x85641,a925)),x85644),f866(f866(f316(x85641),x85645),f195(f937(x85641,a925))))),f866(f866(f23(x85642),f866(f866(f6(x85641,x85642),x85643),x85644)),f866(x85643,x85645)))+~P107(f866(f866(f336(x85641),x85645),x85644))
% 157.76/157.53 [8593]~P3(x85931)+~P107(f866(f66(x85932),x85934))+E(f866(f866(f23(x85931),f866(f866(f6(x85932,x85931),x85933),x85934)),f866(f866(f6(x85932,x85931),x85933),x85935)),f866(f866(f6(x85932,x85931),x85933),f866(f866(f23(f937(x85932,a925)),x85934),x85935)))+~P107(f866(f866(f243(f937(x85932,a925)),x85935),x85934))
% 157.76/157.53 [8612]P107(f866(f66(x86121),f866(x86122,x86123)))+~P107(f866(f66(x86124),x86125))+~P107(f866(f866(f336(x86124),x86123),x86125))+~P107(f866(f66(x86121),f866(f866(f44(x86124,f937(x86121,a925)),x86125),x86122)))
% 157.76/157.53 [9067]~P8(x90671,x90675,x90674)+~E(f866(f293(x90671,x90671,x90674),f866(f866(f316(x90671),x90672),f195(f937(x90671,a925)))),f866(f293(x90671,x90671,x90674),f866(f866(f316(x90671),x90673),f195(f937(x90671,a925)))))+~P107(f866(f866(f336(x90671),x90673),x90675))+P107(f866(f866(f336(f936(x90671,x90671)),f866(f866(f260(x90671,x90671),x90672),x90673)),x90674))
% 157.76/157.53 [9371]~P107(f866(x93711,x93715))+P107(f866(x93711,f639(x93711,x93712,x93713,x93714)))+P107(f866(x93711,f630(x93711,x93712,x93713,x93714)))+~P107(f866(f866(f336(x93714),x93715),f866(f866(f117(f937(x93714,a925)),x93713),x93712)))
% 157.76/157.53 [9554]~P107(f866(x95541,x95545))+P107(f866(x95541,f630(x95541,x95542,x95543,x95544)))+P107(f866(f866(f336(x95544),f639(x95541,x95542,x95543,x95544)),x95542))+~P107(f866(f866(f336(x95544),x95545),f866(f866(f117(f937(x95544,a925)),x95543),x95542)))
% 157.76/157.53 [9555]~P107(f866(x95551,x95555))+P107(f866(x95551,f639(x95551,x95552,x95553,x95554)))+P107(f866(f866(f336(x95554),f630(x95551,x95552,x95553,x95554)),x95553))+~P107(f866(f866(f336(x95554),x95555),f866(f866(f117(f937(x95554,a925)),x95553),x95552)))
% 157.76/157.53 [9559]P107(f866(x95591,x95592))+~P107(f866(x95591,f614(x95591,x95593,x95594,x95595)))+~P107(f866(x95591,f601(x95591,x95593,x95594,x95595)))+~P107(f866(f866(f336(x95595),x95592),f866(f866(f117(f937(x95595,a925)),x95594),x95593)))
% 157.76/157.53 [9564]~P38(x95641,x95644)+~P107(f866(f866(f336(f936(x95641,x95641)),f866(f866(f260(x95641,x95641),x95642),x95645)),x95644))+P107(f866(f866(f336(f936(x95641,x95641)),f866(f866(f260(x95641,x95641),x95642),x95643)),x95644))+~P107(f866(f866(f336(f936(x95641,x95641)),f866(f866(f260(x95641,x95641),x95645),x95643)),x95644))
% 157.76/157.53 [9603]E(x96031,x96032)+~P107(f866(f866(f336(f936(x96033,x96033)),f866(f866(f260(x96033,x96033),x96031),x96032)),f314(x96033,x96035)))+P107(f866(f866(f336(x96033),x96031),x96034))+~P107(f866(f866(f243(f937(f936(x96033,x96033),a925)),x96035),f866(f866(f262(x96033,x96033),x96034),f866(f16(f937(x96033,a925),x96033),x96034))))
% 157.76/157.53 [9621]P107(f866(x96211,x96212))+~P107(f866(x96211,f601(x96211,x96214,x96215,x96213)))+P107(f866(f866(f336(x96213),f614(x96211,x96214,x96215,x96213)),x96214))+~P107(f866(f866(f336(x96213),x96212),f866(f866(f117(f937(x96213,a925)),x96215),x96214)))
% 157.76/157.53 [9622]P107(f866(x96221,x96222))+~P107(f866(x96221,f614(x96221,x96224,x96225,x96223)))+P107(f866(f866(f336(x96223),f601(x96221,x96224,x96225,x96223)),x96225))+~P107(f866(f866(f336(x96223),x96222),f866(f866(f117(f937(x96223,a925)),x96225),x96224)))
% 157.76/157.53 [9687]P107(f866(x96871,x96872))+P107(f866(f866(f336(x96873),f614(x96871,x96874,x96875,x96873)),x96874))+P107(f866(f866(f336(x96873),f601(x96871,x96874,x96875,x96873)),x96875))+~P107(f866(f866(f336(x96873),x96872),f866(f866(f117(f937(x96873,a925)),x96875),x96874)))
% 157.76/157.53 [9689]~P107(f866(x96892,x96895))+P107(f866(f866(f336(x96891),f639(x96892,x96893,x96894,x96891)),x96893))+P107(f866(f866(f336(x96891),f630(x96892,x96893,x96894,x96891)),x96894))+~P107(f866(f866(f336(x96891),x96895),f866(f866(f117(f937(x96891,a925)),x96894),x96893)))
% 157.76/157.53 [9837]~P8(x98371,x98375,x98374)+~P107(f866(f866(f336(x98371),x98373),x98375))+P107(f866(f866(f336(f936(x98371,x98371)),f866(f866(f260(x98371,x98371),x98372),x98373)),x98374))+~P107(f866(f866(f243(f937(x98371,a925)),f866(f293(x98371,x98371,x98374),f866(f866(f316(x98371),x98373),f195(f937(x98371,a925))))),f866(f293(x98371,x98371,x98374),f866(f866(f316(x98371),x98372),f195(f937(x98371,a925))))))
% 157.76/157.53 [9966]~P110(x99665)+~P5(x99665)+P107(f866(f866(f336(x99661),f617(x99662,x99663,x99664,x99661,x99665)),x99664))+~P107(f866(f866(f244(x99665),f866(f866(f45(x99661,x99665),x99664),x99663)),x99662))
% 157.76/157.53 [9999]~P82(x99995)+~P88(x99995)+P107(f866(f866(f336(x99991),f703(x99992,x99993,x99994,x99991,x99995)),f866(f179(x99991),x99994)))+P107(f866(f866(f243(x99995),f866(f172(x99995),f866(f866(f161(x99991,x99995),x99993),x99994))),f866(f172(x99995),f866(f866(f161(x99991,x99995),x99992),x99994))))
% 157.76/157.53 [10107]~P110(x101071)+~P5(x101071)+P107(f866(f866(f244(x101071),f866(x101072,f617(x101073,x101072,x101074,x101075,x101071))),x101073))+~P107(f866(f866(f244(x101071),f866(f866(f45(x101075,x101071),x101074),x101072)),x101073))
% 157.76/157.53 [10238]~P82(x102381)+~P88(x102381)+~P107(f866(f866(f243(x102381),f866(x102383,f703(x102385,x102383,x102384,x102382,x102381))),f866(x102385,f703(x102385,x102383,x102384,x102382,x102381))))+P107(f866(f866(f243(x102381),f866(f172(x102381),f866(f866(f161(x102382,x102381),x102383),x102384))),f866(f172(x102381),f866(f866(f161(x102382,x102381),x102385),x102384))))
% 157.76/157.53 [8906]~P71(x89061)+~P107(f866(f66(x89064),x89065))+~P107(f866(f866(f336(x89064),x89063),x89065))+E(f866(f866(f87(x89061),f866(x89062,x89063)),f866(f866(f9(x89064,x89061),x89062),f866(f866(f23(f937(x89064,a925)),x89065),f866(f866(f316(x89064),x89063),f195(f937(x89064,a925)))))),f866(f866(f9(x89064,x89061),x89062),x89065))
% 157.76/157.53 [8908]~P72(x89081)+~P107(f866(f66(x89084),x89085))+~P107(f866(f866(f336(x89084),x89083),x89085))+E(f866(f866(f86(x89081),f866(x89082,x89083)),f866(f866(f6(x89084,x89081),x89082),f866(f866(f23(f937(x89084,a925)),x89085),f866(f866(f316(x89084),x89083),f195(f937(x89084,a925)))))),f866(f866(f6(x89084,x89081),x89082),x89085))
% 157.76/157.53 [8968]~P18(x89681,x89684,x89685)+~P107(f866(f66(x89681),x89682))+E(f866(f866(f23(f937(x89681,a925)),x89682),f866(f866(f316(x89681),x89683),f195(f937(x89681,a925)))),f195(f937(x89681,a925)))+E(f866(f866(x89684,x89683),f866(x89685,f866(f866(f23(f937(x89681,a925)),x89682),f866(f866(f316(x89681),x89683),f195(f937(x89681,a925)))))),f866(x89685,f866(f866(f316(x89681),x89683),x89682)))
% 157.76/157.53 [9350]~P71(x93501)+~P107(f866(f66(x93502),x93505))+~P107(f866(f66(x93502),x93504))+E(f866(f866(f87(x93501),f866(f866(f9(x93502,x93501),x93503),f866(f866(f117(f937(x93502,a925)),x93504),x93505))),f866(f866(f9(x93502,x93501),x93503),f866(f866(f108(f937(x93502,a925)),x93504),x93505))),f866(f866(f87(x93501),f866(f866(f9(x93502,x93501),x93503),x93504)),f866(f866(f9(x93502,x93501),x93503),x93505)))
% 157.76/157.53 [9351]~P72(x93511)+~P107(f866(f66(x93512),x93515))+~P107(f866(f66(x93512),x93514))+E(f866(f866(f86(x93511),f866(f866(f6(x93512,x93511),x93513),f866(f866(f117(f937(x93512,a925)),x93514),x93515))),f866(f866(f6(x93512,x93511),x93513),f866(f866(f108(f937(x93512,a925)),x93514),x93515))),f866(f866(f86(x93511),f866(f866(f6(x93512,x93511),x93513),x93514)),f866(f866(f6(x93512,x93511),x93513),x93515)))
% 157.76/157.53 [9488]~P3(x94881)+~P107(f866(f66(x94882),x94885))+~P107(f866(f66(x94882),x94884))+E(f866(f866(f23(x94881),f866(f866(f86(x94881),f866(f866(f6(x94882,x94881),x94883),x94884)),f866(f866(f6(x94882,x94881),x94883),x94885))),f866(f866(f6(x94882,x94881),x94883),f866(f866(f108(f937(x94882,a925)),x94884),x94885))),f866(f866(f6(x94882,x94881),x94883),f866(f866(f117(f937(x94882,a925)),x94884),x94885)))
% 157.76/157.53 [9699]~P25(x96991,x96992,x96993,x96995)+~P25(x96991,x96992,x96993,x96994)+P25(x96991,x96992,x96993,f866(f866(f117(f937(x96991,a925)),x96994),x96995))+~E(f866(f866(f108(f937(x96992,a925)),f866(f317(x96991,x96992,x96993),f866(f866(f23(f937(x96991,a925)),x96994),x96995))),f866(f317(x96991,x96992,x96993),f866(f866(f23(f937(x96991,a925)),x96995),x96994))),f195(f937(x96992,a925)))
% 157.76/157.53 [9812]E(x98121,f2(a1))+~P107(f866(f866(f244(a1),f2(a1)),x98123))+~P107(f866(f54(x98122,x98121),f866(f866(f260(a1,a1),x98124),x98125)))+P107(f866(f54(x98122,f866(f866(f87(a1),x98121),x98123)),f866(f866(f260(a1,a1),f866(f866(f41(a1),x98124),x98123)),f866(f866(f86(a1),f866(f866(f87(a1),x98121),f50(a1,x98124,x98123))),x98125))))
% 157.76/157.53 [9820]~P107(f866(f866(f244(a930),f2(a930)),x98203))+~P107(f866(f866(f244(a930),f2(a930)),x98202))+~P107(f866(f53(x98201,x98202),f866(f866(f260(a930,a930),x98204),x98205)))+P107(f866(f53(x98201,f866(f866(f87(a930),x98202),x98203)),f866(f866(f260(a930,a930),f866(f866(f41(a930),x98204),x98203)),f866(f866(f86(a930),f866(f866(f87(a930),x98202),f50(a930,x98204,x98203))),x98205))))
% 157.76/157.53 [9869]~P71(x98691)+~P107(f866(f66(x98692),x98695))+~P107(f866(f66(x98692),x98694))+E(f866(f866(f87(x98691),f866(f866(f866(f70(x98691,x98692,f87(x98691)),x98693),f84(x98691)),f866(f866(f117(f937(x98692,a925)),x98694),x98695))),f866(f866(f866(f70(x98691,x98692,f87(x98691)),x98693),f84(x98691)),f866(f866(f108(f937(x98692,a925)),x98694),x98695))),f866(f866(f87(x98691),f866(f866(f866(f70(x98691,x98692,f87(x98691)),x98693),f84(x98691)),x98694)),f866(f866(f866(f70(x98691,x98692,f87(x98691)),x98693),f84(x98691)),x98695)))
% 157.76/157.53 [9871]~E(f866(f866(f182(x98711),x98715),x98712),f866(f866(f182(x98711),x98715),x98713))+P107(f866(f866(f336(f936(f931(x98711),f931(x98711))),f866(f866(f260(f931(x98711),f931(x98711)),x98712),x98713)),f154(x98711,x98714)))+~P107(f866(f866(f244(a930),x98715),f866(f866(f241(a930),f866(f196(f931(x98711)),x98712)),f866(f196(f931(x98711)),x98713))))+~P107(f866(f866(f336(f936(x98711,x98711)),f866(f866(f260(x98711,x98711),f866(f866(f171(x98711),x98712),x98715)),f866(f866(f171(x98711),x98713),x98715))),x98714))
% 157.76/157.53 [9987]~P88(x99875)+~P148(x99875)+P107(f866(f866(f336(x99871),f412(x99872,x99873,x99874,x99871,x99875)),x99874))+P107(f866(f866(f243(x99875),f866(f866(f6(x99871,x99875),x99873),x99874)),f866(f866(f87(x99875),f866(f107(x99875),f866(f40(x99871),x99874))),x99872)))
% 157.76/157.53 [10166]~P88(x101661)+~P148(x101661)+~P107(f866(f866(f243(x101661),f866(x101663,f412(x101665,x101663,x101664,x101662,x101661))),x101665))+P107(f866(f866(f243(x101661),f866(f866(f6(x101662,x101661),x101663),x101664)),f866(f866(f87(x101661),f866(f107(x101661),f866(f40(x101662),x101664))),x101665)))
% 157.76/157.53 [8936]E(f866(f866(f141(x89361),x89362),x89363),f866(f866(f141(x89361),x89364),x89365))+~E(f866(f866(f182(x89361),f866(f196(f931(x89361)),x89362)),x89364),x89362)+~E(f866(f866(f141(x89361),f866(f866(f145(x89361),f866(f196(f931(x89361)),x89362)),x89364)),x89365),x89363)+P107(f866(f866(f243(a930),f866(f196(f931(x89361)),x89364)),f866(f196(f931(x89361)),x89362)))
% 157.76/157.53 [9066]E(f866(f866(f141(x90661),x90662),x90663),f866(f866(f141(x90661),x90664),x90665))+~E(f866(f866(f182(x90661),f866(f196(f931(x90661)),x90662)),x90664),x90662)+~E(x90663,f866(f866(f141(x90661),f866(f866(f145(x90661),f866(f196(f931(x90661)),x90662)),x90664)),x90665))+~P107(f866(f866(f243(a930),f866(f196(f931(x90661)),x90662)),f866(f196(f931(x90661)),x90664)))
% 157.76/157.53 [10299]~P107(f866(x102995,x102994))+~P107(f866(f66(x102992),f866(f270(x102992),x102995)))+P107(f866(f66(x102991),f866(f270(x102991),f866(f866(f7(x102991,x102992,a925),x102993),x102994))))+~P107(f866(f66(x102991),f866(f270(x102991),f866(f866(f8(f937(x102992,a925),a925,x102991),f93(x102992)),f866(f866(f8(f937(x102992,a925),f937(x102992,a925),x102991),f866(f18(x102992,a925,a925),f866(f866(f8(a925,f937(a925,a925),x102992),a333),x102995))),x102993)))))
% 157.76/157.53 [10371]~P107(f866(f66(x103712),x103715))+~P107(f866(f866(f336(x103712),x103714),x103715))+P107(f866(f66(x103711),f866(f270(x103711),f866(f866(f7(x103711,x103712,a925),x103713),x103714))))+~P107(f866(f66(x103711),f866(f270(x103711),f866(f866(f8(f937(x103712,a925),a925,x103711),f93(x103712)),f866(f866(f8(f937(x103712,a925),f937(x103712,a925),x103711),f866(f18(x103712,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103712),a333),f866(f866(f7(x103712,f937(x103712,a925),a925),f336(x103712)),x103715)))),x103713)))))
% 157.76/157.53 [8721]~P19(x87215,x87211,x87216,x87212)+E(f866(f78(x87211,x87211,x87211,f866(x87212,x87213)),f866(x87212,x87214)),f866(f78(x87211,x87211,x87211,f866(x87212,x87214)),f866(x87212,x87213)))+~P107(f866(f66(x87215),x87214))+~P107(f866(f66(x87215),x87213))
% 157.76/157.53 [8123]~P25(x81231,x81232,x81234,x81233)+~E(f866(x81234,x81236),x81235)+E(f866(f83(x81231,x81232,x81233,x81234),x81235),x81236)+~P107(f866(f866(f336(x81231),x81236),x81233))
% 157.76/157.53 [8124]~P25(x81241,x81242,x81244,x81243)+~E(f866(x81244,x81246),x81245)+E(f866(f97(x81241,x81242,x81243,x81244),x81245),x81246)+~P107(f866(f866(f336(x81241),x81246),x81243))
% 157.76/157.53 [8317]~P20(x83176,x83171,x83174,x83172)+E(f866(f78(x83171,x83171,x83171,f866(x83172,x83173)),f866(x83174,x83175)),f866(x83172,x83173))+~P107(f866(f66(x83176),x83173))+~P107(f866(f866(f336(x83176),x83175),x83173))
% 157.76/157.53 [9440]E(x94401,x94402)+~E(f866(f97(x94403,x94404,x94405,x94406),x94401),f866(f97(x94403,x94404,x94405,x94406),x94402))+~P107(f866(f866(f336(x94404),x94402),f866(f317(x94403,x94404,x94406),x94405)))+~P107(f866(f866(f336(x94404),x94401),f866(f317(x94403,x94404,x94406),x94405)))
% 157.76/157.53 [9538]~P19(x95383,x95381,x95386,x95382)+E(f866(f78(x95381,x95381,x95381,f866(x95382,f866(f866(f23(f937(x95383,a925)),x95384),f866(f866(f316(x95383),x95385),f195(f937(x95383,a925)))))),f866(x95386,x95385)),f866(x95382,x95384))+~P107(f866(f66(x95383),x95384))+~P107(f866(f866(f336(x95383),x95385),x95384))
% 157.76/157.53 [7216]~P63(x72161)+~E(f50(x72161,x72163,x72164),f50(x72161,x72166,x72164))+~E(f50(x72161,x72162,x72164),f50(x72161,x72165,x72164))+E(f50(x72161,f866(f866(f23(x72161),x72162),x72163),x72164),f50(x72161,f866(f866(f23(x72161),x72165),x72166),x72164))
% 157.76/157.53 [7217]~P62(x72171)+~E(f50(x72171,x72173,x72174),f50(x72171,x72176,x72174))+~E(f50(x72171,x72172,x72174),f50(x72171,x72175,x72174))+E(f50(x72171,f866(f866(f87(x72171),x72172),x72173),x72174),f50(x72171,f866(f866(f87(x72171),x72175),x72176),x72174))
% 157.76/157.53 [7218]~P62(x72181)+~E(f50(x72181,x72183,x72184),f50(x72181,x72186,x72184))+~E(f50(x72181,x72182,x72184),f50(x72181,x72185,x72184))+E(f50(x72181,f866(f866(f86(x72181),x72182),x72183),x72184),f50(x72181,f866(f866(f86(x72181),x72185),x72186),x72184))
% 157.76/157.53 [8021]~P16(x80211,x80212,x80213)+~P107(f866(f66(x80211),x80216))+E(f866(f866(f69(x80211,x80212,x80213),x80214),f866(f866(f316(x80211),x80215),x80216)),f866(f866(f69(x80211,x80212,x80213),f866(f866(x80213,x80215),x80214)),x80216))+P107(f866(f866(f336(x80211),x80215),x80216))
% 157.76/157.53 [8082]~P5(x80821)+P107(f866(f866(f243(x80821),x80822),f866(x80823,x80824)))+~P107(f866(f866(f336(x80825),x80824),x80826))+~P107(f866(f866(f243(x80821),x80822),f866(f866(f45(x80825,x80821),x80826),x80823)))
% 157.76/157.53 [8239]~P16(x82391,x82392,x82393)+~P107(f866(f66(x82391),x82396))+E(f866(f866(f69(x82391,x82392,x82393),x82394),f866(f866(f316(x82391),x82395),x82396)),f866(f866(x82393,x82395),f866(f866(f69(x82391,x82392,x82393),x82394),x82396)))+P107(f866(f866(f336(x82391),x82395),x82396))
% 157.76/157.53 [8334]~P110(x83343)+~P107(f866(x83342,x83345))+~P13(x83343,f866(f866(f161(x83341,x83343),x83344),x83346))+E(f866(f143(x83341,x83342),f866(f866(f155(x83341,x83343,x83344),x83345),x83346)),f866(f866(f155(x83341,x83343,x83344),x83345),f866(f143(x83341,x83342),x83346)))
% 157.76/157.53 [8354]E(x83541,x83542)+E(x83543,f2(a1))+~P107(f866(f54(x83544,x83543),f866(f866(f260(a1,a1),x83545),x83542)))+~P107(f866(f54(x83544,x83543),f866(f866(f260(a1,a1),x83546),x83541)))
% 157.76/157.53 [8355]E(x83551,x83552)+E(x83553,f2(a1))+~P107(f866(f54(x83554,x83553),f866(f866(f260(a1,a1),x83552),x83555)))+~P107(f866(f54(x83554,x83553),f866(f866(f260(a1,a1),x83551),x83556)))
% 157.76/157.53 [8375]~P19(x83752,x83755,x83756,x83751)+~P107(f866(f66(x83752),x83754))+E(f866(x83751,f866(f866(f316(x83752),x83753),x83754)),f866(f78(x83755,x83755,x83755,f866(x83751,x83754)),f866(x83756,x83753)))+P107(f866(f866(f336(x83752),x83753),x83754))
% 157.76/157.53 [8596]~P20(x85965,x85961,x85966,x85962)+E(f866(f78(x85961,x85961,x85961,f866(x85962,x85963)),f866(x85962,x85964)),f866(x85962,x85963))+~P107(f866(f66(x85965),x85963))+~P107(f866(f866(f243(f937(x85965,a925)),x85964),x85963))
% 157.76/157.53 [9742]~P25(x97421,x97422,x97424,x97423)+~P107(f866(f866(f336(x97422),x97425),f866(f317(x97421,x97422,x97424),x97423)))+P107(f866(f866(f336(x97421),f866(f83(x97421,x97422,x97423,x97424),x97425)),x97426))+~P107(f866(f866(f243(f937(x97421,a925)),x97423),x97426))
% 157.76/157.53 [10118]~P72(x101182)+~E(f403(x101181,x101183,x101185,x101186,x101184,x101182),f404(x101181,x101183,x101185,x101186,x101184,x101182))+~P107(f866(f66(x101184),x101186))+E(f866(f866(f6(x101181,x101182),x101183),f866(f317(x101184,x101181,x101185),x101186)),f866(f866(f6(x101184,x101182),f866(f78(x101181,x101182,x101184,x101183),x101185)),x101186))
% 157.76/157.53 [10147]~P72(x101476)+E(f866(x101471,f403(x101472,x101473,x101471,x101474,x101475,x101476)),f866(x101471,f404(x101472,x101473,x101471,x101474,x101475,x101476)))+E(f866(f866(f6(x101472,x101476),x101473),f866(f317(x101475,x101472,x101471),x101474)),f866(f866(f6(x101475,x101476),f866(f78(x101472,x101476,x101475,x101473),x101471)),x101474))+~P107(f866(f66(x101475),x101474))
% 157.76/157.53 [10188]~P72(x101882)+~E(f866(x101883,f866(x101885,f404(x101881,x101883,x101885,x101886,x101884,x101882))),f2(x101882))+~P107(f866(f66(x101884),x101886))+E(f866(f866(f6(x101881,x101882),x101883),f866(f317(x101884,x101881,x101885),x101886)),f866(f866(f6(x101884,x101882),f866(f78(x101881,x101882,x101884,x101883),x101885)),x101886))
% 157.76/157.53 [10246]~P72(x102462)+~P107(f866(f66(x102464),x102466))+E(f866(f866(f6(x102461,x102462),x102463),f866(f317(x102464,x102461,x102465),x102466)),f866(f866(f6(x102464,x102462),f866(f78(x102461,x102462,x102464,x102463),x102465)),x102466))+P107(f866(f866(f336(x102464),f404(x102461,x102463,x102465,x102466,x102464,x102462)),x102466))
% 157.76/157.53 [10247]~P72(x102472)+~P107(f866(f66(x102474),x102476))+E(f866(f866(f6(x102471,x102472),x102473),f866(f317(x102474,x102471,x102475),x102476)),f866(f866(f6(x102474,x102472),f866(f78(x102471,x102472,x102474,x102473),x102475)),x102476))+P107(f866(f866(f336(x102474),f403(x102471,x102473,x102475,x102476,x102474,x102472)),x102476))
% 157.76/157.53 [10370]~P71(x103701)+~P107(f866(f66(x103702),x103706))+E(f866(f866(f866(f70(x103701,x103702,f87(x103701)),f866(f866(f18(x103702,f937(x103703,a925),x103701),f866(f866(f7(x103702,x103701,f937(f937(x103703,a925),x103701)),f866(f866(f8(f937(x103703,x103701),f937(x103701,f937(f937(x103703,a925),x103701)),x103702),f70(x103701,x103703,f87(x103701))),x103704)),f84(x103701))),x103705)),f84(x103701)),x103706),f866(f866(f866(f70(x103701,f936(x103702,x103703),f87(x103701)),f866(f265(x103702,x103703,x103701),x103704)),f84(x103701)),f866(f866(f262(x103702,x103703),x103706),x103705)))+P107(f866(f866(f336(x103702),f536(x103704,x103705,x103703,x103706,x103702,x103701)),x103706))
% 157.76/157.53 [10392]~P71(x103921)+~P107(f866(f66(x103922),x103926))+E(f866(f866(f866(f70(x103921,x103922,f87(x103921)),f866(f866(f18(x103922,f937(x103923,a925),x103921),f866(f866(f7(x103922,x103921,f937(f937(x103923,a925),x103921)),f866(f866(f8(f937(x103923,x103921),f937(x103921,f937(f937(x103923,a925),x103921)),x103922),f70(x103921,x103923,f87(x103921))),x103924)),f84(x103921))),x103925)),f84(x103921)),x103926),f866(f866(f866(f70(x103921,f936(x103922,x103923),f87(x103921)),f866(f265(x103922,x103923,x103921),x103924)),f84(x103921)),f866(f866(f262(x103922,x103923),x103926),x103925)))+~P107(f866(f66(x103923),f866(x103925,f536(x103924,x103925,x103923,x103926,x103922,x103921))))
% 157.76/157.53 [8506]~P20(x85062,x85065,x85066,x85061)+~P107(f866(f66(x85062),x85064))+~P107(f866(f66(x85062),x85063))+E(f866(x85061,f866(f866(f117(f937(x85062,a925)),x85063),x85064)),f866(f78(x85065,x85065,x85065,f866(x85061,x85063)),f866(x85061,x85064)))
% 157.76/157.53 [8722]~P5(x87221)+P107(f866(f866(f243(x87221),f866(x87222,x87223)),x87224))+~P107(f866(f866(f336(x87225),x87223),x87226))+~P107(f866(f866(f243(x87221),f866(f866(f44(x87225,x87221),x87226),x87222)),x87224))
% 157.76/157.53 [9156]~P25(x91562,x91561,x91563,x91566)+E(f866(f866(f23(f937(x91561,a925)),f866(f317(x91562,x91561,x91563),x91564)),f866(f317(x91562,x91561,x91563),x91565)),f866(f317(x91562,x91561,x91563),f866(f866(f23(f937(x91562,a925)),x91564),x91565)))+~P107(f866(f866(f243(f937(x91562,a925)),x91565),x91566))+~P107(f866(f866(f243(f937(x91562,a925)),x91564),x91566))
% 157.76/157.53 [9157]~P25(x91572,x91571,x91573,x91576)+E(f866(f866(f108(f937(x91571,a925)),f866(f317(x91572,x91571,x91573),x91574)),f866(f317(x91572,x91571,x91573),x91575)),f866(f317(x91572,x91571,x91573),f866(f866(f108(f937(x91572,a925)),x91574),x91575)))+~P107(f866(f866(f243(f937(x91572,a925)),x91575),x91576))+~P107(f866(f866(f243(f937(x91572,a925)),x91574),x91576))
% 157.76/157.53 [9416]E(x94161,x94162)+~P55(x94163,x94164,x94165)+~P107(f866(f866(f336(f936(x94163,x94164)),f866(f866(f260(x94163,x94164),x94166),x94162)),x94165))+~P107(f866(f866(f336(f936(x94163,x94164)),f866(f866(f260(x94163,x94164),x94166),x94161)),x94165))
% 157.76/157.53 [10184]~P69(x101841)+~E(f866(x101843,f489(x101844,x101846,x101843,x101845,x101842,x101841)),f866(x101846,f489(x101844,x101846,x101843,x101845,x101842,x101841)))+~P107(f866(f66(x101842),x101845))+E(f866(f866(f866(f70(x101841,x101842,f87(x101841)),x101843),x101844),x101845),f866(f866(f866(f70(x101841,x101842,f87(x101841)),x101846),x101844),x101845))
% 157.76/157.53 [10244]~P69(x102441)+~P107(f866(f66(x102442),x102445))+E(f866(f866(f866(f70(x102441,x102442,f87(x102441)),x102443),x102444),x102445),f866(f866(f866(f70(x102441,x102442,f87(x102441)),x102446),x102444),x102445))+P107(f866(f866(f336(x102442),f489(x102444,x102443,x102446,x102445,x102442,x102441)),x102445))
% 157.76/157.53 [8950]~P69(x89501)+~P107(f866(f66(x89502),x89506))+P107(f866(f866(f336(x89502),x89505),x89506))+E(f866(f866(f866(f70(x89501,x89502,f87(x89501)),x89503),x89504),f866(f866(f316(x89502),x89505),x89506)),f866(f866(f87(x89501),f866(x89503,x89505)),f866(f866(f866(f70(x89501,x89502,f87(x89501)),x89503),x89504),x89506)))
% 157.76/157.53 [9003]~P8(x90031,x90036,x90033)+~P11(x90031,f937(x90032,a925),x90033,x90035)+~P107(f866(f866(f336(x90031),x90034),x90036))+E(f866(f866(f44(x90031,f937(x90032,a925)),f866(f293(x90031,x90031,x90033),f866(f866(f316(x90031),x90034),f195(f937(x90031,a925))))),x90035),f866(x90035,x90034))
% 157.76/157.53 [9131]~P16(x91313,x91314,x91311)+~P107(f866(f66(x91313),x91316))+~P107(f866(f866(f336(x91313),x91312),x91316))+E(f866(f866(x91311,x91312),f866(f866(f69(x91313,x91314,x91311),x91315),f866(f866(f23(f937(x91313,a925)),x91316),f866(f866(f316(x91313),x91312),f195(f937(x91313,a925)))))),f866(f866(f69(x91313,x91314,x91311),x91315),x91316))
% 157.76/157.53 [9426]~P19(x94263,x94261,x94266,x94262)+~P107(f866(f66(x94263),x94265))+~P107(f866(f66(x94263),x94264))+E(f866(f78(x94261,x94261,x94261,f866(x94262,f866(f866(f117(f937(x94263,a925)),x94264),x94265))),f866(x94262,f866(f866(f108(f937(x94263,a925)),x94264),x94265))),f866(f78(x94261,x94261,x94261,f866(x94262,x94264)),f866(x94262,x94265)))
% 157.76/157.53 [9765]~E(x97653,f866(f866(f166(x97651,x97652),x97655),x97656))+P107(f866(f866(f336(f936(f931(x97651),f931(x97651))),f866(f866(f260(f931(x97651),f931(x97651)),x97652),x97653)),f164(x97651,x97654)))+~P107(f866(f866(f244(a930),x97655),f866(f196(f931(x97651)),x97652)))+~P107(f866(f866(f336(f936(x97651,x97651)),f866(f866(f260(x97651,x97651),f866(f866(f171(x97651),x97652),x97655)),x97656)),x97654))
% 157.76/157.53 [10256]~P71(x102562)+~P107(f866(f66(x102561),x102566))+P107(f866(f866(f336(x102561),f534(x102564,x102565,x102563,x102566,x102561,x102562)),x102566))+E(f866(f866(f9(x102561,x102562),f866(f866(f18(x102561,f937(x102563,a925),x102562),f866(f866(f8(f937(x102563,x102562),f937(f937(x102563,a925),x102562),x102561),f9(x102563,x102562)),x102564)),x102565)),x102566),f866(f866(f9(f936(x102561,x102563),x102562),f866(f265(x102561,x102563,x102562),x102564)),f866(f866(f262(x102561,x102563),x102566),x102565)))
% 157.76/157.53 [10257]~P72(x102572)+~P107(f866(f66(x102571),x102576))+P107(f866(f866(f336(x102571),f535(x102574,x102575,x102573,x102576,x102571,x102572)),x102576))+E(f866(f866(f6(x102571,x102572),f866(f866(f18(x102571,f937(x102573,a925),x102572),f866(f866(f8(f937(x102573,x102572),f937(f937(x102573,a925),x102572),x102571),f6(x102573,x102572)),x102574)),x102575)),x102576),f866(f866(f6(f936(x102571,x102573),x102572),f866(f265(x102571,x102573,x102572),x102574)),f866(f866(f262(x102571,x102573),x102576),x102575)))
% 157.76/157.53 [10297]~P71(x102972)+~P107(f866(f66(x102971),x102976))+~P107(f866(f66(x102973),f866(x102975,f534(x102974,x102975,x102973,x102976,x102971,x102972))))+E(f866(f866(f9(x102971,x102972),f866(f866(f18(x102971,f937(x102973,a925),x102972),f866(f866(f8(f937(x102973,x102972),f937(f937(x102973,a925),x102972),x102971),f9(x102973,x102972)),x102974)),x102975)),x102976),f866(f866(f9(f936(x102971,x102973),x102972),f866(f265(x102971,x102973,x102972),x102974)),f866(f866(f262(x102971,x102973),x102976),x102975)))
% 157.76/157.53 [10298]~P72(x102982)+~P107(f866(f66(x102981),x102986))+~P107(f866(f66(x102983),f866(x102985,f535(x102984,x102985,x102983,x102986,x102981,x102982))))+E(f866(f866(f6(x102981,x102982),f866(f866(f18(x102981,f937(x102983,a925),x102982),f866(f866(f8(f937(x102983,x102982),f937(f937(x102983,a925),x102982),x102981),f6(x102983,x102982)),x102984)),x102985)),x102986),f866(f866(f6(f936(x102981,x102983),x102982),f866(f265(x102981,x102983,x102982),x102984)),f866(f866(f262(x102981,x102983),x102986),x102985)))
% 157.76/157.53 [10278]~P71(x102782)+~P107(f866(f66(x102781),x102786))+P107(f866(f866(f336(x102781),x102783),x102786))+E(f866(f866(f9(x102781,x102782),f866(f866(f7(x102781,x102782,x102782),f866(f866(f18(x102781,x102782,f937(x102782,x102782)),f866(f866(f8(a925,f937(x102782,f937(x102782,x102782)),x102781),f103(x102782)),f866(f866(f7(x102781,x102781,a925),a332),x102783))),x102784)),x102785)),x102786),f866(f866(f252(x102782),x102785),f866(f40(x102781),x102786)))
% 157.76/157.53 [10281]~P71(x102812)+~P107(f866(f66(x102811),x102816))+~P107(f866(f866(f336(x102811),x102813),x102816))+E(f866(f866(f9(x102811,x102812),f866(f866(f7(x102811,x102812,x102812),f866(f866(f18(x102811,x102812,f937(x102812,x102812)),f866(f866(f8(a925,f937(x102812,f937(x102812,x102812)),x102811),f103(x102812)),f866(f866(f7(x102811,x102811,a925),a332),x102813))),x102814)),x102815)),x102816),f866(f866(f87(x102812),f866(x102814,x102813)),f866(f866(f252(x102812),x102815),f866(f866(f23(a930),f866(f40(x102811),x102816)),f84(a930)))))
% 157.76/157.53 [10361]~P107(f866(f66(x103611),x103615))+~P107(f866(f66(x103612),x103613))+P107(f866(f866(f336(x103612),f405(x103616,x103614,x103613,x103612,x103615,x103611)),x103613))+E(f866(f866(f6(x103611,a930),f866(f866(f8(f937(x103612,a925),a930,x103611),f40(x103612)),f866(f866(f8(f937(x103612,a925),f937(x103612,a925),x103611),f270(x103612)),f866(f866(f8(f937(x103612,a925),f937(x103612,a925),x103611),f866(f18(x103612,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103612),a333),f866(f866(f7(x103612,f937(x103612,a925),a925),f336(x103612)),x103613)))),x103614)))),x103615),f866(f866(f87(a930),x103616),f866(f40(x103612),x103613)))
% 157.76/157.53 [10362]~P107(f866(f66(x103621),x103625))+~P107(f866(f66(x103622),x103623))+P107(f866(f866(f336(x103622),f406(x103626,x103624,x103623,x103622,x103625,x103621)),x103623))+E(f866(f866(f6(x103621,a930),f866(f866(f8(f937(x103622,a925),a930,x103621),f40(x103622)),f866(f866(f8(f937(x103622,a925),f937(x103622,a925),x103621),f270(x103622)),f866(f866(f8(f937(x103622,a925),f937(x103622,a925),x103621),f866(f18(x103622,a925,a925),f866(f866(f8(a925,f937(a925,a925),x103622),a333),f866(f866(f7(x103622,f937(x103622,a925),a925),f336(x103622)),x103623)))),x103624)))),x103625),f866(f866(f6(x103622,a930),x103626),x103623))
% 157.76/157.53 [10406]~P107(f866(f66(x104062),x104063))+~P107(f866(f66(x104061),x104065))+~E(f866(f40(x104061),f866(f270(x104061),f866(f866(f18(x104061,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104061),a333),f866(f866(f7(x104061,f937(x104061,a925),a925),f336(x104061)),x104065))),f866(f866(f7(x104061,x104062,a925),x104064),f405(x104066,x104064,x104063,x104062,x104065,x104061))))),x104066)+E(f866(f866(f6(x104061,a930),f866(f866(f8(f937(x104062,a925),a930,x104061),f40(x104062)),f866(f866(f8(f937(x104062,a925),f937(x104062,a925),x104061),f270(x104062)),f866(f866(f8(f937(x104062,a925),f937(x104062,a925),x104061),f866(f18(x104062,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104062),a333),f866(f866(f7(x104062,f937(x104062,a925),a925),f336(x104062)),x104063)))),x104064)))),x104065),f866(f866(f87(a930),x104066),f866(f40(x104062),x104063)))
% 157.76/157.53 [10408]~P107(f866(f66(x104082),x104083))+~P107(f866(f66(x104081),x104085))+~E(f866(f40(x104081),f866(f270(x104081),f866(f866(f18(x104081,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104081),a333),f866(f866(f7(x104081,f937(x104081,a925),a925),f336(x104081)),x104085))),f866(f866(f7(x104081,x104082,a925),x104084),f406(x104086,x104084,x104083,x104082,x104085,x104081))))),f866(x104086,f406(x104086,x104084,x104083,x104082,x104085,x104081)))+E(f866(f866(f6(x104081,a930),f866(f866(f8(f937(x104082,a925),a930,x104081),f40(x104082)),f866(f866(f8(f937(x104082,a925),f937(x104082,a925),x104081),f270(x104082)),f866(f866(f8(f937(x104082,a925),f937(x104082,a925),x104081),f866(f18(x104082,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104082),a333),f866(f866(f7(x104082,f937(x104082,a925),a925),f336(x104082)),x104083)))),x104084)))),x104085),f866(f866(f6(x104082,a930),x104086),x104083))
% 157.76/157.53 [10044]E(x100441,x100442)+~P16(x100443,x100444,x100445)+~P107(f866(f71(x100443,x100444,x100445,x100446,x100447),x100442))+~P107(f866(f71(x100443,x100444,x100445,x100446,x100447),x100441))
% 157.76/157.53 [9841]P107(f866(x98411,x98412))+~P107(f866(f866(f336(x98417),x98412),f866(x98416,x98414)))+~P107(f866(x98411,f826(x98411,x98416,x98415,x98413,x98417)))+~P107(f866(f866(f336(x98413),x98414),x98415))
% 157.76/157.53 [10270]~P16(x102707,x102706,x102701)+E(f866(f866(x102701,x102702),f612(x102702,x102703,x102704,x102705,x102701,x102706,x102707)),x102703)+~P107(f866(f71(x102707,x102706,x102701,x102705,x102704),x102703))+~P107(f866(f866(f336(x102707),x102702),x102704))
% 157.76/157.53 [10339]~P16(x103391,x103392,x103393)+~P107(f866(f71(x103391,x103392,x103393,x103394,x103395),x103397))+P107(f866(f71(x103391,x103392,x103393,x103394,f866(f866(f23(f937(x103391,a925)),x103395),f866(f866(f316(x103391),x103396),f195(f937(x103391,a925))))),f612(x103396,x103397,x103395,x103394,x103393,x103392,x103391)))+~P107(f866(f866(f336(x103391),x103396),x103395))
% 157.76/157.53 [9495]P26(x94951,x94952,x94953,x94954,x94955)+~P26(x94951,x94952,x94953,x94956,x94957)+~E(f866(f317(x94951,x94952,x94953),x94954),x94955)+~P107(f866(f866(f243(f937(x94951,a925)),x94954),x94956))
% 157.76/157.53 [9733]~P26(x97331,x97332,x97333,x97335,x97337)+~P26(x97331,x97332,x97333,x97334,x97336)+P26(x97331,x97332,x97333,f866(f866(f117(f937(x97331,a925)),x97334),x97335),f866(f866(f117(f937(x97332,a925)),x97336),x97337))+~E(f866(f866(f108(f937(x97332,a925)),x97336),x97337),f195(f937(x97332,a925)))
% 157.76/157.53 [9738]~P69(x97381)+~P25(x97385,x97382,x97386,x97387)+~P107(f866(f66(x97385),x97387))+E(f866(f866(f866(f70(x97381,x97382,f87(x97381)),x97383),x97384),f866(f317(x97385,x97382,x97386),x97387)),f866(f866(f866(f70(x97381,x97385,f87(x97381)),f866(f78(x97382,x97381,x97385,x97383),x97386)),x97384),x97387))
% 157.76/157.53 [9864]~E(f866(f866(f316(x98641),x98645),x98646),f866(f866(f316(x98641),x98642),x98643))+~P107(f866(f71(x98641,x98641,x98644,x98642,x98643),x98647))+P107(f866(f866(f336(x98641),x98642),x98643))+P107(f866(f67(x98641,x98644,f866(f866(f316(x98641),x98645),x98646)),x98647))
% 157.76/157.53 [9949]P107(f866(x99491,x99492))+~P107(f866(f866(f336(x99493),x99492),f866(x99494,x99497)))+~P107(f866(f866(f336(x99496),x99497),x99495))+P107(f866(f866(f336(x99493),f826(x99491,x99494,x99495,x99496,x99493)),f866(f866(f44(x99496,f937(x99493,a925)),x99495),x99494)))
% 157.76/157.53 [9967]~P25(x99672,x99671,x99675,x99674)+~P25(x99671,x99673,x99676,f866(f317(x99672,x99671,x99675),x99674))+E(f866(f866(f78(x99671,x99672,x99673,f83(x99672,x99671,x99674,x99675)),f83(x99671,x99673,f866(f317(x99672,x99671,x99675),x99674),x99676)),x99677),f866(f83(x99672,x99673,x99674,f866(f78(x99671,x99673,x99672,x99676),x99675)),x99677))+~P107(f866(f866(f336(x99673),x99677),f866(f317(x99671,x99673,x99676),f866(f317(x99672,x99671,x99675),x99674))))
% 157.76/157.53 [9968]~P25(x99682,x99681,x99685,x99684)+~P25(x99681,x99683,x99686,f866(f317(x99682,x99681,x99685),x99684))+E(f866(f866(f78(x99681,x99682,x99683,f97(x99682,x99681,x99684,x99685)),f97(x99681,x99683,f866(f317(x99682,x99681,x99685),x99684),x99686)),x99687),f866(f97(x99682,x99683,x99684,f866(f78(x99681,x99683,x99682,x99686),x99685)),x99687))+~P107(f866(f866(f336(x99683),x99687),f866(f317(x99681,x99683,x99686),f866(f317(x99682,x99681,x99685),x99684))))
% 157.76/157.53 [10271]~P16(x102717,x102716,x102711)+E(f866(f866(x102711,x102712),f638(x102713,x102714,x102712,x102715,x102711,x102716,x102717)),x102713)+P107(f866(f866(f336(x102717),x102712),x102714))+~P107(f866(f71(x102717,x102716,x102711,x102715,f866(f866(f316(x102717),x102712),x102714)),x102713))
% 157.76/157.53 [10338]~P16(x103381,x103384,x103385)+P107(f866(f71(x103381,x103384,x103385,x103386,x103383),f638(x103387,x103383,x103382,x103386,x103385,x103384,x103381)))+P107(f866(f866(f336(x103381),x103382),x103383))+~P107(f866(f71(x103381,x103384,x103385,x103386,f866(f866(f316(x103381),x103382),x103383)),x103387))
% 157.76/157.53 [10026]E(x100261,f2(a1))+~P107(f866(f54(x100263,x100261),f866(f866(f260(a1,a1),x100265),x100267)))+~P107(f866(f54(x100262,x100261),f866(f866(f260(a1,a1),x100264),x100266)))+P107(f866(f54(f866(f866(f86(a1),x100262),x100263),x100261),f866(f866(f260(a1,a1),f866(f866(f86(a1),f866(f866(f86(a1),x100264),x100265)),f866(f866(f41(a1),f866(f866(f86(a1),x100266),x100267)),x100261))),f50(a1,f866(f866(f86(a1),x100266),x100267),x100261))))
% 157.76/157.53 [10028]~P107(f866(f866(f244(a930),f2(a930)),x100283))+~P107(f866(f53(x100282,x100283),f866(f866(f260(a930,a930),x100285),x100287)))+~P107(f866(f53(x100281,x100283),f866(f866(f260(a930,a930),x100284),x100286)))+P107(f866(f53(f866(f866(f86(a930),x100281),x100282),x100283),f866(f866(f260(a930,a930),f866(f866(f86(a930),f866(f866(f86(a930),x100284),x100285)),f866(f866(f41(a930),f866(f866(f86(a930),x100286),x100287)),x100283))),f50(a930,f866(f866(f86(a930),x100286),x100287),x100283))))
% 157.76/157.53 [10405]~P72(x104052)+~P107(f866(f66(x104053),x104055))+~P107(f866(f66(x104051),x104057))+E(f866(f866(f6(x104051,x104052),f866(f866(f18(x104051,f937(x104053,a925),x104052),f866(f866(f8(f937(x104053,x104052),f937(f937(x104053,a925),x104052),x104051),f6(x104053,x104052)),x104054)),f866(f866(f8(f937(x104053,a925),f937(x104053,a925),x104051),f270(x104053)),f866(f866(f8(f937(x104053,a925),f937(x104053,a925),x104051),f866(f18(x104053,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104053),a333),f866(f866(f7(x104053,f937(x104053,a925),a925),f336(x104053)),x104055)))),x104056)))),x104057),f866(f866(f6(x104053,x104052),f866(f866(f18(x104053,f937(x104051,a925),x104052),f866(f866(f8(f937(x104051,x104052),f937(f937(x104051,a925),x104052),x104053),f6(x104051,x104052)),f866(f7(x104051,x104053,x104052),x104054))),f866(f866(f8(f937(x104051,a925),f937(x104051,a925),x104053),f270(x104051)),f866(f866(f8(f937(x104051,a925),f937(x104051,a925),x104053),f866(f18(x104051,a925,a925),f866(f866(f8(a925,f937(a925,a925),x104051),a333),f866(f866(f7(x104051,f937(x104051,a925),a925),f336(x104051)),x104057)))),f866(f7(x104051,x104053,a925),x104056))))),x104055))
% 157.76/157.53 [10359]~P21(x103598,x103597,x103596,x103595,x103591)+~E(f866(x103592,f862(x103594,x103592,x103593,x103591,x103595,x103596,x103597)),f866(x103594,f862(x103594,x103592,x103593,x103591,x103595,x103596,x103597)))+E(f866(f866(x103591,x103592),x103593),f866(f866(x103591,x103594),x103593))+~P107(f866(f66(x103597),x103593))
% 157.76/157.53 [9900]~P22(x99007,x99006,x99001,x99008,x99002,x99004)+E(f866(f866(x99001,f866(x99002,x99003)),f866(x99004,x99005)),f866(x99004,x99005))+~P107(f866(f66(x99006),x99005))+~P107(f866(f866(f336(x99006),x99003),x99005))
% 157.76/157.53 [9905]~P12(x99056,x99051,x99052,x99058,x99053,x99054)+~P8(x99056,x99057,x99058)+P11(x99051,x99052,x99053,f866(x99054,x99055))+~P107(f866(f866(f336(x99056),x99055),x99057))
% 157.76/157.53 [10377]~P21(x103778,x103775,x103777,x103776,x103771)+E(f866(f866(x103771,x103772),x103773),f866(f866(x103771,x103774),x103773))+~P107(f866(f66(x103775),x103773))+P107(f866(f866(f336(x103775),f862(x103772,x103774,x103773,x103771,x103776,x103777,x103775)),x103773))
% 157.76/157.53 [10458]~P107(f866(f866(x104581,x104586),x104585))+P107(f866(f866(x104581,f850(x104581,x104584,x104585,x104586,x104583,x104582,x104587,x104588)),f851(x104581,x104584,x104585,x104586,x104583,x104582,x104587,x104588)))+P107(f866(f866(x104581,x104582),x104583))+~P107(f866(f866(f336(f936(f936(x104588,x104587),f936(x104588,x104587))),f866(f866(f260(f936(x104588,x104587),f936(x104588,x104587)),f866(f866(f260(x104588,x104587),x104582),x104583)),f866(f866(f260(x104588,x104587),x104586),x104585))),f314(f936(x104588,x104587),x104584)))
% 157.76/157.53 [10459]~P107(f866(f866(x104591,x104596),x104595))+P107(f866(f866(x104591,f852(x104591,x104594,x104593,x104592,x104595,x104596,x104597,x104598)),f853(x104591,x104594,x104593,x104592,x104595,x104596,x104597,x104598)))+P107(f866(f866(x104591,x104592),x104593))+~P107(f866(f866(f336(f936(f936(x104598,x104597),f936(x104598,x104597))),f866(f866(f260(f936(x104598,x104597),f936(x104598,x104597)),f866(f866(f260(x104598,x104597),x104596),x104595)),f866(f866(f260(x104598,x104597),x104592),x104593))),f314(f936(x104598,x104597),x104594)))
% 157.76/157.53 [10469]~P107(f866(f866(x104691,f846(x104691,x104696,x104695,x104694,x104693,x104692,x104697,x104698)),f849(x104691,x104696,x104695,x104694,x104693,x104692,x104697,x104698)))+P107(f866(f866(x104691,x104692),x104693))+~P107(f866(f866(x104691,x104694),x104695))+~P107(f866(f866(f336(f936(f936(x104698,x104697),f936(x104698,x104697))),f866(f866(f260(f936(x104698,x104697),f936(x104698,x104697)),f866(f866(f260(x104698,x104697),x104692),x104693)),f866(f866(f260(x104698,x104697),x104694),x104695))),f314(f936(x104698,x104697),x104696)))
% 157.76/157.53 [10470]~P107(f866(f866(x104701,f854(x104701,x104706,x104703,x104702,x104705,x104704,x104707,x104708)),f855(x104701,x104706,x104703,x104702,x104705,x104704,x104707,x104708)))+P107(f866(f866(x104701,x104702),x104703))+~P107(f866(f866(x104701,x104704),x104705))+~P107(f866(f866(f336(f936(f936(x104708,x104707),f936(x104708,x104707))),f866(f866(f260(f936(x104708,x104707),f936(x104708,x104707)),f866(f866(f260(x104708,x104707),x104704),x104705)),f866(f866(f260(x104708,x104707),x104702),x104703))),f314(f936(x104708,x104707),x104706)))
% 157.76/157.53 [10483]~P107(f866(f866(x104831,x104836),x104837))+P107(f866(f866(x104831,x104832),x104833))+P107(f866(f866(f336(f936(f936(x104834,x104835),f936(x104834,x104835))),f866(f866(f260(f936(x104834,x104835),f936(x104834,x104835)),f866(f866(f260(x104834,x104835),x104836),x104837)),f866(f866(f260(x104834,x104835),f852(x104831,x104838,x104833,x104832,x104837,x104836,x104835,x104834)),f853(x104831,x104838,x104833,x104832,x104837,x104836,x104835,x104834)))),f314(f936(x104834,x104835),x104838)))+~P107(f866(f866(f336(f936(f936(x104834,x104835),f936(x104834,x104835))),f866(f866(f260(f936(x104834,x104835),f936(x104834,x104835)),f866(f866(f260(x104834,x104835),x104836),x104837)),f866(f866(f260(x104834,x104835),x104832),x104833))),f314(f936(x104834,x104835),x104838)))
% 157.76/157.53 [10485]~P107(f866(f866(x104851,x104858),x104857))+P107(f866(f866(x104851,x104852),x104853))+P107(f866(f866(f336(f936(f936(x104854,x104855),f936(x104854,x104855))),f866(f866(f260(f936(x104854,x104855),f936(x104854,x104855)),f866(f866(f260(x104854,x104855),f850(x104851,x104856,x104857,x104858,x104853,x104852,x104855,x104854)),f851(x104851,x104856,x104857,x104858,x104853,x104852,x104855,x104854))),f866(f866(f260(x104854,x104855),x104858),x104857))),f314(f936(x104854,x104855),x104856)))+~P107(f866(f866(f336(f936(f936(x104854,x104855),f936(x104854,x104855))),f866(f866(f260(f936(x104854,x104855),f936(x104854,x104855)),f866(f866(f260(x104854,x104855),x104852),x104853)),f866(f866(f260(x104854,x104855),x104858),x104857))),f314(f936(x104854,x104855),x104856)))
% 157.76/157.53 [9521]~P19(x95217,x95211,x95218,x95213)+~P107(f866(f66(x95217),x95215))+~P107(f866(f66(x95217),x95214))+E(f866(f78(x95211,x95211,x95212,f866(x95213,x95214)),f866(f78(x95211,x95211,x95212,f866(x95213,x95215)),x95216)),f866(f78(x95211,x95211,x95212,f866(x95213,x95215)),f866(f78(x95211,x95211,x95212,f866(x95213,x95214)),x95216)))
% 157.76/157.53 [9530]~P34(x95301,x95302,x95303,x95304,x95307)+P34(x95301,x95302,x95303,f866(f866(f166(x95301,x95304),x95305),x95306),f866(f866(f166(x95302,x95307),x95305),x95308))+~P107(f866(f866(x95303,x95306),x95308))+~P107(f866(f866(f244(a930),x95305),f866(f196(f931(x95301)),x95304)))
% 157.76/157.53 [9531]~P34(x95311,x95312,x95313,x95314,x95317)+P34(x95311,x95312,x95313,f866(f866(f166(x95311,x95314),x95315),x95316),f866(f866(f166(x95312,x95317),x95315),x95318))+~P107(f866(f866(x95313,x95316),x95318))+~P107(f866(f866(f244(a930),x95315),f866(f196(f931(x95312)),x95317)))
% 157.76/157.53 [9610]~P25(x96102,x96102,x96105,x96106)+~P21(x96103,x96102,x96107,x96108,x96101)+~P107(f866(f66(x96102),x96106))+E(f866(f866(x96101,f866(f78(x96102,x96103,x96102,x96104),x96105)),x96106),f866(f866(x96101,x96104),f866(f317(x96102,x96102,x96105),x96106)))
% 157.76/157.53 [9865]P26(x98651,x98652,x98653,x98654,x98655)+~P26(x98652,x98656,x98657,x98655,x98658)+~P26(x98651,x98656,f866(f78(x98652,x98656,x98651,x98657),x98653),x98654,x98658)+~P107(f866(f866(f243(f937(x98652,a925)),f866(f317(x98651,x98652,x98653),x98654)),x98655))
% 157.76/157.53 [9902]~P23(x99027,x99022,x99025,x99028,x99026,x99021)+~P107(f866(f66(x99022),x99024))+E(f866(x99021,f866(f866(f316(x99022),x99023),x99024)),f866(f866(x99025,f866(x99026,x99023)),f866(x99021,x99024)))+P107(f866(f866(f336(x99022),x99023),x99024))
% 157.76/157.53 [9914]~P22(x99146,x99145,x99141,x99147,x99148,x99142)+E(f866(f866(x99141,f866(x99142,x99143)),f866(x99142,x99144)),f866(x99142,x99144))+~P107(f866(f66(x99145),x99144))+~P107(f866(f866(f243(f937(x99145,a925)),x99143),x99144))
% 157.76/157.53 [10403]P24(x104038,x104037,f866(f866(f316(f929(x104038)),f98(x104038,x104034,x104035,x104033)),f195(f937(f929(x104038),a925))))+~P24(x104038,x104037,f866(f866(f316(f929(x104038)),f98(x104038,x104036,x104035,x104031)),f195(f937(f929(x104038),a925))))+~P107(f866(f866(x104036,x104032),f903(x104033,x104034,x104031,x104035,x104036,x104037,x104038)))+P107(f866(f866(x104031,x104032),f914(x104033,x104034,x104031,x104035,x104036,x104037,x104038)))
% 157.76/157.53 [9508]P107(f866(f866(f336(f936(f931(x95081),f931(x95081))),f866(f866(f260(f931(x95081),f931(x95081)),x95082),x95083)),f164(x95081,x95084)))+~E(x95083,f866(f866(f141(x95081),x95085),f866(f866(f158(x95081),x95086),x95087)))+~E(x95082,f866(f866(f141(x95081),x95085),f866(f866(f158(x95081),x95088),x95087)))+~P107(f866(f866(f336(f936(x95081,x95081)),f866(f866(f260(x95081,x95081),x95088),x95086)),x95084))
% 157.76/157.53 [9908]~P22(x99086,x99082,x99085,x99087,x99088,x99081)+~P107(f866(f66(x99082),x99084))+~P107(f866(f66(x99082),x99083))+E(f866(x99081,f866(f866(f117(f937(x99082,a925)),x99083),x99084)),f866(f866(x99085,f866(x99081,x99083)),f866(x99081,x99084)))
% 157.76/157.53 [10448]~P25(x104484,x104482,x104485,x104488)+E(f866(f866(f45(x104481,f937(x104482,a925)),x104483),f866(f866(f8(f937(x104484,a925),f937(x104482,a925),x104481),f317(x104484,x104482,x104485)),x104486)),f866(f317(x104484,x104482,x104485),f866(f866(f45(x104481,f937(x104484,a925)),x104483),x104486)))+~P107(f866(f866(f336(x104481),x104487),x104483))+P107(f866(f866(f336(x104481),f627(x104487,x104486,x104483,x104481,x104488,x104485,x104482,x104484)),x104483))
% 157.76/157.53 [10474]~P25(x104744,x104742,x104745,x104747)+E(f866(f866(f45(x104741,f937(x104742,a925)),x104743),f866(f866(f8(f937(x104744,a925),f937(x104742,a925),x104741),f317(x104744,x104742,x104745)),x104746)),f866(f317(x104744,x104742,x104745),f866(f866(f45(x104741,f937(x104744,a925)),x104743),x104746)))+~P107(f866(f866(f336(x104741),x104748),x104743))+~P107(f866(f866(f243(f937(x104744,a925)),f866(x104746,f627(x104748,x104746,x104743,x104741,x104747,x104745,x104742,x104744))),x104747))
% 157.76/157.53 [10486]~P107(f866(f866(x104861,x104868),x104867))+P107(f866(f866(x104861,x104862),x104863))+~P107(f866(f866(f336(f936(f936(x104864,x104865),f936(x104864,x104865))),f866(f866(f260(f936(x104864,x104865),f936(x104864,x104865)),f866(f866(f260(x104864,x104865),x104862),x104863)),f866(f866(f260(x104864,x104865),x104868),x104867))),f314(f936(x104864,x104865),x104866)))+P107(f866(f866(f336(f936(f936(x104864,x104865),f936(x104864,x104865))),f866(f866(f260(f936(x104864,x104865),f936(x104864,x104865)),f866(f866(f260(x104864,x104865),f846(x104861,x104866,x104867,x104868,x104863,x104862,x104865,x104864)),f849(x104861,x104866,x104867,x104868,x104863,x104862,x104865,x104864))),f866(f866(f260(x104864,x104865),f850(x104861,x104866,x104867,x104868,x104863,x104862,x104865,x104864)),f851(x104861,x104866,x104867,x104868,x104863,x104862,x104865,x104864)))),x104866))
% 157.76/157.53 [10487]~P107(f866(f866(x104871,x104878),x104877))+P107(f866(f866(x104871,x104872),x104873))+~P107(f866(f866(f336(f936(f936(x104874,x104875),f936(x104874,x104875))),f866(f866(f260(f936(x104874,x104875),f936(x104874,x104875)),f866(f866(f260(x104874,x104875),x104878),x104877)),f866(f866(f260(x104874,x104875),x104872),x104873))),f314(f936(x104874,x104875),x104876)))+P107(f866(f866(f336(f936(f936(x104874,x104875),f936(x104874,x104875))),f866(f866(f260(f936(x104874,x104875),f936(x104874,x104875)),f866(f866(f260(x104874,x104875),f852(x104871,x104876,x104873,x104872,x104877,x104878,x104875,x104874)),f853(x104871,x104876,x104873,x104872,x104877,x104878,x104875,x104874))),f866(f866(f260(x104874,x104875),f854(x104871,x104876,x104873,x104872,x104877,x104878,x104875,x104874)),f855(x104871,x104876,x104873,x104872,x104877,x104878,x104875,x104874)))),x104876))
% 157.76/157.53 [9977]~P23(x99777,x99775,x99771,x99778,x99772,x99774)+~P107(f866(f66(x99775),x99776))+~P107(f866(f866(f336(x99775),x99773),x99776))+E(f866(f866(x99771,f866(x99772,x99773)),f866(x99774,f866(f866(f23(f937(x99775,a925)),x99776),f866(f866(f316(x99775),x99773),f195(f937(x99775,a925)))))),f866(x99774,x99776))
% 157.76/157.53 [9985]~P23(x99856,x99853,x99851,x99857,x99858,x99852)+~P107(f866(f66(x99853),x99855))+~P107(f866(f66(x99853),x99854))+E(f866(f866(x99851,f866(x99852,f866(f866(f117(f937(x99853,a925)),x99854),x99855))),f866(x99852,f866(f866(f108(f937(x99853,a925)),x99854),x99855))),f866(f866(x99851,f866(x99852,x99854)),f866(x99852,x99855)))
% 157.76/157.53 [10068]P42(x100681,x100682,x100683,x100684,x100685,f866(f866(x100683,x100686),x100687))+~P42(x100681,x100682,x100683,x100684,f866(f866(f23(f937(x100681,a925)),x100685),f866(f866(f316(x100681),x100688),f195(f937(x100681,a925)))),x100689)+~E(f866(f866(x100683,x100686),x100687),f866(f866(x100683,x100688),x100689))+~P107(f866(f866(f336(x100681),x100688),x100685))
% 157.76/157.53 [10010]~P12(x100106,x100107,x100108,x100109,x1001010,x100101)+E(f866(f866(x100101,x100102),x100103),f866(f866(x100101,x100104),x100105))+~P107(f866(f866(f336(f936(x100107,x100107)),f866(f866(f260(x100107,x100107),x100103),x100105)),x1001010))+~P107(f866(f866(f336(f936(x100106,x100106)),f866(f866(f260(x100106,x100106),x100102),x100104)),x100109))
% 157.76/157.53 [9612]~P83(x96122)+E(x96121,f195(f937(x96122,a925)))+~P107(f866(f66(x96122),x96121))+P107(f866(f866(f336(x96122),f13(x96122,x96121)),x96121))+~P107(f866(f866(f336(x96122),f866(f866(f117(x96122),f908(x96121,x96122)),f909(x96121,x96122))),f866(f866(f316(x96122),f908(x96121,x96122)),f866(f866(f316(x96122),f909(x96121,x96122)),f195(f937(x96122,a925))))))
% 157.76/157.53 [9613]~P83(x96132)+E(x96131,f195(f937(x96132,a925)))+~P107(f866(f66(x96132),x96131))+P107(f866(f866(f336(x96132),f10(x96132,x96131)),x96131))+~P107(f866(f866(f336(x96132),f866(f866(f108(x96132),f918(x96131,x96132)),f347(x96131,x96132))),f866(f866(f316(x96132),f918(x96131,x96132)),f866(f866(f316(x96132),f347(x96131,x96132)),f195(f937(x96132,a925))))))
% 157.76/157.53 [9644]~P69(x96442)+E(x96441,f195(f937(x96442,a925)))+~P107(f866(f66(x96442),x96441))+P107(f866(f866(f336(x96442),f866(f68(x96442,f87(x96442)),x96441)),x96441))+~P107(f866(f866(f336(x96442),f866(f866(f87(x96442),f893(x96441,x96442)),f894(x96441,x96442))),f866(f866(f316(x96442),f893(x96441,x96442)),f866(f866(f316(x96442),f894(x96441,x96442)),f195(f937(x96442,a925))))))
% 157.76/157.53 [9649]~P110(x96492)+E(x96491,f195(f937(x96492,a925)))+~P107(f866(f66(x96492),x96491))+P107(f866(f866(f336(x96492),f11(x96492,f241(x96492),x96491)),x96491))+~P107(f866(f866(f336(x96492),f866(f866(f241(x96492),f370(x96491,x96492)),f383(x96491,x96492))),f866(f866(f316(x96492),f370(x96491,x96492)),f866(f866(f316(x96492),f383(x96491,x96492)),f195(f937(x96492,a925))))))
% 157.76/157.53 [9650]~P110(x96502)+E(x96501,f195(f937(x96502,a925)))+~P107(f866(f66(x96502),x96501))+P107(f866(f866(f336(x96502),f12(x96502,f242(x96502),x96501)),x96501))+~P107(f866(f866(f336(x96502),f866(f866(f242(x96502),f371(x96501,x96502)),f372(x96501,x96502))),f866(f866(f316(x96502),f371(x96501,x96502)),f866(f866(f316(x96502),f372(x96501,x96502)),f195(f937(x96502,a925))))))
% 157.76/157.53 [6790]~P86(x67902)+E(x67901,f2(x67902))+~E(f866(f866(f86(x67902),x67903),x67901),f2(x67902))+~P107(f866(f866(f243(x67902),f2(x67902)),x67903))+~P107(f866(f866(f243(x67902),f2(x67902)),x67901))
% 157.76/157.53 [6791]~P86(x67912)+E(x67911,f2(x67912))+~E(f866(f866(f86(x67912),x67911),x67913),f2(x67912))+~P107(f866(f866(f243(x67912),f2(x67912)),x67913))+~P107(f866(f866(f243(x67912),f2(x67912)),x67911))
% 157.76/157.53 [7315]~P110(x73152)+~P13(x73152,x73151)+E(x73151,f120(x73152))+~P107(f866(f866(f336(x73152),x73153),f866(f179(x73152),f715(x73151,x73152))))+P107(f866(f866(f243(x73152),f735(x73151,x73152)),x73153))
% 157.76/157.53 [7483]~P110(x74831)+E(f15(x74831,x74832),x74833)+~P107(f866(f66(x74831),x74832))+~P107(f866(f866(f243(x74831),x74833),f487(x74833,x74832,x74831)))+~P107(f866(f866(f336(x74831),x74833),x74832))
% 157.76/157.53 [7516]~P110(x75161)+~P13(x75161,x75162)+~P13(x75161,x75163)+P13(x75161,f866(f866(f141(x75161),x75162),x75163))+P107(f866(f866(f336(x75161),f722(x75163,x75162,x75161)),f866(f179(x75161),x75162)))
% 157.76/157.53 [7517]~P110(x75171)+~P13(x75171,x75172)+~P13(x75171,x75173)+P13(x75171,f866(f866(f141(x75171),x75172),x75173))+P107(f866(f866(f336(x75171),f723(x75173,x75172,x75171)),f866(f179(x75171),x75173)))
% 157.76/157.53 [7579]~P110(x75791)+E(f14(x75791,x75792),x75793)+~P107(f866(f66(x75791),x75792))+P107(f866(f866(f336(x75791),f488(x75793,x75792,x75791)),x75792))+~P107(f866(f866(f336(x75791),x75793),x75792))
% 157.76/157.53 [7580]~P110(x75801)+E(f15(x75801,x75802),x75803)+~P107(f866(f66(x75801),x75802))+P107(f866(f866(f336(x75801),f487(x75803,x75802,x75801)),x75802))+~P107(f866(f866(f336(x75801),x75803),x75802))
% 157.76/157.53 [8142]~P110(x81421)+E(f14(x81421,x81422),x81423)+~P107(f866(f66(x81421),x81422))+~P107(f866(f866(f336(x81421),x81423),x81422))+~P107(f866(f866(f243(x81421),f488(x81423,x81422,x81421)),x81423))
% 157.76/157.53 [8454]~P110(x84541)+~P13(x84541,x84542)+~P13(x84541,x84543)+P13(x84541,f866(f866(f141(x84541),x84542),x84543))+~P107(f866(f866(f243(x84541),f722(x84543,x84542,x84541)),f723(x84543,x84542,x84541)))
% 157.76/157.53 [9251]~P83(x92512)+E(x92511,f195(f937(x92512,a925)))+~E(f866(f866(f117(x92512),f866(x92513,f907(x92511,x92513,x92512))),f866(x92513,f910(x92511,x92513,x92512))),f866(x92513,f866(f866(f117(x92512),f907(x92511,x92513,x92512)),f910(x92511,x92513,x92512))))+E(f13(x92512,f866(f317(x92512,x92512,x92513),x92511)),f866(x92513,f13(x92512,x92511)))+~P107(f866(f66(x92512),x92511))
% 157.76/157.53 [9252]~P83(x92522)+E(x92521,f195(f937(x92522,a925)))+~E(f866(f866(f108(x92522),f866(x92523,f346(x92521,x92523,x92522))),f866(x92523,f348(x92521,x92523,x92522))),f866(x92523,f866(f866(f108(x92522),f346(x92521,x92523,x92522)),f348(x92521,x92523,x92522))))+E(f10(x92522,f866(f317(x92522,x92522,x92523),x92521)),f866(x92523,f10(x92522,x92521)))+~P107(f866(f66(x92522),x92521))
% 157.76/157.53 [9253]~P110(x92532)+E(x92531,f195(f937(x92532,a925)))+~E(f866(f866(f242(x92532),f866(x92533,f379(x92531,x92533,x92532))),f866(x92533,f391(x92531,x92533,x92532))),f866(x92533,f866(f866(f242(x92532),f379(x92531,x92533,x92532)),f391(x92531,x92533,x92532))))+E(f14(x92532,f866(f317(x92532,x92532,x92533),x92531)),f866(x92533,f14(x92532,x92531)))+~P107(f866(f66(x92532),x92531))
% 157.76/157.53 [9254]~P110(x92542)+E(x92541,f195(f937(x92542,a925)))+~E(f866(f866(f241(x92542),f866(x92543,f392(x92541,x92543,x92542))),f866(x92543,f393(x92541,x92543,x92542))),f866(x92543,f866(f866(f241(x92542),f392(x92541,x92543,x92542)),f393(x92541,x92543,x92542))))+E(f15(x92542,f866(f317(x92542,x92542,x92543),x92541)),f866(x92543,f15(x92542,x92541)))+~P107(f866(f66(x92542),x92541))
% 157.76/157.53 [9322]~P110(x93222)+E(x93221,f195(f937(x93222,a925)))+~E(f866(f866(f241(x93222),f866(x93223,f380(x93221,x93223,x93222))),f866(x93223,f388(x93221,x93223,x93222))),f866(x93223,f866(f866(f241(x93222),f380(x93221,x93223,x93222)),f388(x93221,x93223,x93222))))+E(f11(x93222,f241(x93222),f866(f317(x93222,x93222,x93223),x93221)),f866(x93223,f11(x93222,f241(x93222),x93221)))+~P107(f866(f66(x93222),x93221))
% 157.76/157.53 [9323]~P110(x93232)+E(x93231,f195(f937(x93232,a925)))+~E(f866(f866(f242(x93232),f866(x93233,f381(x93231,x93233,x93232))),f866(x93233,f387(x93231,x93233,x93232))),f866(x93233,f866(f866(f242(x93232),f381(x93231,x93233,x93232)),f387(x93231,x93233,x93232))))+E(f12(x93232,f242(x93232),f866(f317(x93232,x93232,x93233),x93231)),f866(x93233,f12(x93232,f242(x93232),x93231)))+~P107(f866(f66(x93232),x93231))
% 157.76/157.53 [6806]~P69(x68062)+E(x68061,f195(f937(x68062,a925)))+~P107(f866(f66(x68062),x68061))+E(f866(f68(x68062,f87(x68062)),f866(f866(f316(x68062),x68063),x68061)),f866(f866(f87(x68062),x68063),f866(f68(x68062,f87(x68062)),x68061)))+P107(f866(f866(f336(x68062),x68063),x68061))
% 157.76/157.53 [7321]~P83(x73212)+E(f866(f866(f117(x73212),f13(x73212,x73211)),f13(x73212,x73213)),f13(x73212,x73213))+E(x73211,f195(f937(x73212,a925)))+~P107(f866(f66(x73212),x73213))+~P107(f866(f866(f243(f937(x73212,a925)),x73211),x73213))
% 157.76/157.53 [7322]~P83(x73222)+E(f866(f866(f108(x73222),f10(x73222,x73221)),f10(x73222,x73223)),f10(x73222,x73223))+E(x73221,f195(f937(x73222,a925)))+~P107(f866(f66(x73222),x73223))+~P107(f866(f866(f243(f937(x73222,a925)),x73221),x73223))
% 157.76/157.53 [7323]~P110(x73232)+E(f866(f866(f241(x73232),f15(x73232,x73231)),f15(x73232,x73233)),f15(x73232,x73233))+E(x73231,f195(f937(x73232,a925)))+~P107(f866(f66(x73232),x73233))+~P107(f866(f866(f243(f937(x73232,a925)),x73231),x73233))
% 157.76/157.53 [7324]~P110(x73242)+E(f866(f866(f242(x73242),f14(x73242,x73241)),f14(x73242,x73243)),f14(x73242,x73243))+E(x73241,f195(f937(x73242,a925)))+~P107(f866(f66(x73242),x73243))+~P107(f866(f866(f243(f937(x73242,a925)),x73241),x73243))
% 157.76/157.53 [7626]~P110(x76262)+E(x76261,f195(f937(x76262,a925)))+~P107(f866(f66(x76262),x76263))+P107(f866(f866(f243(x76262),f14(x76262,x76261)),f14(x76262,x76263)))+~P107(f866(f866(f243(f937(x76262,a925)),x76261),x76263))
% 157.76/157.53 [7627]~P110(x76272)+E(x76271,f195(f937(x76272,a925)))+~P107(f866(f66(x76272),x76273))+P107(f866(f866(f243(x76272),f15(x76272,x76273)),f15(x76272,x76271)))+~P107(f866(f866(f243(f937(x76272,a925)),x76271),x76273))
% 157.76/157.53 [7681]~P83(x76811)+E(f13(x76811,x76812),x76813)+~P107(f866(f66(x76811),x76812))+~E(f866(f866(f23(f937(x76811,a925)),x76812),f866(f866(f316(x76811),x76813),f195(f937(x76811,a925)))),f195(f937(x76811,a925)))+~P107(f866(f866(f336(x76811),x76813),x76812))
% 157.76/157.53 [7682]~P83(x76821)+E(f10(x76821,x76822),x76823)+~P107(f866(f66(x76821),x76822))+~E(f866(f866(f23(f937(x76821,a925)),x76822),f866(f866(f316(x76821),x76823),f195(f937(x76821,a925)))),f195(f937(x76821,a925)))+~P107(f866(f866(f336(x76821),x76823),x76822))
% 157.76/157.53 [7683]~P110(x76831)+E(f14(x76831,x76832),x76833)+~P107(f866(f66(x76831),x76832))+~E(f866(f866(f23(f937(x76831,a925)),x76832),f866(f866(f316(x76831),x76833),f195(f937(x76831,a925)))),f195(f937(x76831,a925)))+~P107(f866(f866(f336(x76831),x76833),x76832))
% 157.76/157.53 [7684]~P110(x76841)+E(f15(x76841,x76842),x76843)+~P107(f866(f66(x76841),x76842))+~E(f866(f866(f23(f937(x76841,a925)),x76842),f866(f866(f316(x76841),x76843),f195(f937(x76841,a925)))),f195(f937(x76841,a925)))+~P107(f866(f866(f336(x76841),x76843),x76842))
% 157.76/157.53 [7776]~P110(x77761)+E(f11(x77761,f241(x77761),x77762),x77763)+~P107(f866(f66(x77761),x77762))+~E(f866(f866(f23(f937(x77761,a925)),x77762),f866(f866(f316(x77761),x77763),f195(f937(x77761,a925)))),f195(f937(x77761,a925)))+~P107(f866(f866(f336(x77761),x77763),x77762))
% 157.76/157.53 [7777]~P110(x77771)+E(f12(x77771,f242(x77771),x77772),x77773)+~P107(f866(f66(x77771),x77772))+~E(f866(f866(f23(f937(x77771,a925)),x77772),f866(f866(f316(x77771),x77773),f195(f937(x77771,a925)))),f195(f937(x77771,a925)))+~P107(f866(f866(f336(x77771),x77773),x77772))
% 157.76/157.53 [7813]~P103(x78132)+E(x78131,f195(f937(x78132,a925)))+~P107(f866(f66(x78132),x78131))+~P107(f866(f866(f243(x78132),x78133),f915(x78133,x78131,x78132)))+P107(f866(f866(f243(x78132),x78133),f866(f68(x78132,f108(x78132)),x78131)))
% 157.76/157.53 [7814]~P110(x78142)+E(x78141,f195(f937(x78142,a925)))+~P107(f866(f66(x78142),x78141))+~P107(f866(f866(f243(x78142),x78143),f366(x78143,x78141,x78142)))+P107(f866(f866(f243(x78142),x78143),f866(f68(x78142,f241(x78142)),x78141)))
% 157.76/157.53 [7815]~P110(x78152)+E(x78151,f195(f937(x78152,a925)))+~P107(f866(f66(x78152),x78151))+~P107(f866(f866(f244(x78152),x78153),f367(x78153,x78151,x78152)))+P107(f866(f866(f244(x78152),x78153),f866(f68(x78152,f241(x78152)),x78151)))
% 157.76/157.53 [7900]~P103(x79002)+E(x79001,f195(f937(x79002,a925)))+~P107(f866(f66(x79002),x79001))+P107(f866(f866(f336(x79002),f915(x79003,x79001,x79002)),x79001))+P107(f866(f866(f243(x79002),x79003),f866(f68(x79002,f108(x79002)),x79001)))
% 157.76/157.53 [7901]~P110(x79012)+E(x79011,f195(f937(x79012,a925)))+~P107(f866(f66(x79012),x79011))+P107(f866(f866(f336(x79012),f366(x79013,x79011,x79012)),x79011))+P107(f866(f866(f243(x79012),x79013),f866(f68(x79012,f241(x79012)),x79011)))
% 157.76/157.53 [7902]~P110(x79022)+E(x79021,f195(f937(x79022,a925)))+~P107(f866(f66(x79022),x79021))+P107(f866(f866(f336(x79022),f367(x79023,x79021,x79022)),x79021))+P107(f866(f866(f244(x79022),x79023),f866(f68(x79022,f241(x79022)),x79021)))
% 157.76/157.53 [8023]~P110(x80232)+E(x80231,f195(f937(x80232,a925)))+E(f866(f866(f241(x80232),f11(x80232,f241(x80232),x80231)),f11(x80232,f241(x80232),x80233)),f11(x80232,f241(x80232),x80233))+~P107(f866(f66(x80232),x80233))+~P107(f866(f866(f243(f937(x80232,a925)),x80231),x80233))
% 157.76/157.53 [8024]~P110(x80242)+E(x80241,f195(f937(x80242,a925)))+E(f866(f866(f242(x80242),f12(x80242,f242(x80242),x80241)),f12(x80242,f242(x80242),x80243)),f12(x80242,f242(x80242),x80243))+~P107(f866(f66(x80242),x80243))+~P107(f866(f866(f243(f937(x80242,a925)),x80241),x80243))
% 157.76/157.53 [8220]~E(f624(x82201,x82203,x82202),f625(x82201,x82203,x82202))+~E(f866(f40(x82202),f626(x82201,x82203,x82202)),x82201)+E(f866(f866(f87(a930),x82201),f866(f40(f937(x82202,a925)),x82203)),f866(f40(x82202),f42(f937(x82202,a925),x82203)))+~P107(f866(f66(x82202),f42(f937(x82202,a925),x82203)))+~P107(f866(f66(f937(x82202,a925)),x82203))
% 157.76/157.53 [8394]~P110(x83942)+E(x83941,f195(f937(x83942,a925)))+~P107(f866(f66(x83942),x83943))+P107(f866(f866(f243(x83942),f866(f68(x83942,f241(x83942)),x83943)),f866(f68(x83942,f241(x83942)),x83941)))+~P107(f866(f866(f243(f937(x83942,a925)),x83941),x83943))
% 157.76/157.53 [8692]~E(f624(x86921,x86923,x86922),f625(x86921,x86923,x86922))+E(f866(f866(f87(a930),x86921),f866(f40(f937(x86922,a925)),x86923)),f866(f40(x86922),f42(f937(x86922,a925),x86923)))+P107(f866(f866(f336(f937(x86922,a925)),f626(x86921,x86923,x86922)),x86923))+~P107(f866(f66(x86922),f42(f937(x86922,a925),x86923)))+~P107(f866(f66(f937(x86922,a925)),x86923))
% 157.76/157.53 [8718]~E(f866(f40(x87182),f626(x87181,x87183,x87182)),x87181)+E(f866(f866(f87(a930),x87181),f866(f40(f937(x87182,a925)),x87183)),f866(f40(x87182),f42(f937(x87182,a925),x87183)))+P107(f866(f866(f336(f937(x87182,a925)),f625(x87181,x87183,x87182)),x87183))+~P107(f866(f66(x87182),f42(f937(x87182,a925),x87183)))+~P107(f866(f66(f937(x87182,a925)),x87183))
% 157.76/157.53 [8719]~E(f866(f40(x87192),f626(x87191,x87193,x87192)),x87191)+E(f866(f866(f87(a930),x87191),f866(f40(f937(x87192,a925)),x87193)),f866(f40(x87192),f42(f937(x87192,a925),x87193)))+P107(f866(f866(f336(f937(x87192,a925)),f624(x87191,x87193,x87192)),x87193))+~P107(f866(f66(x87192),f42(f937(x87192,a925),x87193)))+~P107(f866(f66(f937(x87192,a925)),x87193))
% 157.76/157.53 [8745]~E(f866(f40(x87452),f626(x87451,x87453,x87452)),x87451)+~E(f866(f866(f108(f937(x87452,a925)),f625(x87451,x87453,x87452)),f624(x87451,x87453,x87452)),f195(f937(x87452,a925)))+E(f866(f866(f87(a930),x87451),f866(f40(f937(x87452,a925)),x87453)),f866(f40(x87452),f42(f937(x87452,a925),x87453)))+~P107(f866(f66(f937(x87452,a925)),x87453))+~P107(f866(f66(x87452),f42(f937(x87452,a925),x87453)))
% 157.76/157.53 [9009]E(f866(f866(f87(a930),x90091),f866(f40(f937(x90092,a925)),x90093)),f866(f40(x90092),f42(f937(x90092,a925),x90093)))+P107(f866(f866(f336(f937(x90092,a925)),f626(x90091,x90093,x90092)),x90093))+P107(f866(f866(f336(f937(x90092,a925)),f625(x90091,x90093,x90092)),x90093))+~P107(f866(f66(f937(x90092,a925)),x90093))+~P107(f866(f66(x90092),f42(f937(x90092,a925),x90093)))
% 157.76/157.53 [9010]E(f866(f866(f87(a930),x90101),f866(f40(f937(x90102,a925)),x90103)),f866(f40(x90102),f42(f937(x90102,a925),x90103)))+P107(f866(f866(f336(f937(x90102,a925)),f626(x90101,x90103,x90102)),x90103))+P107(f866(f866(f336(f937(x90102,a925)),f624(x90101,x90103,x90102)),x90103))+~P107(f866(f66(f937(x90102,a925)),x90103))+~P107(f866(f66(x90102),f42(f937(x90102,a925),x90103)))
% 157.76/157.53 [9036]~E(f866(f866(f108(f937(x90362,a925)),f625(x90361,x90363,x90362)),f624(x90361,x90363,x90362)),f195(f937(x90362,a925)))+E(f866(f866(f87(a930),x90361),f866(f40(f937(x90362,a925)),x90363)),f866(f40(x90362),f42(f937(x90362,a925),x90363)))+~P107(f866(f66(f937(x90362,a925)),x90363))+P107(f866(f866(f336(f937(x90362,a925)),f626(x90361,x90363,x90362)),x90363))+~P107(f866(f66(x90362),f42(f937(x90362,a925),x90363)))
% 157.76/157.53 [9297]~P99(x92972)+E(x92971,f195(f937(x92972,a925)))+~E(f866(f866(f87(x92972),f866(x92973,f892(x92971,x92973,x92972))),f866(x92973,f896(x92971,x92973,x92972))),f866(x92973,f866(f866(f87(x92972),f892(x92971,x92973,x92972)),f896(x92971,x92973,x92972))))+~P107(f866(f66(x92972),x92971))+E(f866(f68(x92972,f87(x92972)),f866(f317(x92972,x92972,x92973),x92971)),f866(x92973,f866(f68(x92972,f87(x92972)),x92971)))
% 157.76/157.53 [10218]P107(f866(f866(x102181,x102182),x102183))+P107(f866(f866(f244(a1),f498(x102181,x102183,x102182)),f499(x102181,x102183,x102182)))+P107(f866(f866(f243(a1),f499(x102181,x102183,x102182)),f2(a1)))+P107(f866(f866(x102181,f498(x102181,x102183,x102182)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f499(x102181,x102183,x102182))))+~P107(f866(f322(f936(a1,a1),a63),f866(f866(f260(a1,a1),x102182),x102183)))
% 157.76/157.53 [10224]P107(f866(f866(x102241,x102242),x102243))+P107(f866(f866(f243(a1),f496(x102241,x102243,x102242)),f2(a1)))+P107(f866(f866(x102241,f492(x102241,x102243,x102242)),f866(f866(f87(a1),f866(f110(a1),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f496(x102241,x102243,x102242))))+P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),f492(x102241,x102243,x102242)),f496(x102241,x102243,x102242))))+~P107(f866(f322(f936(a1,a1),a57),f866(f866(f260(a1,a1),x102242),x102243)))
% 157.76/157.53 [8191]~P128(x81911)+~P107(f866(f866(f243(x81911),x81912),f84(x81911)))+~P107(f866(f866(f243(x81911),f2(x81911)),x81912))+~P107(f866(f866(f243(x81911),f2(x81911)),x81913))+P107(f866(f866(f243(x81911),f866(f866(f87(x81911),x81912),x81913)),x81913))
% 157.76/157.53 [8192]~P128(x81921)+~P107(f866(f866(f243(x81921),x81923),f84(x81921)))+~P107(f866(f866(f243(x81921),f2(x81921)),x81923))+~P107(f866(f866(f243(x81921),f2(x81921)),x81922))+P107(f866(f866(f243(x81921),f866(f866(f87(x81921),x81922),x81923)),x81922))
% 157.76/157.53 [8540]~P110(x85402)+E(x85401,f195(f937(x85402,a925)))+~P107(f866(f66(x85402),x85401))+P107(f866(f866(f243(x85402),f368(x85403,x85401,x85402)),x85403))+~P107(f866(f866(f243(x85402),f866(f68(x85402,f241(x85402)),x85401)),x85403))
% 157.76/157.53 [8541]~P110(x85412)+E(x85411,f195(f937(x85412,a925)))+~P107(f866(f66(x85412),x85411))+P107(f866(f866(f336(x85412),f368(x85413,x85411,x85412)),x85411))+~P107(f866(f866(f243(x85412),f866(f68(x85412,f241(x85412)),x85411)),x85413))
% 157.76/157.53 [8542]~P110(x85422)+E(x85421,f195(f937(x85422,a925)))+~P107(f866(f66(x85422),x85421))+P107(f866(f866(f336(x85422),f369(x85423,x85421,x85422)),x85421))+~P107(f866(f866(f244(x85422),f866(f68(x85422,f241(x85422)),x85421)),x85423))
% 157.76/157.53 [8543]~P110(x85432)+E(x85431,f195(f937(x85432,a925)))+~P107(f866(f66(x85432),x85431))+P107(f866(f866(f244(x85432),f369(x85433,x85431,x85432)),x85433))+~P107(f866(f866(f244(x85432),f866(f68(x85432,f241(x85432)),x85431)),x85433))
% 157.76/157.53 [8629]~P107(f866(x86291,x86293))+P107(f866(x86291,f460(x86291,x86292)))+P107(f866(x86291,f454(x86291,x86292)))+~P107(f866(f866(f244(a1),f2(a1)),x86292))+P107(f866(x86291,f866(f866(f23(a1),f454(x86291,x86292)),f866(f866(f87(a1),f461(x86291,x86292)),x86292))))
% 157.76/157.53 [8846]~P107(f866(x88461,x88463))+P107(f866(x88461,f454(x88461,x88462)))+~P107(f866(f866(f244(a1),f2(a1)),x88462))+P107(f866(f866(f336(a1),f460(x88461,x88462)),f310(a1,f84(a1),x88462)))+P107(f866(x88461,f866(f866(f23(a1),f454(x88461,x88462)),f866(f866(f87(a1),f461(x88461,x88462)),x88462))))
% 157.76/157.53 [9058]~P107(f866(x90581,x90583))+~P107(f866(x90581,f454(x90581,x90582)))+P107(f866(x90581,f460(x90581,x90582)))+~P107(f866(f866(f244(a1),f2(a1)),x90582))+~P107(f866(x90581,f866(f866(f23(a1),f454(x90581,x90582)),f866(f866(f87(a1),f461(x90581,x90582)),x90582))))
% 157.76/157.53 [9188]~P107(f866(x91881,x91883))+~P107(f866(x91881,f454(x91881,x91882)))+~P107(f866(f866(f244(a1),f2(a1)),x91882))+P107(f866(f866(f336(a1),f460(x91881,x91882)),f310(a1,f84(a1),x91882)))+~P107(f866(x91881,f866(f866(f23(a1),f454(x91881,x91882)),f866(f866(f87(a1),f461(x91881,x91882)),x91882))))
% 157.76/157.53 [8964]~P83(x89641)+~P107(f866(f66(x89641),x89642))+E(f866(f866(f23(f937(x89641,a925)),x89642),f866(f866(f316(x89641),x89643),f195(f937(x89641,a925)))),f195(f937(x89641,a925)))+~P107(f866(f866(f336(x89641),x89643),x89642))+E(f866(f866(f117(x89641),x89643),f13(x89641,f866(f866(f23(f937(x89641,a925)),x89642),f866(f866(f316(x89641),x89643),f195(f937(x89641,a925)))))),f13(x89641,x89642))
% 157.76/157.53 [8965]~P83(x89651)+~P107(f866(f66(x89651),x89652))+E(f866(f866(f23(f937(x89651,a925)),x89652),f866(f866(f316(x89651),x89653),f195(f937(x89651,a925)))),f195(f937(x89651,a925)))+~P107(f866(f866(f336(x89651),x89653),x89652))+E(f866(f866(f108(x89651),x89653),f10(x89651,f866(f866(f23(f937(x89651,a925)),x89652),f866(f866(f316(x89651),x89653),f195(f937(x89651,a925)))))),f10(x89651,x89652))
% 157.76/157.53 [8966]~P110(x89661)+~P107(f866(f66(x89661),x89662))+E(f866(f866(f23(f937(x89661,a925)),x89662),f866(f866(f316(x89661),x89663),f195(f937(x89661,a925)))),f195(f937(x89661,a925)))+~P107(f866(f866(f336(x89661),x89663),x89662))+E(f866(f866(f242(x89661),x89663),f14(x89661,f866(f866(f23(f937(x89661,a925)),x89662),f866(f866(f316(x89661),x89663),f195(f937(x89661,a925)))))),f14(x89661,x89662))
% 157.76/157.53 [8967]~P110(x89671)+~P107(f866(f66(x89671),x89672))+E(f866(f866(f23(f937(x89671,a925)),x89672),f866(f866(f316(x89671),x89673),f195(f937(x89671,a925)))),f195(f937(x89671,a925)))+~P107(f866(f866(f336(x89671),x89673),x89672))+E(f866(f866(f241(x89671),x89673),f15(x89671,f866(f866(f23(f937(x89671,a925)),x89672),f866(f866(f316(x89671),x89673),f195(f937(x89671,a925)))))),f15(x89671,x89672))
% 157.76/157.53 [9029]~P110(x90291)+~P107(f866(f66(x90291),x90292))+E(f866(f866(f23(f937(x90291,a925)),x90292),f866(f866(f316(x90291),x90293),f195(f937(x90291,a925)))),f195(f937(x90291,a925)))+~P107(f866(f866(f336(x90291),x90293),x90292))+E(f866(f866(f241(x90291),x90293),f11(x90291,f241(x90291),f866(f866(f23(f937(x90291,a925)),x90292),f866(f866(f316(x90291),x90293),f195(f937(x90291,a925)))))),f11(x90291,f241(x90291),x90292))
% 157.76/157.53 [9030]~P110(x90301)+~P107(f866(f66(x90301),x90302))+E(f866(f866(f23(f937(x90301,a925)),x90302),f866(f866(f316(x90301),x90303),f195(f937(x90301,a925)))),f195(f937(x90301,a925)))+~P107(f866(f866(f336(x90301),x90303),x90302))+E(f866(f866(f242(x90301),x90303),f12(x90301,f242(x90301),f866(f866(f23(f937(x90301,a925)),x90302),f866(f866(f316(x90301),x90303),f195(f937(x90301,a925)))))),f12(x90301,f242(x90301),x90302))
% 157.76/157.53 [9045]~P83(x90451)+~P107(f866(f66(x90451),x90453))+~P107(f866(f66(x90451),x90452))+E(f866(f866(f108(f937(x90451,a925)),x90452),x90453),f195(f937(x90451,a925)))+E(f866(f866(f117(x90451),f13(x90451,f866(f866(f117(f937(x90451,a925)),x90452),x90453))),f13(x90451,f866(f866(f108(f937(x90451,a925)),x90452),x90453))),f866(f866(f117(x90451),f13(x90451,x90452)),f13(x90451,x90453)))
% 157.76/157.53 [9046]~P83(x90461)+~P107(f866(f66(x90461),x90463))+~P107(f866(f66(x90461),x90462))+E(f866(f866(f108(f937(x90461,a925)),x90462),x90463),f195(f937(x90461,a925)))+E(f866(f866(f108(x90461),f10(x90461,f866(f866(f117(f937(x90461,a925)),x90462),x90463))),f10(x90461,f866(f866(f108(f937(x90461,a925)),x90462),x90463))),f866(f866(f108(x90461),f10(x90461,x90462)),f10(x90461,x90463)))
% 157.76/157.53 [9047]~P110(x90471)+~P107(f866(f66(x90471),x90473))+~P107(f866(f66(x90471),x90472))+E(f866(f866(f108(f937(x90471,a925)),x90472),x90473),f195(f937(x90471,a925)))+E(f866(f866(f241(x90471),f15(x90471,f866(f866(f117(f937(x90471,a925)),x90472),x90473))),f15(x90471,f866(f866(f108(f937(x90471,a925)),x90472),x90473))),f866(f866(f241(x90471),f15(x90471,x90472)),f15(x90471,x90473)))
% 157.76/157.53 [9048]~P110(x90481)+~P107(f866(f66(x90481),x90483))+~P107(f866(f66(x90481),x90482))+E(f866(f866(f108(f937(x90481,a925)),x90482),x90483),f195(f937(x90481,a925)))+E(f866(f866(f242(x90481),f14(x90481,f866(f866(f117(f937(x90481,a925)),x90482),x90483))),f14(x90481,f866(f866(f108(f937(x90481,a925)),x90482),x90483))),f866(f866(f242(x90481),f14(x90481,x90482)),f14(x90481,x90483)))
% 157.76/157.53 [9269]~P110(x92691)+~P107(f866(f66(x92691),x92693))+~P107(f866(f66(x92691),x92692))+E(f866(f866(f108(f937(x92691,a925)),x92692),x92693),f195(f937(x92691,a925)))+E(f866(f866(f241(x92691),f11(x92691,f241(x92691),f866(f866(f117(f937(x92691,a925)),x92692),x92693))),f11(x92691,f241(x92691),f866(f866(f108(f937(x92691,a925)),x92692),x92693))),f866(f866(f241(x92691),f11(x92691,f241(x92691),x92692)),f11(x92691,f241(x92691),x92693)))
% 157.76/157.53 [9270]~P110(x92701)+~P107(f866(f66(x92701),x92703))+~P107(f866(f66(x92701),x92702))+E(f866(f866(f108(f937(x92701,a925)),x92702),x92703),f195(f937(x92701,a925)))+E(f866(f866(f242(x92701),f12(x92701,f242(x92701),f866(f866(f117(f937(x92701,a925)),x92702),x92703))),f12(x92701,f242(x92701),f866(f866(f108(f937(x92701,a925)),x92702),x92703))),f866(f866(f242(x92701),f12(x92701,f242(x92701),x92702)),f12(x92701,f242(x92701),x92703)))
% 157.76/157.53 [10065]~P113(x100653)+E(x100651,x100652)+~P107(f866(f866(f243(x100653),f2(x100653)),x100652))+~P107(f866(f866(f243(x100653),f2(x100653)),x100651))+~E(f866(f866(f252(x100653),x100651),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))),f866(f866(f252(x100653),x100652),f866(f110(a930),f866(f866(f86(a1),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)),f866(f866(f23(a1),f866(f866(f86(a1),a89),a89)),a104)))))
% 157.76/157.53 [5792]~P62(x57922)+~P57(x57922,x57921,x57923)+E(x57921,f2(x57922))+~E(f866(f866(f41(x57922),x57923),x57921),x57924)+E(x57923,f866(f866(f87(x57922),x57924),x57921))
% 157.76/157.53 [5793]~P62(x57932)+~P57(x57932,x57931,x57933)+E(x57931,f2(x57932))+~E(x57933,f866(f866(f87(x57932),x57934),x57931))+E(f866(f866(f41(x57932),x57933),x57931),x57934)
% 157.76/157.53 [6599]E(f389(x65991,x65992,x65993),x65994)+E(f866(x65991,x65994),f2(a930))+~E(f866(f866(f6(x65993,a930),x65991),x65992),f84(a930))+~P107(f866(f66(x65993),x65992))+~P107(f866(f866(f336(x65993),x65994),x65992))
% 157.76/157.53 [6663]E(f394(x66631,x66632,x66633),x66634)+E(f866(x66631,x66634),f2(a930))+~E(f866(f866(f6(x66633,a930),x66631),x66632),f866(a119,f2(a930)))+~P107(f866(f66(x66633),x66632))+~P107(f866(f866(f336(x66633),x66634),x66632))
% 157.76/157.53 [6774]~P110(x67741)+~P5(x67741)+P107(f866(f866(f244(x67741),x67742),f42(x67741,x67743)))+~P107(f866(f866(f244(x67741),x67742),x67744))+~P107(f866(f866(f336(x67741),x67744),x67743))
% 157.76/157.53 [6948]~P110(x69481)+~P5(x69481)+~P107(f866(f866(f244(x69481),x69484),x69483))+P107(f866(f866(f244(x69481),f43(x69481,x69482)),x69483))+~P107(f866(f866(f336(x69481),x69484),x69482))
% 157.76/157.53 [7202]~P113(x72023)+E(x72021,x72022)+~E(f866(f866(f252(x72023),x72021),f866(a119,x72024)),f866(f866(f252(x72023),x72022),f866(a119,x72024)))+~P107(f866(f866(f243(x72023),f2(x72023)),x72022))+~P107(f866(f866(f243(x72023),f2(x72023)),x72021))
% 157.76/157.53 [7410]~E(f396(x74102,x74103,x74101,x74104),x74104)+~E(f866(x74102,x74104),f84(a930))+E(f866(f866(f6(x74101,a930),x74102),x74103),f84(a930))+~P107(f866(f66(x74101),x74103))+~P107(f866(f866(f336(x74101),x74104),x74103))
% 157.76/157.53 [7417]~P114(x74174)+~P135(x74174)+E(f866(x74171,f913(x74171,x74172,x74173,x74174)),f2(x74174))+~E(f866(f866(f9(x74173,x74174),x74171),x74172),f2(x74174))+~P107(f866(f66(x74173),x74172))
% 157.76/157.53 [7506]~E(f395(x75062,x75063,x75061,x75064),x75064)+~E(f866(x75062,x75064),f866(a119,f2(a930)))+E(f866(f866(f6(x75061,a930),x75062),x75063),f866(a119,f2(a930)))+~P107(f866(f66(x75061),x75063))+~P107(f866(f866(f336(x75061),x75064),x75063))
% 157.76/157.53 [7984]~P147(x79842)+~P124(x79842)+~P57(x79842,x79843,f866(f866(f86(x79842),x79844),f2(x79842)))+~P107(f866(x79841,x79844))+P107(f866(x79841,f866(f866(f87(x79842),x79843),f864(x79843,x79841,x79842))))
% 157.76/157.53 [8232]~E(f866(x82322,x82324),f84(a930))+~E(f866(x82322,f396(x82322,x82323,x82321,x82324)),f2(a930))+E(f866(f866(f6(x82321,a930),x82322),x82323),f84(a930))+~P107(f866(f66(x82321),x82323))+~P107(f866(f866(f336(x82321),x82324),x82323))
% 157.76/157.53 [8270]~E(f866(x82702,x82704),f866(a119,f2(a930)))+~E(f866(x82702,f395(x82702,x82703,x82701,x82704)),f2(a930))+E(f866(f866(f6(x82701,a930),x82702),x82703),f866(a119,f2(a930)))+~P107(f866(f66(x82701),x82703))+~P107(f866(f866(f336(x82701),x82704),x82703))
% 157.76/157.53 [8813]~P110(x88131)+~P13(x88131,x88134)+P13(x88131,x88132)+~E(x88132,f866(f866(f158(x88131),x88133),x88134))+~P107(f866(f866(f243(x88131),x88133),f737(x88132,x88131,x88134,x88133)))
% 157.76/157.53 [8850]E(x88501,x88502)+E(f866(f866(f23(a1),f434(x88503,x88502,x88504,x88501)),f435(x88503,x88502,x88504,x88501)),x88501)+~E(f866(f866(f86(a1),x88501),x88504),x88502)+~P107(f866(f866(f244(a1),f2(a1)),x88504))+~P107(f866(f866(f336(a1),x88502),x88503))
% 157.76/157.53 [8851]E(x88511,x88512)+E(f866(f866(f86(a1),f446(x88513,x88512,x88514,x88511)),f447(x88513,x88512,x88514,x88511)),x88511)+~E(f866(f866(f23(a1),x88511),x88514),x88512)+~P107(f866(f866(f244(a1),f2(a1)),x88514))+~P107(f866(f866(f336(a1),x88512),x88513))
% 157.76/157.53 [9043]E(f866(x90431,f573(x90432,x90431,x90433,x90434)),x90432)+P107(f866(f866(f243(a930),x90434),f574(x90432,x90431,x90433,x90434)))+~P107(f866(f866(f243(a1),x90432),f866(x90431,x90433)))+~P107(f866(f866(f244(a930),x90434),x90433))+~P107(f866(f866(f243(a1),f866(x90431,x90434)),x90432))
% 157.76/157.53 [9044]~P110(x90441)+~P13(x90441,x90443)+P13(x90441,x90442)+~E(x90442,f866(f866(f158(x90441),x90444),x90443))+P107(f866(f866(f336(x90441),f737(x90442,x90441,x90443,x90444)),f866(f179(x90441),x90443)))
% 157.76/157.53 [9062]~P114(x90624)+~P135(x90624)+~E(f866(f866(f9(x90621,x90624),x90622),x90623),f2(x90624))+~P107(f866(f66(x90621),x90623))+P107(f866(f866(f336(x90621),f913(x90622,x90623,x90621,x90624)),x90623))
% 157.76/157.53 [9100]~E(f866(x91002,x91004),f84(a930))+E(f866(f866(f6(x91001,a930),x91002),x91003),f84(a930))+~P107(f866(f66(x91001),x91003))+~P107(f866(f866(f336(x91001),x91004),x91003))+P107(f866(f866(f336(x91001),f396(x91002,x91003,x91001,x91004)),x91003))
% 157.76/157.53 [9114]E(x91141,x91142)+~E(f866(f866(f86(a1),x91142),x91144),x91141)+~P107(f866(f866(f244(a1),f2(a1)),x91144))+~P107(f866(f866(f336(a1),x91141),x91143))+P107(f866(f866(f336(a1),f434(x91143,x91141,x91144,x91142)),x91143))
% 157.76/157.53 [9115]E(x91151,x91152)+~E(f866(f866(f23(a1),x91152),x91154),x91151)+~P107(f866(f866(f244(a1),f2(a1)),x91154))+~P107(f866(f866(f336(a1),x91151),x91153))+P107(f866(f866(f336(a1),f446(x91153,x91151,x91154,x91152)),x91153))
% 157.76/157.53 [9117]~E(f866(x91172,x91174),f866(a119,f2(a930)))+E(f866(f866(f6(x91171,a930),x91172),x91173),f866(a119,f2(a930)))+~P107(f866(f66(x91171),x91173))+~P107(f866(f866(f336(x91171),x91174),x91173))+P107(f866(f866(f336(x91171),f395(x91172,x91173,x91171,x91174)),x91173))
% 157.76/157.53 [9122]P60(x91222,x91223,x91224,x91221)+E(x91221,f195(f937(x91222,a925)))+~P107(f866(f66(x91222),x91224))+~P107(f866(f66(x91222),x91221))+P107(f866(f866(f336(x91222),f808(x91223,x91221,x91224,x91222)),x91224))
% 157.76/157.53 [9123]P60(x91232,x91233,x91234,x91231)+E(x91231,f195(f937(x91232,a925)))+~P107(f866(f66(x91232),x91234))+~P107(f866(f66(x91232),x91231))+P107(f866(f866(f336(x91232),f520(x91231,x91234,x91233,x91232)),x91234))
% 157.76/157.53 [9124]P60(x91242,x91243,x91244,x91241)+E(x91241,f195(f937(x91242,a925)))+~P107(f866(f66(x91242),x91244))+~P107(f866(f66(x91242),x91241))+P107(f866(f866(f336(x91242),f809(x91241,x91244,x91243,x91242)),x91244))
% 157.76/157.53 [9201]E(x92011,x92012)+~E(f866(f866(f86(a1),x92012),x92014),x92011)+~P107(f866(f866(f244(a1),f2(a1)),x92014))+~P107(f866(f866(f336(a1),x92011),x92013))+P107(f866(f866(f336(a1),f435(x92013,x92011,x92014,x92012)),f310(a1,f84(a1),x92014)))
% 157.76/157.53 [9202]E(x92021,x92022)+~E(f866(f866(f23(a1),x92022),x92024),x92021)+~P107(f866(f866(f244(a1),f2(a1)),x92024))+~P107(f866(f866(f336(a1),x92021),x92023))+P107(f866(f866(f336(a1),f447(x92023,x92021,x92024,x92022)),f310(a1,f84(a1),x92024)))
% 157.76/157.53 [9275]P107(f866(f866(f243(a930),x92751),f573(x92752,x92753,x92754,x92751)))+~P107(f866(f866(f243(a1),x92752),f866(x92753,x92754)))+P107(f866(f866(f243(a930),x92751),f574(x92752,x92753,x92754,x92751)))+~P107(f866(f866(f244(a930),x92751),x92754))+~P107(f866(f866(f243(a1),f866(x92753,x92751)),x92752))
% 157.76/157.53 [9390]E(f866(x93901,f573(x93902,x93901,x93903,x93904)),x93902)+~P107(f866(f866(f243(a1),x93902),f866(x93901,x93903)))+P107(f866(f866(f244(a930),f574(x93902,x93901,x93903,x93904)),x93903))+~P107(f866(f866(f244(a930),x93904),x93903))+~P107(f866(f866(f243(a1),f866(x93901,x93904)),x93902))
% 157.76/157.53 [9518]~P107(f866(f866(f243(a1),x95182),f866(x95183,x95184)))+P107(f866(f866(f243(a930),x95181),f574(x95182,x95183,x95184,x95181)))+P107(f866(f866(f243(a930),f573(x95182,x95183,x95184,x95181)),x95184))+~P107(f866(f866(f244(a930),x95181),x95184))+~P107(f866(f866(f243(a1),f866(x95183,x95181)),x95182))
% 157.76/157.53 [9519]~P107(f866(f866(f243(a1),x95192),f866(x95193,x95194)))+P107(f866(f866(f243(a930),x95191),f573(x95192,x95193,x95194,x95191)))+P107(f866(f866(f244(a930),f574(x95192,x95193,x95194,x95191)),x95194))+~P107(f866(f866(f244(a930),x95191),x95194))+~P107(f866(f866(f243(a1),f866(x95193,x95191)),x95192))
% 157.76/157.53 [9627]~P107(f866(f866(f243(a1),x96271),f866(x96272,x96273)))+P107(f866(f866(f244(a930),f574(x96271,x96272,x96273,x96274)),x96273))+~P107(f866(f866(f244(a930),x96274),x96273))+~P107(f866(f866(f243(a1),f866(x96272,x96274)),x96271))+P107(f866(f866(f243(a930),f573(x96271,x96272,x96273,x96274)),x96273))
% 157.76/157.53 [9711]E(x97111,f195(f937(x97112,a925)))+~P107(f866(f66(x97112),x97114))+~P107(f866(f66(x97112),x97111))+P107(f866(f866(f336(f936(f937(x97112,a925),f937(x97112,a925))),f866(f866(f260(f937(x97112,a925),f937(x97112,a925)),x97114),x97111)),f325(x97112,x97113)))+P107(f866(f866(f336(x97112),f522(x97113,x97111,x97114,x97112)),x97114))
% 157.76/157.53 [9712]E(x97121,f195(f937(x97122,a925)))+~P107(f866(f66(x97122),x97124))+~P107(f866(f66(x97122),x97121))+P107(f866(f866(f336(f936(f937(x97122,a925),f937(x97122,a925))),f866(f866(f260(f937(x97122,a925),f937(x97122,a925)),x97124),x97121)),f325(x97122,x97123)))+P107(f866(f866(f336(x97122),f575(x97123,x97121,x97124,x97122)),x97124))
% 157.76/157.53 [10372]E(f866(x103721,f573(x103722,x103721,x103723,x103724)),x103722)+~P107(f866(f866(f243(a1),x103722),f866(x103721,x103723)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x103721,f866(f866(f86(a930),f574(x103722,x103721,x103723,x103724)),f84(a930)))),f866(x103721,f574(x103722,x103721,x103723,x103724))))),f84(a1)))+~P107(f866(f866(f244(a930),x103724),x103723))+~P107(f866(f866(f243(a1),f866(x103721,x103724)),x103722))
% 157.76/157.53 [10373]~P107(f866(f866(f243(a1),x103732),f866(x103733,x103734)))+P107(f866(f866(f243(a930),x103731),f573(x103732,x103733,x103734,x103731)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x103733,f866(f866(f86(a930),f574(x103732,x103733,x103734,x103731)),f84(a930)))),f866(x103733,f574(x103732,x103733,x103734,x103731))))),f84(a1)))+~P107(f866(f866(f244(a930),x103731),x103734))+~P107(f866(f866(f243(a1),f866(x103733,x103731)),x103732))
% 157.76/157.53 [10374]~P107(f866(f866(f243(a1),x103741),f866(x103742,x103743)))+~P107(f866(f866(f243(a1),f866(f81(a1),f866(f866(f23(a1),f866(x103742,f866(f866(f86(a930),f574(x103741,x103742,x103743,x103744)),f84(a930)))),f866(x103742,f574(x103741,x103742,x103743,x103744))))),f84(a1)))+~P107(f866(f866(f244(a930),x103744),x103743))+~P107(f866(f866(f243(a1),f866(x103742,x103744)),x103741))+P107(f866(f866(f243(a930),f573(x103741,x103742,x103743,x103744)),x103743))
% 157.76/157.53 [7469]~P67(x74691)+P107(f866(f866(f244(x74691),x74692),f2(x74691)))+~P107(f866(f866(f243(x74691),x74693),f2(x74691)))+P107(f866(f866(f244(x74691),f2(x74691)),x74692))+P107(f866(f866(f243(x74691),x74693),f866(f866(f297(x74691),x74694),x74692)))
% 157.76/157.53 [7470]~P67(x74701)+P107(f866(f866(f244(x74701),x74702),f2(x74701)))+~P107(f866(f866(f244(x74701),x74703),f2(x74701)))+P107(f866(f866(f244(x74701),f2(x74701)),x74702))+P107(f866(f866(f244(x74701),x74703),f866(f866(f297(x74701),x74704),x74702)))
% 157.76/157.53 [7718]~P67(x77181)+P107(f866(f866(f243(x77181),x77182),f2(x77181)))+P107(f866(f866(f244(x77181),x77183),f2(x77181)))+P107(f866(f866(f244(x77181),f2(x77181)),x77183))+~P107(f866(f866(f243(x77181),x77182),f866(f866(f297(x77181),x77184),x77183)))
% 157.76/157.53 [7719]~P67(x77191)+P107(f866(f866(f244(x77191),x77192),f2(x77191)))+P107(f866(f866(f244(x77191),x77193),f2(x77191)))+P107(f866(f866(f244(x77191),f2(x77191)),x77193))+~P107(f866(f866(f244(x77191),x77192),f866(f866(f297(x77191),x77194),x77193)))
% 157.76/157.53 [7834]E(x78341,x78342)+~E(f866(f866(f171(x78343),x78344),x78341),f866(f866(f171(x78343),x78344),x78342))+~P107(f866(f144(x78343),x78344))+~P107(f866(f866(f244(a930),x78342),f866(f196(f931(x78343)),x78344)))+~P107(f866(f866(f244(a930),x78341),f866(f196(f931(x78343)),x78344)))
% 157.76/157.53 [8193]~P67(x81931)+~P107(f866(f866(f243(x81931),x81933),f2(x81931)))+P107(f866(f866(f244(x81931),f2(x81931)),x81932))+~P107(f866(f866(f243(x81931),x81934),f866(f866(f87(x81931),x81933),x81932)))+P107(f866(f866(f243(x81931),x81933),f866(f866(f297(x81931),x81934),x81932)))
% 157.76/157.53 [8194]~P67(x81941)+~P107(f866(f866(f244(x81941),x81943),f2(x81941)))+P107(f866(f866(f244(x81941),f2(x81941)),x81942))+~P107(f866(f866(f244(x81941),x81944),f866(f866(f87(x81941),x81943),x81942)))+P107(f866(f866(f244(x81941),x81943),f866(f866(f297(x81941),x81944),x81942)))
% 157.76/157.53 [8195]~P67(x81951)+~P107(f866(f866(f244(x81951),x81952),f2(x81951)))+P107(f866(f866(f244(x81951),f2(x81951)),x81952))+~P107(f866(f866(f243(x81951),x81954),f866(f866(f87(x81951),x81953),x81952)))+P107(f866(f866(f243(x81951),x81953),f866(f866(f297(x81951),x81954),x81952)))
% 157.76/157.53 [8196]~P67(x81961)+~P107(f866(f866(f244(x81961),x81962),f2(x81961)))+P107(f866(f866(f244(x81961),f2(x81961)),x81962))+~P107(f866(f866(f243(x81961),x81964),f866(f866(f297(x81961),x81963),x81962)))+P107(f866(f866(f243(x81961),x81963),f866(f866(f87(x81961),x81964),x81962)))
% 157.76/157.53 [8197]~P67(x81971)+~P107(f866(f866(f244(x81971),x81972),f2(x81971)))+P107(f866(f866(f244(x81971),f2(x81971)),x81972))+~P107(f866(f866(f244(x81971),x81974),f866(f866(f87(x81971),x81973),x81972)))+P107(f866(f866(f244(x81971),x81973),f866(f866(f297(x81971),x81974),x81972)))
% 157.76/157.53 [8198]~P67(x81981)+~P107(f866(f866(f244(x81981),x81982),f2(x81981)))+P107(f866(f866(f244(x81981),f2(x81981)),x81982))+~P107(f866(f866(f244(x81981),x81984),f866(f866(f297(x81981),x81983),x81982)))+P107(f866(f866(f244(x81981),x81983),f866(f866(f87(x81981),x81984),x81982)))
% 157.76/157.53 [8338]~P110(x83381)+~P13(x83381,x83382)+~P107(f866(f866(f243(a930),x83383),x83384))+P107(f866(f866(f243(x83381),f866(f866(f171(x83381),x83382),x83383)),f866(f866(f171(x83381),x83382),x83384)))+~P107(f866(f866(f244(a930),x83384),f866(f196(f931(x83381)),x83382)))
% 157.76/157.53 [8385]~P113(x83851)+~P107(f866(f866(f243(x83851),x83852),f84(x83851)))+~P107(f866(f866(f243(x83851),f2(x83851)),x83852))+~P107(f866(f866(f243(a930),x83854),x83853))+P107(f866(f866(f243(x83851),f866(f866(f252(x83851),x83852),x83853)),f866(f866(f252(x83851),x83852),x83854)))
% 157.76/157.53 [8386]~P113(x83861)+~P107(f866(f866(f244(x83861),x83862),f84(x83861)))+~P107(f866(f866(f244(x83861),f2(x83861)),x83862))+~P107(f866(f866(f244(a930),x83864),x83863))+P107(f866(f866(f244(x83861),f866(f866(f252(x83861),x83862),x83863)),f866(f866(f252(x83861),x83862),x83864)))
% 157.76/157.53 [8387]~P113(x83871)+~P107(f866(f866(f243(x83871),f2(x83871)),x83872))+~P107(f866(f866(f244(a930),f2(a930)),x83873))+~P107(f866(f866(f244(x83871),x83872),x83874))+P107(f866(f866(f244(x83871),f866(f866(f252(x83871),x83872),x83873)),f866(f866(f252(x83871),x83874),x83873)))
% 157.76/157.53 [8405]~P110(x84051)+~P13(x84051,f866(f175(x84051),x84052))+~P107(f866(f866(f243(a930),x84054),x84053))+P107(f866(f866(f243(x84051),f866(f866(f171(x84051),x84052),x84053)),f866(f866(f171(x84051),x84052),x84054)))+~P107(f866(f866(f244(a930),x84053),f866(f196(f931(x84051)),x84052)))
% 157.76/157.53 [8649]~P67(x86491)+~P107(f866(f866(f243(x86491),x86492),f2(x86491)))+~P107(f866(f866(f243(x86491),x86493),x86494))+~P107(f866(f866(f244(x86491),f2(x86491)),f866(f866(f87(x86491),x86493),x86494)))+P107(f866(f866(f243(x86491),f866(f866(f297(x86491),x86492),x86493)),f866(f866(f297(x86491),x86492),x86494)))
% 157.76/157.53 [8650]~P68(x86501)+~P107(f866(f866(f244(x86501),x86502),f2(x86501)))+~P107(f866(f866(f244(x86501),x86503),x86504))+~P107(f866(f866(f244(x86501),f2(x86501)),f866(f866(f87(x86501),x86503),x86504)))+P107(f866(f866(f244(x86501),f866(f866(f297(x86501),x86502),x86503)),f866(f866(f297(x86501),x86502),x86504)))
% 157.76/157.53 [8659]~P68(x86591)+~P107(f866(f866(f243(x86591),x86594),x86593))+~P107(f866(f866(f243(x86591),f2(x86591)),x86592))+~P107(f866(f866(f244(x86591),f2(x86591)),f866(f866(f87(x86591),x86593),x86594)))+P107(f866(f866(f243(x86591),f866(f866(f297(x86591),x86592),x86593)),f866(f866(f297(x86591),x86592),x86594)))
% 157.76/157.53 [8660]~P68(x86601)+~P107(f866(f866(f244(x86601),x86604),x86603))+~P107(f866(f866(f244(x86601),f2(x86601)),x86602))+~P107(f866(f866(f244(x86601),f2(x86601)),f866(f866(f87(x86601),x86603),x86604)))+P107(f866(f866(f244(x86601),f866(f866(f297(x86601),x86602),x86603)),f866(f866(f297(x86601),x86602),x86604)))
% 157.76/157.53 [8761]P107(f866(x87611,x87612))+~P107(f866(f66(x87614),x87612))+P107(f866(x87611,f887(x87611,x87613,x87612,x87614)))+~P107(f866(x87611,f195(f937(x87614,a925))))+~P107(f866(f866(f243(f937(x87614,a925)),x87612),x87613))
% 157.76/157.53 [8770]P107(f866(x87701,x87702))+P107(f866(f66(x87703),f887(x87701,x87704,x87702,x87703)))+~P107(f866(f66(x87703),x87702))+~P107(f866(x87701,f195(f937(x87703,a925))))+~P107(f866(f866(f243(f937(x87703,a925)),x87702),x87704))
% 157.76/157.53 [9038]E(f866(f866(f86(a1),f448(x90381,x90382,x90383,x90384)),f449(x90381,x90382,x90383,x90384)),x90384)+~P107(f866(f866(f244(a1),f2(a1)),x90383))+~P107(f866(f866(f244(a1),x90382),x90384))+~P107(f866(f866(f336(a1),x90382),x90381))+P107(f866(f866(f244(a1),x90382),f866(f866(f23(a1),x90384),x90383)))
% 157.76/157.53 [9257]~P107(f866(f866(f244(a1),f2(a1)),x92573))+~P107(f866(f866(f244(a1),x92572),x92574))+~P107(f866(f866(f336(a1),x92572),x92571))+P107(f866(f866(f336(a1),f448(x92571,x92572,x92573,x92574)),x92571))+P107(f866(f866(f244(a1),x92572),f866(f866(f23(a1),x92574),x92573)))
% 157.76/157.53 [9268]P107(f866(x92681,x92682))+~P107(f866(f66(x92683),x92682))+P107(f866(f866(f336(x92683),f888(x92681,x92684,x92682,x92683)),x92684))+~P107(f866(x92681,f195(f937(x92683,a925))))+~P107(f866(f866(f243(f937(x92683,a925)),x92682),x92684))
% 157.76/157.53 [9285]E(f866(f866(f86(a1),f436(x92851,x92852,x92853,x92854)),f437(x92851,x92852,x92853,x92854)),x92854)+~P107(f866(f866(f244(a1),f2(a1)),x92853))+~P107(f866(f866(f243(a1),x92852),x92854))+P107(f866(f866(f243(a1),x92852),f866(f866(f23(a1),x92854),x92853)))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x92852),f84(a1))),x92851))
% 157.76/157.53 [9340]~P107(f866(f866(f244(a1),f2(a1)),x93403))+~P107(f866(f866(f244(a1),x93401),x93402))+~P107(f866(f866(f336(a1),x93401),x93404))+P107(f866(f866(f336(a1),f449(x93404,x93401,x93403,x93402)),f310(a1,f84(a1),x93403)))+P107(f866(f866(f244(a1),x93401),f866(f866(f23(a1),x93402),x93403)))
% 157.76/157.53 [9366]~P72(x93662)+~E(f793(x93663,x93664,x93661,x93662),f794(x93663,x93664,x93661,x93662))+~P107(f866(f66(x93661),f795(x93663,x93664,x93661,x93662)))+E(f866(f866(f6(f937(x93661,a925),x93662),f866(f6(x93661,x93662),x93663)),x93664),f866(f866(f6(x93661,x93662),x93663),f42(f937(x93661,a925),x93664)))+~P107(f866(f66(f937(x93661,a925)),x93664))
% 157.76/157.53 [9370]~P72(x93702)+~E(f866(x93703,f796(x93703,x93704,x93701,x93702)),f2(x93702))+~P107(f866(f66(x93701),f795(x93703,x93704,x93701,x93702)))+E(f866(f866(f6(f937(x93701,a925),x93702),f866(f6(x93701,x93702),x93703)),x93704),f866(f866(f6(x93701,x93702),x93703),f42(f937(x93701,a925),x93704)))+~P107(f866(f66(f937(x93701,a925)),x93704))
% 157.76/157.53 [9433]~P107(f866(f866(f244(a1),f2(a1)),x94333))+~P107(f866(f866(f243(a1),x94332),x94334))+P107(f866(f866(f336(a1),f436(x94331,x94332,x94333,x94334)),x94331))+P107(f866(f866(f243(a1),x94332),f866(f866(f23(a1),x94334),x94333)))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x94332),f84(a1))),x94331))
% 157.76/157.53 [9475]~P107(f866(f866(f244(a1),f2(a1)),x94753))+~P107(f866(f866(f243(a1),x94751),x94752))+P107(f866(f866(f336(a1),f437(x94754,x94751,x94753,x94752)),f310(a1,f84(a1),x94753)))+P107(f866(f866(f243(a1),x94751),f866(f866(f23(a1),x94752),x94753)))+~P107(f866(f866(f336(a1),f866(f866(f23(a1),x94751),f84(a1))),x94754))
% 157.76/157.53 [9497]~P72(x94972)+~E(f793(x94973,x94974,x94971,x94972),f794(x94973,x94974,x94971,x94972))+E(f866(f866(f6(f937(x94971,a925),x94972),f866(f6(x94971,x94972),x94973)),x94974),f866(f866(f6(x94971,x94972),x94973),f42(f937(x94971,a925),x94974)))+P107(f866(f866(f336(f937(x94971,a925)),f795(x94973,x94974,x94971,x94972)),x94974))+~P107(f866(f66(f937(x94971,a925)),x94974))
% 157.76/157.53 [9502]~P72(x95022)+~E(f866(x95023,f796(x95023,x95024,x95021,x95022)),f2(x95022))+E(f866(f866(f6(f937(x95021,a925),x95022),f866(f6(x95021,x95022),x95023)),x95024),f866(f866(f6(x95021,x95022),x95023),f42(f937(x95021,a925),x95024)))+P107(f866(f866(f336(f937(x95021,a925)),f795(x95023,x95024,x95021,x95022)),x95024))+~P107(f866(f66(f937(x95021,a925)),x95024))
% 157.76/157.53 [9604]~P72(x96042)+~P107(f866(f66(x96041),f795(x96043,x96044,x96041,x96042)))+E(f866(f866(f6(f937(x96041,a925),x96042),f866(f6(x96041,x96042),x96043)),x96044),f866(f866(f6(x96041,x96042),x96043),f42(f937(x96041,a925),x96044)))+P107(f866(f866(f336(f937(x96041,a925)),f794(x96043,x96044,x96041,x96042)),x96044))+~P107(f866(f66(f937(x96041,a925)),x96044))
% 157.76/157.53 [9605]~P72(x96052)+~P107(f866(f66(x96051),f795(x96053,x96054,x96051,x96052)))+E(f866(f866(f6(f937(x96051,a925),x96052),f866(f6(x96051,x96052),x96053)),x96054),f866(f866(f6(x96051,x96052),x96053),f42(f937(x96051,a925),x96054)))+P107(f866(f866(f336(f937(x96051,a925)),f793(x96053,x96054,x96051,x96052)),x96054))+~P107(f866(f66(f937(x96051,a925)),x96054))
% 157.76/157.53 [9682]~P72(x96822)+E(f866(f866(f6(f937(x96821,a925),x96822),f866(f6(x96821,x96822),x96823)),x96824),f866(f866(f6(x96821,x96822),x96823),f42(f937(x96821,a925),x96824)))+P107(f866(f866(f336(f937(x96821,a925)),f795(x96823,x96824,x96821,x96822)),x96824))+P107(f866(f866(f336(f937(x96821,a925)),f794(x96823,x96824,x96821,x96822)),x96824))+~P107(f866(f66(f937(x96821,a925)),x96824))
% 157.76/157.53 [9683]~P72(x96832)+E(f866(f866(f6(f937(x96831,a925),x96832),f866(f6(x96831,x96832),x96833)),x96834),f866(f866(f6(x96831,x96832),x96833),f42(f937(x96831,a925),x96834)))+P107(f866(f866(f336(f937(x96831,a925)),f795(x96833,x96834,x96831,x96832)),x96834))+P107(f866(f866(f336(f937(x96831,a925)),f793(x96833,x96834,x96831,x96832)),x96834))+~P107(f866(f66(f937(x96831,a925)),x96834))
% 157.76/157.53 [9700]~P72(x97002)+P107(f866(f866(f336(x97001),f796(x97003,x97004,x97001,x97002)),f794(x97003,x97004,x97001,x97002)))+~P107(f866(f66(x97001),f795(x97003,x97004,x97001,x97002)))+E(f866(f866(f6(f937(x97001,a925),x97002),f866(f6(x97001,x97002),x97003)),x97004),f866(f866(f6(x97001,x97002),x97003),f42(f937(x97001,a925),x97004)))+~P107(f866(f66(f937(x97001,a925)),x97004))
% 157.76/157.53 [9701]~P72(x97012)+P107(f866(f866(f336(x97011),f796(x97013,x97014,x97011,x97012)),f793(x97013,x97014,x97011,x97012)))+~P107(f866(f66(x97011),f795(x97013,x97014,x97011,x97012)))+E(f866(f866(f6(f937(x97011,a925),x97012),f866(f6(x97011,x97012),x97013)),x97014),f866(f866(f6(x97011,x97012),x97013),f42(f937(x97011,a925),x97014)))+~P107(f866(f66(f937(x97011,a925)),x97014))
% 157.76/157.53 [9714]P107(f866(x97141,x97142))+~P107(f866(f866(f336(x97143),f888(x97141,x97144,x97142,x97143)),f887(x97141,x97144,x97142,x97143)))+~P107(f866(f66(x97143),x97142))+~P107(f866(x97141,f195(f937(x97143,a925))))+~P107(f866(f866(f243(f937(x97143,a925)),x97142),x97144))
% 157.76/157.53 [9751]~P72(x97512)+P107(f866(f866(f336(x97511),f796(x97513,x97514,x97511,x97512)),f794(x97513,x97514,x97511,x97512)))+E(f866(f866(f6(f937(x97511,a925),x97512),f866(f6(x97511,x97512),x97513)),x97514),f866(f866(f6(x97511,x97512),x97513),f42(f937(x97511,a925),x97514)))+P107(f866(f866(f336(f937(x97511,a925)),f795(x97513,x97514,x97511,x97512)),x97514))+~P107(f866(f66(f937(x97511,a925)),x97514))
% 157.76/157.53 [9752]~P72(x97522)+P107(f866(f866(f336(x97521),f796(x97523,x97524,x97521,x97522)),f793(x97523,x97524,x97521,x97522)))+E(f866(f866(f6(f937(x97521,a925),x97522),f866(f6(x97521,x97522),x97523)),x97524),f866(f866(f6(x97521,x97522),x97523),f42(f937(x97521,a925),x97524)))+P107(f866(f866(f336(f937(x97521,a925)),f795(x97523,x97524,x97521,x97522)),x97524))+~P107(f866(f66(f937(x97521,a925)),x97524))
% 157.76/157.53 [9928]P107(f866(x99281,x99282))+~P107(f866(f66(x99283),x99282))+~P107(f866(x99281,f866(f866(f316(x99283),f888(x99281,x99284,x99282,x99283)),f887(x99281,x99284,x99282,x99283))))+~P107(f866(x99281,f195(f937(x99283,a925))))+~P107(f866(f866(f243(f937(x99283,a925)),x99282),x99284))
% 157.76/157.53 [7966]~P67(x79661)+P107(f866(f866(f244(x79661),x79662),f2(x79661)))+~P107(f866(f866(f243(x79661),f2(x79661)),x79664))+P107(f866(f866(f244(x79661),f2(x79661)),x79662))+P107(f866(f866(f243(x79661),f866(f866(f297(x79661),x79663),x79662)),x79664))
% 157.76/157.53 [7967]~P67(x79671)+P107(f866(f866(f244(x79671),x79672),f2(x79671)))+P107(f866(f866(f244(x79671),f2(x79671)),x79672))+~P107(f866(f866(f244(x79671),f2(x79671)),x79674))+P107(f866(f866(f244(x79671),f866(f866(f297(x79671),x79673),x79672)),x79674))
% 157.76/157.53 [8245]~P107(f866(f866(f243(a1),x82454),f2(a1)))+~E(x82452,f866(f866(f86(a1),f866(f866(f87(a1),x82451),x82453)),x82454))+P107(f866(f866(f244(a1),f2(a1)),x82451))+~P107(f866(f866(f244(a1),x82451),x82454))+P107(f866(f54(x82452,x82451),f866(f866(f260(a1,a1),x82453),x82454)))
% 157.76/157.53 [8279]~P107(f866(x82791,x82794))+P107(f866(x82791,f464(x82792,x82791,x82793)))+~P107(f866(f866(f243(a1),f2(a1)),x82792))+~P107(f866(f866(f244(a1),f2(a1)),x82793))+P107(f866(x82791,f866(f866(f23(a1),x82794),f866(f866(f87(a1),x82792),x82793))))
% 157.76/157.53 [8280]~P107(f866(x82801,x82804))+P107(f866(x82801,f468(x82802,x82801,x82803)))+~P107(f866(f866(f243(a1),f2(a1)),x82802))+~P107(f866(f866(f244(a1),f2(a1)),x82803))+P107(f866(x82801,f866(f866(f86(a1),x82804),f866(f866(f87(a1),x82802),x82803))))
% 157.76/157.53 [8281]~P67(x82811)+P107(f866(f866(f244(x82811),x82812),f2(x82811)))+P107(f866(f866(f244(x82811),f2(x82811)),x82812))+P107(f866(f866(f243(x82811),f2(x82811)),x82813))+~P107(f866(f866(f243(x82811),f866(f866(f297(x82811),x82814),x82812)),x82813))
% 157.76/157.53 [8282]~P67(x82821)+P107(f866(f866(f244(x82821),x82822),f2(x82821)))+P107(f866(f866(f244(x82821),f2(x82821)),x82822))+P107(f866(f866(f244(x82821),f2(x82821)),x82823))+~P107(f866(f866(f244(x82821),f866(f866(f297(x82821),x82824),x82822)),x82823))
% 157.76/157.53 [8333]~E(x83331,f866(f866(f86(a1),f866(f866(f87(a1),x83332),x83333)),x83334))+~P107(f866(f866(f243(a1),f2(a1)),x83334))+~P107(f866(f866(f244(a1),f2(a1)),x83332))+~P107(f866(f866(f244(a1),x83334),x83332))+P107(f866(f54(x83331,x83332),f866(f866(f260(a1,a1),x83333),x83334)))
% 157.76/157.53 [8444]~P67(x84441)+P107(f866(f866(f244(x84441),x84442),f2(x84441)))+~P107(f866(f866(f243(x84441),f2(x84441)),x84444))+~P107(f866(f866(f243(x84441),x84443),f866(f866(f87(x84441),x84444),x84442)))+P107(f866(f866(f243(x84441),f866(f866(f297(x84441),x84443),x84442)),x84444))
% 157.76/157.53 [8445]~P67(x84451)+P107(f866(f866(f244(x84451),x84452),f2(x84451)))+~P107(f866(f866(f244(x84451),f2(x84451)),x84454))+~P107(f866(f866(f244(x84451),x84453),f866(f866(f87(x84451),x84454),x84452)))+P107(f866(f866(f244(x84451),f866(f866(f297(x84451),x84453),x84452)),x84454))
% 157.76/157.53 [8530]~P67(x85301)+P107(f866(f866(f244(x85301),x85302),f2(x85301)))+~P107(f866(f866(f243(x85301),x85303),f2(x85301)))+P107(f866(f866(f243(x85301),x85303),f866(f866(f297(x85301),x85304),x85302)))+~P107(f866(f866(f243(x85301),f866(f866(f87(x85301),x85303),x85302)),x85304))
% 157.76/157.53 [8531]~P67(x85311)+P107(f866(f866(f244(x85311),x85312),f2(x85311)))+~P107(f866(f866(f244(x85311),x85313),f2(x85311)))+P107(f866(f866(f244(x85311),x85313),f866(f866(f297(x85311),x85314),x85312)))+~P107(f866(f866(f244(x85311),f866(f866(f87(x85311),x85313),x85312)),x85314))
% 157.76/157.53 [8681]~P67(x86811)+~P107(f866(f866(f244(x86811),x86812),f2(x86811)))+P107(f866(f866(f244(x86811),f2(x86811)),x86812))+~P107(f866(f866(f243(x86811),f866(f866(f297(x86811),x86814),x86812)),x86813))+P107(f866(f866(f243(x86811),f866(f866(f87(x86811),x86813),x86812)),x86814))
% 157.76/157.53 [8682]~P67(x86821)+~P107(f866(f866(f244(x86821),x86822),f2(x86821)))+P107(f866(f866(f244(x86821),f2(x86821)),x86822))+~P107(f866(f866(f243(x86821),f866(f866(f87(x86821),x86824),x86822)),x86823))+P107(f866(f866(f243(x86821),f866(f866(f297(x86821),x86823),x86822)),x86824))
% 157.76/157.53 [8683]~P67(x86831)+~P107(f866(f866(f244(x86831),x86832),f2(x86831)))+P107(f866(f866(f244(x86831),f2(x86831)),x86832))+~P107(f866(f866(f244(x86831),f866(f866(f297(x86831),x86834),x86832)),x86833))+P107(f866(f866(f244(x86831),f866(f866(f87(x86831),x86833),x86832)),x86834))
% 157.76/157.53 [8684]~P67(x86841)+~P107(f866(f866(f244(x86841),x86842),f2(x86841)))+P107(f866(f866(f244(x86841),f2(x86841)),x86842))+~P107(f866(f866(f244(x86841),f866(f866(f87(x86841),x86844),x86842)),x86843))+P107(f866(f866(f244(x86841),f866(f866(f297(x86841),x86843),x86842)),x86844))
% 157.76/157.53 [8700]~P67(x87001)+~P107(f866(f866(f243(x87001),f2(x87001)),x87004))+P107(f866(f866(f244(x87001),f2(x87001)),x87002))+~P107(f866(f866(f243(x87001),f866(f866(f87(x87001),x87004),x87002)),x87003))+P107(f866(f866(f243(x87001),f866(f866(f297(x87001),x87003),x87002)),x87004))
% 157.76/157.53 [8701]~P67(x87011)+~P107(f866(f866(f244(x87011),f2(x87011)),x87014))+P107(f866(f866(f244(x87011),f2(x87011)),x87012))+~P107(f866(f866(f244(x87011),f866(f866(f87(x87011),x87014),x87012)),x87013))+P107(f866(f866(f244(x87011),f866(f866(f297(x87011),x87013),x87012)),x87014))
% 157.76/157.53 [8778]~P67(x87781)+~P107(f866(f866(f244(x87781),x87784),f2(x87781)))+~P107(f866(f866(f243(x87781),x87783),f866(f866(f87(x87781),x87782),x87784)))+P107(f866(f866(f243(x87781),x87782),f866(f866(f297(x87781),x87783),x87784)))+~P107(f866(f866(f243(x87781),f866(f866(f87(x87781),x87782),x87784)),x87783))
% 157.76/157.53 [8779]~P67(x87791)+~P107(f866(f866(f243(x87791),x87792),f2(x87791)))+~P107(f866(f866(f243(x87791),x87793),f866(f866(f87(x87791),x87792),x87794)))+P107(f866(f866(f243(x87791),x87792),f866(f866(f297(x87791),x87793),x87794)))+~P107(f866(f866(f243(x87791),f866(f866(f87(x87791),x87792),x87794)),x87793))
% 157.76/157.53 [8780]~P67(x87801)+~P107(f866(f866(f244(x87801),x87804),f2(x87801)))+~P107(f866(f866(f244(x87801),x87803),f866(f866(f87(x87801),x87802),x87804)))+P107(f866(f866(f244(x87801),x87802),f866(f866(f297(x87801),x87803),x87804)))+~P107(f866(f866(f244(x87801),f866(f866(f87(x87801),x87802),x87804)),x87803))
% 157.76/157.53 [8781]~P67(x87811)+~P107(f866(f866(f244(x87811),x87812),f2(x87811)))+~P107(f866(f866(f244(x87811),x87813),f866(f866(f87(x87811),x87812),x87814)))+P107(f866(f866(f244(x87811),x87812),f866(f866(f297(x87811),x87813),x87814)))+~P107(f866(f866(f244(x87811),f866(f866(f87(x87811),x87812),x87814)),x87813))
% 157.76/157.53 [8903]~P67(x89031)+~P107(f866(f866(f244(x89031),x89033),f2(x89031)))+~P107(f866(f866(f243(x89031),x89032),f866(f866(f87(x89031),x89034),x89033)))+~P107(f866(f866(f243(x89031),f866(f866(f87(x89031),x89034),x89033)),x89032))+P107(f866(f866(f243(x89031),f866(f866(f297(x89031),x89032),x89033)),x89034))
% 157.76/157.53 [8904]~P67(x89041)+~P107(f866(f866(f244(x89041),x89043),f2(x89041)))+~P107(f866(f866(f244(x89041),x89042),f866(f866(f87(x89041),x89044),x89043)))+~P107(f866(f866(f244(x89041),f866(f866(f87(x89041),x89044),x89043)),x89042))+P107(f866(f866(f244(x89041),f866(f866(f297(x89041),x89042),x89043)),x89044))
% 157.76/157.53 [8921]~P67(x89211)+~P107(f866(f866(f243(x89211),f2(x89211)),x89214))+~P107(f866(f866(f243(x89211),x89212),f866(f866(f87(x89211),x89214),x89213)))+~P107(f866(f866(f243(x89211),f866(f866(f87(x89211),x89214),x89213)),x89212))+P107(f866(f866(f243(x89211),f866(f866(f297(x89211),x89212),x89213)),x89214))
% 157.76/157.53 [8922]~P67(x89221)+~P107(f866(f866(f244(x89221),f2(x89221)),x89224))+~P107(f866(f866(f244(x89221),x89222),f866(f866(f87(x89221),x89224),x89223)))+~P107(f866(f866(f244(x89221),f866(f866(f87(x89221),x89224),x89223)),x89222))+P107(f866(f866(f244(x89221),f866(f866(f297(x89221),x89222),x89223)),x89224))
% 157.76/157.53 [9107]E(f866(f866(f23(a1),f442(x91071,x91072,x91073,x91074)),f443(x91071,x91072,x91073,x91074)),x91074)+~P107(f866(f866(f244(a1),f2(a1)),x91073))+~P107(f866(f866(f336(a1),x91072),x91071))+~P107(f866(f866(f244(a1),x91074),x91072))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x91074),x91073)),x91072))
% 157.76/157.53 [9182]~P107(f866(x91821,x91822))+~P107(f866(f866(f243(a1),f2(a1)),x91823))+~P107(f866(f866(f244(a1),f2(a1)),x91824))+~P107(f866(x91821,f866(f866(f23(a1),f464(x91823,x91821,x91824)),x91824)))+P107(f866(x91821,f866(f866(f23(a1),x91822),f866(f866(f87(a1),x91823),x91824))))
% 157.76/157.53 [9183]~P107(f866(x91831,x91832))+~P107(f866(f866(f243(a1),f2(a1)),x91833))+~P107(f866(f866(f244(a1),f2(a1)),x91834))+~P107(f866(x91831,f866(f866(f86(a1),f468(x91833,x91831,x91834)),x91834)))+P107(f866(x91831,f866(f866(f86(a1),x91832),f866(f866(f87(a1),x91833),x91834))))
% 157.76/157.53 [9333]~P107(f866(f866(f244(a1),f2(a1)),x93333))+~P107(f866(f866(f336(a1),x93332),x93331))+~P107(f866(f866(f244(a1),x93334),x93332))+P107(f866(f866(f336(a1),f442(x93331,x93332,x93333,x93334)),x93331))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x93334),x93333)),x93332))
% 157.76/157.53 [9353]E(f866(f866(f23(a1),f438(x93531,x93532,x93533,x93534)),f439(x93531,x93532,x93533,x93534)),x93534)+~P107(f866(f866(f244(a1),f2(a1)),x93533))+~P107(f866(f866(f243(a1),x93534),x93532))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x93532),f84(a1))),x93531))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x93534),x93533)),x93532))
% 157.76/157.53 [9381]~P107(f866(f866(f244(a1),f2(a1)),x93812))+~P107(f866(f866(f336(a1),x93813),x93814))+~P107(f866(f866(f244(a1),x93811),x93813))+P107(f866(f866(f336(a1),f443(x93814,x93813,x93812,x93811)),f310(a1,f84(a1),x93812)))+P107(f866(f866(f244(a1),f866(f866(f86(a1),x93811),x93812)),x93813))
% 157.76/157.53 [9467]~P107(f866(f866(f244(a1),f2(a1)),x94673))+~P107(f866(f866(f243(a1),x94674),x94672))+P107(f866(f866(f336(a1),f438(x94671,x94672,x94673,x94674)),x94671))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x94672),f84(a1))),x94671))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x94674),x94673)),x94672))
% 157.76/157.53 [9514]~P107(f866(f866(f244(a1),f2(a1)),x95142))+~P107(f866(f866(f243(a1),x95141),x95143))+P107(f866(f866(f336(a1),f439(x95144,x95143,x95142,x95141)),f310(a1,f84(a1),x95142)))+~P107(f866(f866(f336(a1),f866(f866(f86(a1),x95143),f84(a1))),x95144))+P107(f866(f866(f243(a1),f866(f866(f86(a1),x95141),x95142)),x95143))
% 157.76/157.53 [9805]~P37(x98051,x98053)+~P27(x98051,x98054)+P37(x98051,f866(f866(f117(f937(f936(x98051,x98051),a925)),x98052),x98053))+~P107(f866(f866(f243(f937(f936(x98051,x98051),a925)),x98052),f866(f259(f937(f936(x98051,x98051),a925),f937(f936(x98051,x98051),a925)),x98054)))+~P107(f866(f866(f243(f937(f936(x98051,x98051),a925)),x98053),f866(f264(f937(f936(x98051,x98051),a925),f937(f936(x98051,x98051),a925)),x98054)))
% 157.76/157.53 [10187]~P18(x101872,x101874,x101873)+E(x101871,f195(f937(x101872,a925)))+~P107(f866(f66(x101872),x101871))+P107(f866(f866(f336(x101872),f866(x101873,x101871)),x101871))+~P107(f866(f866(f336(x101872),f866(f866(x101874,f710(x101871,x101873,x101874,x101872)),f719(x101871,x101873,x101874,x101872))),f866(f866(f316(x101872),f710(x101871,x101873,x101874,x101872)),f866(f866(f316(x101872),f719(x101871,x101873,x101874,x101872)),f195(f937(x101872,a925))))))
% 157.76/157.53 [10120]~P111(x101202)+~P64(x101201)+~P107(f866(f866(f243(f937(x101201,x101202)),x101203),x101204))+P107(f866(f866(f244(f937(x101201,x101202)),x101203),x101204))+~P107(f866(f61(x101201),f866(f866(f8(a925,a925,x101201),a329),f866(f866(f18(x101201,x101202,a925),f866(f866(f8(x101202,f937(x101202,a925),x101201),a332),x101203)),x101204))))
% 157.76/157.53 [9720]~P55(x97201,x97201,x97204)+P107(f866(f866(f336(f936(x97201,x97201)),f866(f866(f260(x97201,x97201),x97202),x97203)),f314(x97201,x97204)))+P107(f866(f866(f336(f936(x97201,x97201)),f866(f866(f260(x97201,x97201),x97203),x97202)),f314(x97201,x97204)))+~P107(f866(f866(f336(f936(x97201,x97201)),f866(f866(f260(x97201,x97201),x97205),x97202)),f314(x97201,x97204)))+~P107(f866(f866(f336(f936(x97201,x97201)),f866(f866(f260(x97201,x97201),x97205),x97203)),f314(x97201,x97204)))
% 157.76/157.53 [5874]E(x58741,f2(a930))+~E(f866(f40(x58742),x58745),x58741)+E(f866(f40(x58742),x58743),f866(a119,x58741))+~E(x58743,f866(f866(f316(x58742),x58744),x58745))+P107(f866(f866(f336(x58742),x58744),x58745))
% 157.76/157.53 [5998]~P66(x59982)+E(x59981,f2(x59982))+E(x59983,f2(x59982))+~E(f866(f866(f297(x59982),x59984),x59983),f866(f866(f297(x59982),x59985),x59981))+E(f866(f866(f87(x59982),x59984),x59981),f866(f866(f87(x59982),x59985),x59983))
% 157.76/157.53 [5999]~P66(x59992)+E(x59991,f2(x59992))+E(x59993,f2(x59992))+~E(f866(f866(f87(x59992),x59994),x59993),f866(f866(f87(x59992),x59995),x59991))+E(f866(f866(f297(x59992),x59994),x59991),f866(f866(f297(x59992),x59995),x59993))
% 157.76/157.53 [6068]~E(f866(f40(x60681),x60685),x60683)+~E(x60685,f195(f937(x60681,a925)))+E(f866(f40(x60681),x60682),f866(a119,x60683))+~E(x60682,f866(f866(f316(x60681),x60684),x60685))+P107(f866(f866(f336(x60681),x60684),x60685))
% 157.76/157.53 [6306]~P114(x63062)+~E(f866(x63063,x63065),f2(x63062))+E(f866(f866(f9(x63061,x63062),x63063),x63064),f2(x63062))+~P107(f866(f66(x63061),x63064))+~P107(f866(f866(f336(x63061),x63065),x63064))
% 157.76/157.53 [6676]~P110(x66763)+E(x66761,x66762)+~E(f866(f309(x66763,x66764),x66761),f866(f309(x66763,x66765),x66762))+~P107(f866(f866(f244(x66763),x66765),x66762))+~P107(f866(f866(f244(x66763),x66764),x66761))
% 157.76/157.53 [6677]~P110(x66773)+E(x66771,x66772)+~E(f866(f309(x66773,x66771),x66774),f866(f309(x66773,x66772),x66775))+~P107(f866(f866(f244(x66773),x66772),x66775))+~P107(f866(f866(f244(x66773),x66771),x66774))
% 157.76/157.53 [7735]~P110(x77351)+~P13(x77351,f866(f866(f141(x77351),x77354),x77355))+~P107(f866(f866(f336(x77351),x77353),f866(f179(x77351),x77355)))+~P107(f866(f866(f336(x77351),x77352),f866(f179(x77351),x77354)))+P107(f866(f866(f243(x77351),x77352),x77353))
% 157.76/157.53 [8815]~P111(x88151)+~P107(f866(f866(f244(f937(x88151,a925)),f310(x88151,x88155,x88152)),f310(x88151,x88154,x88153)))+~P107(f866(f866(f243(x88151),x88155),x88152))+P107(f866(f866(f244(x88151),x88152),x88153))+P107(f866(f866(f244(x88151),x88154),x88155))
% 157.76/157.53 [10230]~P17(x102302,x102305,x102303)+E(x102301,f195(f937(x102302,a925)))+~E(f866(f866(x102305,f866(x102304,f898(x102301,x102304,x102303,x102305,x102302))),f866(x102304,f899(x102301,x102304,x102303,x102305,x102302))),f866(x102304,f866(f866(x102305,f898(x102301,x102304,x102303,x102305,x102302)),f899(x102301,x102304,x102303,x102305,x102302))))+E(f866(x102303,f866(f317(x102302,x102302,x102304),x102301)),f866(x102304,f866(x102303,x102301)))+~P107(f866(f66(x102302),x102301))
% 157.76/157.53 [6673]~P18(x66732,x66735,x66733)+E(x66731,f195(f937(x66732,a925)))+~P107(f866(f66(x66732),x66731))+E(f866(x66733,f866(f866(f316(x66732),x66734),x66731)),f866(f866(x66735,x66734),f866(x66733,x66731)))+P107(f866(f866(f336(x66732),x66734),x66731))
% 157.76/157.53 [7497]~P17(x74972,x74973,x74974)+E(f866(f866(x74973,f866(x74974,x74971)),f866(x74974,x74975)),f866(x74974,x74975))+E(x74971,f195(f937(x74972,a925)))+~P107(f866(f66(x74972),x74975))+~P107(f866(f866(f243(f937(x74972,a925)),x74971),x74975))
% 157.76/157.53 [7867]~P18(x78674,x78675,x78671)+E(f866(x78671,x78672),x78673)+~P107(f866(f66(x78674),x78672))+~E(f866(f866(f23(f937(x78674,a925)),x78672),f866(f866(f316(x78674),x78673),f195(f937(x78674,a925)))),f195(f937(x78674,a925)))+~P107(f866(f866(f336(x78674),x78673),x78672))
% 157.76/157.53 [8785]E(x87851,x87852)+~P8(x87853,x87854,x87855)+E(f866(f866(f108(f937(x87853,a925)),x87851),x87852),f195(f937(x87853,a925)))+~P107(f866(f866(f336(f937(x87853,a925)),x87852),f866(f866(f65(x87853),x87854),x87855)))+~P107(f866(f866(f336(f937(x87853,a925)),x87851),f866(f866(f65(x87853),x87854),x87855)))
% 157.76/157.53 [9597]~P71(x95972)+~E(f866(x95973,f352(x95973,x95974,x95975,x95971,x95972)),f84(x95972))+E(f866(f866(f9(x95971,x95972),x95973),x95974),f866(f866(f9(x95971,x95972),x95973),x95975))+~P107(f866(f66(x95971),x95975))+~P107(f866(f866(f243(f937(x95971,a925)),x95974),x95975))
% 157.76/157.53 [9598]~P71(x95982)+~E(f866(x95983,f354(x95983,x95984,x95985,x95981,x95982)),f84(x95982))+E(f866(f866(f9(x95981,x95982),x95983),x95984),f866(f866(f9(x95981,x95982),x95983),x95985))+~P107(f866(f66(x95981),x95985))+~P107(f866(f866(f243(f937(x95981,a925)),x95984),x95985))
% 157.76/157.53 [9599]~P72(x95992)+~E(f866(x95993,f474(x95993,x95994,x95995,x95991,x95992)),f2(x95992))+E(f866(f866(f6(x95991,x95992),x95993),x95994),f866(f866(f6(x95991,x95992),x95993),x95995))+~P107(f866(f66(x95991),x95995))+~P107(f866(f866(f243(f937(x95991,a925)),x95994),x95995))
% 157.76/157.53 [9600]~P72(x96002)+~E(f866(x96003,f475(x96003,x96004,x96005,x96001,x96002)),f2(x96002))+E(f866(f866(f6(x96001,x96002),x96003),x96004),f866(f866(f6(x96001,x96002),x96003),x96005))+~P107(f866(f66(x96001),x96005))+~P107(f866(f866(f243(f937(x96001,a925)),x96004),x96005))
% 157.76/157.53 [10073]~P86(x100731)+~P107(f866(f66(x100732),x100735))+~P107(f866(f866(f243(x100731),f2(x100731)),f866(x100733,f398(x100733,x100734,x100735,x100732,x100731))))+P107(f866(f866(f243(x100731),f866(f866(f6(x100732,x100731),x100733),x100734)),f866(f866(f6(x100732,x100731),x100733),x100735)))+~P107(f866(f866(f243(f937(x100732,a925)),x100734),x100735))
% 157.76/157.53 [7732]E(x77321,f2(a930))+P107(f866(x77322,x77323))+~E(x77324,f866(f866(f86(a930),f866(f866(f87(a930),x77321),x77323)),x77325))+~P107(f866(f866(f244(a930),x77325),x77321))+~P107(f866(x77322,f866(f866(f41(a930),x77324),x77321)))
% 157.76/157.53 [7807]E(x78071,f2(a930))+P107(f866(x78072,x78073))+~P107(f866(x78072,f50(a930,x78074,x78071)))+~E(x78074,f866(f866(f86(a930),f866(f866(f87(a930),x78071),x78075)),x78073))+~P107(f866(f866(f244(a930),x78073),x78071))
% 157.76/157.53 [8095]~P66(x80953)+E(f866(x80951,x80952),f2(x80953))+~P107(f866(f66(x80954),x80955))+E(f866(f866(f9(x80954,x80953),x80951),f866(f866(f23(f937(x80954,a925)),x80955),f866(f866(f316(x80954),x80952),f195(f937(x80954,a925))))),f866(f866(f9(x80954,x80953),x80951),x80955))+P107(f866(f866(f336(x80954),x80952),x80955))
% 157.76/157.53 [8485]~P71(x84851)+~P107(f866(f66(x84852),x84855))+~P107(f866(f66(x84852),x84854))+~E(f866(f866(f108(f937(x84852,a925)),x84854),x84855),f195(f937(x84852,a925)))+E(f866(f866(f87(x84851),f866(f866(f9(x84852,x84851),x84853),x84854)),f866(f866(f9(x84852,x84851),x84853),x84855)),f866(f866(f9(x84852,x84851),x84853),f866(f866(f117(f937(x84852,a925)),x84854),x84855)))
% 157.76/157.53 [8486]~P72(x84861)+~P107(f866(f66(x84862),x84865))+~P107(f866(f66(x84862),x84864))+~E(f866(f866(f108(f937(x84862,a925)),x84864),x84865),f195(f937(x84862,a925)))+E(f866(f866(f86(x84861),f866(f866(f6(x84862,x84861),x84863),x84864)),f866(f866(f6(x84862,x84861),x84863),x84865)),f866(f866(f6(x84862,x84861),x84863),f866(f866(f117(f937(x84862,a925)),x84864),x84865)))
% 157.76/157.53 [8585]~P66(x85853)+E(f866(x85851,x85852),f2(x85853))+~P107(f866(f66(x85854),x85855))+E(f866(f866(f9(x85854,x85853),x85851),f866(f866(f23(f937(x85854,a925)),x85855),f866(f866(f316(x85854),x85852),f195(f937(x85854,a925))))),f866(f866(f297(x85853),f866(f866(f9(x85854,x85853),x85851),x85855)),f866(x85851,x85852)))+~P107(f866(f866(f336(x85854),x85852),x85855))
% 157.76/157.53 [9310]~P8(x93101,x93105,x93104)+~E(f866(f866(f65(x93101),f866(f866(f316(x93101),x93102),f195(f937(x93101,a925)))),x93104),f866(f866(f65(x93101),f866(f866(f316(x93101),x93103),f195(f937(x93101,a925)))),x93104))+~P107(f866(f866(f336(x93101),x93103),x93105))+~P107(f866(f866(f336(x93101),x93102),x93105))+P107(f866(f866(f336(f936(x93101,x93101)),f866(f866(f260(x93101,x93101),x93102),x93103)),x93104))
% 157.76/157.53 [9332]~P8(x93321,x93325,x93323)+E(f866(f866(f65(x93321),f866(f866(f316(x93321),x93322),f195(f937(x93321,a925)))),x93323),f866(f866(f65(x93321),f866(f866(f316(x93321),x93324),f195(f937(x93321,a925)))),x93323))+~P107(f866(f866(f336(x93321),x93324),x93325))+~P107(f866(f866(f336(x93321),x93322),x93325))+~P107(f866(f866(f336(f936(x93321,x93321)),f866(f866(f260(x93321,x93321),x93322),x93324)),x93323))
% 157.76/157.53 [9626]~P71(x96261)+~P107(f866(f66(x96262),x96265))+~P107(f866(f66(x96262),x96264))+~E(f866(f866(f108(f937(x96262,a925)),x96264),x96265),f195(f937(x96262,a925)))+E(f866(f866(f87(x96261),f866(f866(f866(f70(x96261,x96262,f87(x96261)),x96263),f84(x96261)),x96264)),f866(f866(f866(f70(x96261,x96262,f87(x96261)),x96263),f84(x96261)),x96265)),f866(f866(f866(f70(x96261,x96262,f87(x96261)),x96263),f84(x96261)),f866(f866(f117(f937(x96262,a925)),x96264),x96265)))
% 157.76/157.53 [9635]~P71(x96351)+~E(f866(x96353,f919(x96353,x96355,x96354,x96352,x96351)),f84(x96351))+~P107(f866(f66(x96352),x96354))+~P107(f866(f66(x96352),x96355))+E(f866(f866(f87(x96351),f866(f866(f9(x96352,x96351),x96353),x96354)),f866(f866(f9(x96352,x96351),x96353),x96355)),f866(f866(f9(x96352,x96351),x96353),f866(f866(f117(f937(x96352,a925)),x96354),x96355)))
% 157.76/157.53 [9636]~P71(x96361)+~E(f866(x96363,f921(x96363,x96365,x96364,x96362,x96361)),f84(x96361))+~P107(f866(f66(x96362),x96364))+~P107(f866(f66(x96362),x96365))+E(f866(f866(f87(x96361),f866(f866(f9(x96362,x96361),x96363),x96364)),f866(f866(f9(x96362,x96361),x96363),x96365)),f866(f866(f9(x96362,x96361),x96363),f866(f866(f117(f937(x96362,a925)),x96364),x96365)))
% 157.76/157.53 [9637]~P72(x96371)+~E(f866(x96373,f397(x96373,x96375,x96374,x96372,x96371)),f2(x96371))+~P107(f866(f66(x96372),x96374))+~P107(f866(f66(x96372),x96375))+E(f866(f866(f86(x96371),f866(f866(f6(x96372,x96371),x96373),x96374)),f866(f866(f6(x96372,x96371),x96373),x96375)),f866(f866(f6(x96372,x96371),x96373),f866(f866(f117(f937(x96372,a925)),x96374),x96375)))
% 157.76/157.53 [9638]~P72(x96381)+~E(f866(x96383,f400(x96383,x96385,x96384,x96382,x96381)),f2(x96381))+~P107(f866(f66(x96382),x96384))+~P107(f866(f66(x96382),x96385))+E(f866(f866(f86(x96381),f866(f866(f6(x96382,x96381),x96383),x96384)),f866(f866(f6(x96382,x96381),x96383),x96385)),f866(f866(f6(x96382,x96381),x96383),f866(f866(f117(f937(x96382,a925)),x96384),x96385)))
% 157.76/157.53 [9848]~P71(x98481)+~E(f866(x98483,f920(x98483,x98485,x98484,x98482,x98481)),f84(x98481))+~P107(f866(f66(x98482),x98484))+~P107(f866(f66(x98482),x98485))+E(f866(f866(f87(x98481),f866(f866(f866(f70(x98481,x98482,f87(x98481)),x98483),f84(x98481)),x98484)),f866(f866(f866(f70(x98481,x98482,f87(x98481)),x98483),f84(x98481)),x98485)),f866(f866(f866(f70(x98481,x98482,f87(x98481)),x98483),f84(x98481)),f866(f866(f117(f937(x98482,a925)),x98484),x98485)))
% 157.76/157.53 [9960]~P71(x99602)+E(f866(f866(f9(x99601,x99602),x99603),x99604),f866(f866(f9(x99601,x99602),x99603),x99605))+~P107(f866(f66(x99601),x99605))+~P107(f866(f866(f243(f937(x99601,a925)),x99604),x99605))+P107(f866(f866(f336(x99601),f352(x99603,x99604,x99605,x99601,x99602)),f866(f866(f23(f937(x99601,a925)),x99605),x99604)))
% 157.76/157.53 [9961]~P71(x99612)+E(f866(f866(f9(x99611,x99612),x99613),x99614),f866(f866(f9(x99611,x99612),x99613),x99615))+~P107(f866(f66(x99611),x99615))+~P107(f866(f866(f243(f937(x99611,a925)),x99614),x99615))+P107(f866(f866(f336(x99611),f354(x99613,x99614,x99615,x99611,x99612)),f866(f866(f23(f937(x99611,a925)),x99615),x99614)))
% 157.76/157.53 [9962]~P72(x99622)+E(f866(f866(f6(x99621,x99622),x99623),x99624),f866(f866(f6(x99621,x99622),x99623),x99625))+~P107(f866(f66(x99621),x99625))+~P107(f866(f866(f243(f937(x99621,a925)),x99624),x99625))+P107(f866(f866(f336(x99621),f474(x99623,x99624,x99625,x99621,x99622)),f866(f866(f23(f937(x99621,a925)),x99625),x99624)))
% 157.76/157.53 [9963]~P72(x99632)+E(f866(f866(f6(x99631,x99632),x99633),x99634),f866(f866(f6(x99631,x99632),x99633),x99635))+~P107(f866(f66(x99631),x99635))+~P107(f866(f866(f243(f937(x99631,a925)),x99634),x99635))+P107(f866(f866(f336(x99631),f475(x99633,x99634,x99635,x99631,x99632)),f866(f866(f23(f937(x99631,a925)),x99635),x99634)))
% 157.76/157.53 [9981]~P71(x99811)+~P107(f866(f66(x99812),x99814))+~P107(f866(f66(x99812),x99815))+E(f866(f866(f87(x99811),f866(f866(f9(x99812,x99811),x99813),x99814)),f866(f866(f9(x99812,x99811),x99813),x99815)),f866(f866(f9(x99812,x99811),x99813),f866(f866(f117(f937(x99812,a925)),x99814),x99815)))+P107(f866(f866(f336(x99812),f919(x99813,x99815,x99814,x99812,x99811)),f866(f866(f108(f937(x99812,a925)),x99814),x99815)))
% 157.76/157.53 [9982]~P71(x99821)+~P107(f866(f66(x99822),x99824))+~P107(f866(f66(x99822),x99825))+E(f866(f866(f87(x99821),f866(f866(f9(x99822,x99821),x99823),x99824)),f866(f866(f9(x99822,x99821),x99823),x99825)),f866(f866(f9(x99822,x99821),x99823),f866(f866(f117(f937(x99822,a925)),x99824),x99825)))+P107(f866(f866(f336(x99822),f921(x99823,x99825,x99824,x99822,x99821)),f866(f866(f108(f937(x99822,a925)),x99824),x99825)))
% 157.76/157.53 [9983]~P72(x99831)+~P107(f866(f66(x99832),x99834))+~P107(f866(f66(x99832),x99835))+E(f866(f866(f86(x99831),f866(f866(f6(x99832,x99831),x99833),x99834)),f866(f866(f6(x99832,x99831),x99833),x99835)),f866(f866(f6(x99832,x99831),x99833),f866(f866(f117(f937(x99832,a925)),x99834),x99835)))+P107(f866(f866(f336(x99832),f397(x99833,x99835,x99834,x99832,x99831)),f866(f866(f108(f937(x99832,a925)),x99834),x99835)))
% 157.76/157.53 [9984]~P72(x99841)+~P107(f866(f66(x99842),x99844))+~P107(f866(f66(x99842),x99845))+E(f866(f866(f86(x99841),f866(f866(f6(x99842,x99841),x99843),x99844)),f866(f866(f6(x99842,x99841),x99843),x99845)),f866(f866(f6(x99842,x99841),x99843),f866(f866(f117(f937(x99842,a925)),x99844),x99845)))+P107(f866(f866(f336(x99842),f400(x99843,x99845,x99844,x99842,x99841)),f866(f866(f108(f937(x99842,a925)),x99844),x99845)))
% 157.76/157.53 [9990]~P86(x99905)+~P107(f866(f66(x99901),x99904))+P107(f866(f866(f243(x99905),f866(f866(f6(x99901,x99905),x99902),x99903)),f866(f866(f6(x99901,x99905),x99902),x99904)))+~P107(f866(f866(f243(f937(x99901,a925)),x99903),x99904))+P107(f866(f866(f336(x99901),f398(x99902,x99903,x99904,x99901,x99905)),f866(f866(f23(f937(x99901,a925)),x99904),x99903)))
% 157.76/157.53 [10035]~P71(x100351)+~P107(f866(f66(x100352),x100354))+~P107(f866(f66(x100352),x100355))+E(f866(f866(f87(x100351),f866(f866(f866(f70(x100351,x100352,f87(x100351)),x100353),f84(x100351)),x100354)),f866(f866(f866(f70(x100351,x100352,f87(x100351)),x100353),f84(x100351)),x100355)),f866(f866(f866(f70(x100351,x100352,f87(x100351)),x100353),f84(x100351)),f866(f866(f117(f937(x100352,a925)),x100354),x100355)))+P107(f866(f866(f336(x100352),f920(x100353,x100355,x100354,x100352,x100351)),f866(f866(f108(f937(x100352,a925)),x100354),x100355)))
% 157.76/157.53 [8994]~P18(x89941,x89944,x89945)+~P107(f866(f66(x89941),x89942))+E(f866(f866(f23(f937(x89941,a925)),x89942),f866(f866(f316(x89941),x89943),f195(f937(x89941,a925)))),f195(f937(x89941,a925)))+~P107(f866(f866(f336(x89941),x89943),x89942))+E(f866(f866(x89944,x89943),f866(x89945,f866(f866(f23(f937(x89941,a925)),x89942),f866(f866(f316(x89941),x89943),f195(f937(x89941,a925)))))),f866(x89945,x89942))
% 157.76/157.53 [9072]~P18(x90721,x90724,x90725)+~P107(f866(f66(x90721),x90723))+~P107(f866(f66(x90721),x90722))+E(f866(f866(f108(f937(x90721,a925)),x90722),x90723),f195(f937(x90721,a925)))+E(f866(f866(x90724,f866(x90725,f866(f866(f117(f937(x90721,a925)),x90722),x90723))),f866(x90725,f866(f866(f108(f937(x90721,a925)),x90722),x90723))),f866(f866(x90724,f866(x90725,x90722)),f866(x90725,x90723)))
% 157.76/157.53 [9640]~P107(f866(f866(f243(a1),x96404),f2(a1)))+~P107(f866(f866(f244(a1),x96403),x96405))+P107(f866(f866(f243(a1),x96401),x96402))+~P107(f866(f866(f244(a1),x96403),x96404))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),f866(f866(f87(a1),x96403),x96402)),x96405)),f866(f866(f86(a1),f866(f866(f87(a1),x96403),x96401)),x96404)))
% 157.76/157.53 [9642]~P107(f866(f866(f243(a1),f2(a1)),x96425))+P107(f866(f866(f243(a1),x96421),x96422))+~P107(f866(f866(f244(a1),x96423),x96424))+~P107(f866(f866(f244(a1),x96425),x96424))+~P107(f866(f866(f243(a1),f866(f866(f86(a1),f866(f866(f87(a1),x96424),x96421)),x96425)),f866(f866(f86(a1),f866(f866(f87(a1),x96424),x96422)),x96423)))
% 157.76/157.53 [9757]~P66(x97575)+E(f866(x97571,f353(x97571,x97572,x97573,x97574,x97575)),f2(x97575))+~P107(f866(f66(x97574),x97573))+~P107(f866(f66(x97574),x97572))+E(f866(f866(f297(x97575),f866(f866(f87(x97575),f866(f866(f9(x97574,x97575),x97571),x97573)),f866(f866(f9(x97574,x97575),x97571),x97572))),f866(f866(f9(x97574,x97575),x97571),f866(f866(f108(f937(x97574,a925)),x97573),x97572))),f866(f866(f9(x97574,x97575),x97571),f866(f866(f117(f937(x97574,a925)),x97573),x97572)))
% 157.76/157.53 [10027]~P66(x100271)+~P107(f866(f66(x100272),x100274))+~P107(f866(f66(x100272),x100275))+E(f866(f866(f297(x100271),f866(f866(f87(x100271),f866(f866(f9(x100272,x100271),x100273),x100274)),f866(f866(f9(x100272,x100271),x100273),x100275))),f866(f866(f9(x100272,x100271),x100273),f866(f866(f108(f937(x100272,a925)),x100274),x100275))),f866(f866(f9(x100272,x100271),x100273),f866(f866(f117(f937(x100272,a925)),x100274),x100275)))+P107(f866(f866(f336(x100272),f353(x100273,x100275,x100274,x100272,x100271)),f866(f866(f108(f937(x100272,a925)),x100274),x100275)))
% 157.76/157.53 [9352]E(f866(f866(f141(x93521),x93522),x93523),f866(f866(f141(x93521),x93524),x93525))+~E(f866(f866(f182(x93521),f866(f196(f931(x93521)),x93524)),x93522),x93524)+~E(f866(f866(f182(x93521),f866(f196(f931(x93521)),x93522)),x93524),x93522)+~E(x93525,f866(f866(f141(x93521),f866(f866(f145(x93521),f866(f196(f931(x93521)),x93524)),x93522)),x93523))+~E(f866(f866(f141(x93521),f866(f866(f145(x93521),f866(f196(f931(x93521)),x93522)),x93524)),x93525),x93523)
% 157.76/157.53 [9755]~P110(x97552)+E(f866(f866(f155(x97551,x97552,x97553),x97554),f177(x97551,x97554,x97555)),x97555)+~P13(x97552,f866(f866(f161(x97551,x97552),x97553),x97555))+~P107(f866(f866(f336(x97551),x97554),f866(f179(x97551),x97555)))+~E(f866(f148(x97551),f866(f143(x97551,f866(f866(f8(x97552,a925,x97551),f866(a332,f866(x97553,x97554))),x97553)),x97555)),x97554)
% 157.76/157.53 [10091]~P69(x100911)+~P107(f866(f71(x100911,x100911,f87(x100911),x100912,x100913),x100915))+~P107(f866(f866(f336(x100911),x100914),x100913))+P107(f866(f866(f336(x100911),x100912),x100913))+P107(f866(f71(x100911,x100911,f87(x100911),x100914,f866(f866(f316(x100911),x100912),f866(f866(f23(f937(x100911,a925)),x100913),f866(f866(f316(x100911),x100914),f195(f937(x100911,a925)))))),x100915))
% 157.76/157.53 [7505]E(x75051,x75052)+~P25(x75054,x75055,x75053,x75056)+~E(f866(x75053,x75051),f866(x75053,x75052))+~P107(f866(f866(f336(x75054),x75052),x75056))+~P107(f866(f866(f336(x75054),x75051),x75056))
% 157.76/157.53 [6767]~P144(x67674)+E(x67671,x67672)+~E(x67675,x67676)+E(x67673,f2(x67674))+~E(f866(f866(f86(x67674),x67675),f866(f866(f87(x67674),x67673),x67671)),f866(f866(f86(x67674),x67676),f866(f866(f87(x67674),x67673),x67672)))
% 157.76/157.53 [7787]~P110(x77871)+~P5(x77871)+~P107(f866(f866(f244(x77871),x77872),f866(x77875,x77876)))+~P107(f866(f866(f336(x77873),x77876),x77874))+P107(f866(f866(f244(x77871),x77872),f866(f866(f44(x77873,x77871),x77874),x77875)))
% 157.76/157.53 [10087]~P25(x100872,x100871,x100873,x100874)+~P25(x100871,x100872,x100876,x100875)+P26(x100871,x100872,f833(x100873,x100874,x100875,x100876,x100872,x100871),x100875,x100874)+~P107(f866(f866(f243(f937(x100872,a925)),f866(f317(x100871,x100872,x100876),x100875)),x100874))+~P107(f866(f866(f243(f937(x100871,a925)),f866(f317(x100872,x100871,x100873),x100874)),x100875))
% 157.76/157.53 [8455]~P110(x84551)+~P5(x84551)+~P107(f866(f866(f244(x84551),f866(x84554,x84556)),x84555))+~P107(f866(f866(f336(x84552),x84556),x84553))+P107(f866(f866(f244(x84551),f866(f866(f45(x84552,x84551),x84553),x84554)),x84555))
% 157.76/157.53 [8707]~P19(x87072,x87075,x87076,x87071)+~P107(f866(f66(x87072),x87074))+~P107(f866(f66(x87072),x87073))+~E(f866(f866(f108(f937(x87072,a925)),x87073),x87074),f195(f937(x87072,a925)))+E(f866(x87071,f866(f866(f117(f937(x87072,a925)),x87073),x87074)),f866(f78(x87075,x87075,x87075,f866(x87071,x87073)),f866(x87071,x87074)))
% 157.76/157.53 [10287]~P71(x102871)+~E(f823(x102874,x102875,x102873,x102876,x102872,x102871),f824(x102874,x102875,x102873,x102876,x102872,x102871))+~P107(f866(f66(x102872),x102876))+E(f866(f866(f866(f70(x102871,x102872,f87(x102871)),f866(f866(f8(f937(x102873,a925),x102871,x102872),f866(f866(f70(x102871,x102873,f87(x102871)),x102874),f84(x102871))),x102875)),f84(x102871)),x102876),f866(f866(f866(f70(x102871,x102873,f87(x102871)),x102874),f84(x102871)),f866(f866(f44(x102872,f937(x102873,a925)),x102876),x102875)))+P107(f866(f866(f336(x102872),f821(x102874,x102875,x102873,x102876,x102872,x102871)),x102876))
% 157.76/157.53 [10317]~P71(x103171)+~E(f823(x103174,x103175,x103173,x103176,x103172,x103171),f824(x103174,x103175,x103173,x103176,x103172,x103171))+~P107(f866(f66(x103172),x103176))+E(f866(f866(f866(f70(x103171,x103172,f87(x103171)),f866(f866(f8(f937(x103173,a925),x103171,x103172),f866(f866(f70(x103171,x103173,f87(x103171)),x103174),f84(x103171))),x103175)),f84(x103171)),x103176),f866(f866(f866(f70(x103171,x103173,f87(x103171)),x103174),f84(x103171)),f866(f866(f44(x103172,f937(x103173,a925)),x103176),x103175)))+~P107(f866(f66(x103173),f866(x103175,f821(x103174,x103175,x103173,x103176,x103172,x103171))))
% 157.76/157.53 [10320]~P71(x103201)+~P107(f866(f66(x103202),x103206))+E(f866(f866(f866(f70(x103201,x103202,f87(x103201)),f866(f866(f8(f937(x103203,a925),x103201,x103202),f866(f866(f70(x103201,x103203,f87(x103201)),x103204),f84(x103201))),x103205)),f84(x103201)),x103206),f866(f866(f866(f70(x103201,x103203,f87(x103201)),x103204),f84(x103201)),f866(f866(f44(x103202,f937(x103203,a925)),x103206),x103205)))+P107(f866(f866(f336(x103202),f821(x103204,x103205,x103203,x103206,x103202,x103201)),x103206))+P107(f866(f866(f336(x103202),f824(x103204,x103205,x103203,x103206,x103202,x103201)),x103206))
% 157.76/157.53 [10321]~P71(x103211)+~P107(f866(f66(x103212),x103216))+E(f866(f866(f866(f70(x103211,x103212,f87(x103211)),f866(f866(f8(f937(x103213,a925),x103211,x103212),f866(f866(f70(x103211,x103213,f87(x103211)),x103214),f84(x103211))),x103215)),f84(x103211)),x103216),f866(f866(f866(f70(x103211,x103213,f87(x103211)),x103214),f84(x103211)),f866(f866(f44(x103212,f937(x103213,a925)),x103216),x103215)))+P107(f866(f866(f336(x103212),f821(x103214,x103215,x103213,x103216,x103212,x103211)),x103216))+P107(f866(f866(f336(x103212),f823(x103214,x103215,x103213,x103216,x103212,x103211)),x103216))
% 157.76/157.53 [10340]~P71(x103401)+~P107(f866(f66(x103402),x103406))+E(f866(f866(f866(f70(x103401,x103402,f87(x103401)),f866(f866(f8(f937(x103403,a925),x103401,x103402),f866(f866(f70(x103401,x103403,f87(x103401)),x103404),f84(x103401))),x103405)),f84(x103401)),x103406),f866(f866(f866(f70(x103401,x103403,f87(x103401)),x103404),f84(x103401)),f866(f866(f44(x103402,f937(x103403,a925)),x103406),x103405)))+P107(f866(f866(f336(x103402),f824(x103404,x103405,x103403,x103406,x103402,x103401)),x103406))+~P107(f866(f66(x103403),f866(x103405,f821(x103404,x103405,x103403,x103406,x103402,x103401))))
% 157.76/157.53 [10341]~P71(x103411)+~P107(f866(f66(x103412),x103416))+E(f866(f866(f866(f70(x103411,x103412,f87(x103411)),f866(f866(f8(f937(x103413,a925),x103411,x103412),f866(f866(f70(x103411,x103413,f87(x103411)),x103414),f84(x103411))),x103415)),f84(x103411)),x103416),f866(f866(f866(f70(x103411,x103413,f87(x103411)),x103414),f84(x103411)),f866(f866(f44(x103412,f937(x103413,a925)),x103416),x103415)))+P107(f866(f866(f336(x103412),f823(x103414,x103415,x103413,x103416,x103412,x103411)),x103416))+~P107(f866(f66(x103413),f866(x103415,f821(x103414,x103415,x103413,x103416,x103412,x103411))))
% 157.76/157.53 [10352]~P71(x103521)+~E(f866(f866(f108(f937(x103523,a925)),f866(x103525,f824(x103524,x103525,x103523,x103526,x103522,x103521))),f866(x103525,f823(x103524,x103525,x103523,x103526,x103522,x103521))),f195(f937(x103523,a925)))+~P107(f866(f66(x103522),x103526))+E(f866(f866(f866(f70(x103521,x103522,f87(x103521)),f866(f866(f8(f937(x103523,a925),x103521,x103522),f866(f866(f70(x103521,x103523,f87(x103521)),x103524),f84(x103521))),x103525)),f84(x103521)),x103526),f866(f866(f866(f70(x103521,x103523,f87(x103521)),x103524),f84(x103521)),f866(f866(f44(x103522,f937(x103523,a925)),x103526),x103525)))+P107(f866(f866(f336(x103522),f821(x103524,x103525,x103523,x103526,x103522,x103521)),x103526))
% 157.76/157.53 [10363]~P71(x103631)+~E(f866(f866(f108(f937(x103633,a925)),f866(x103635,f824(x103634,x103635,x103633,x103636,x103632,x103631))),f866(x103635,f823(x103634,x103635,x103633,x103636,x103632,x103631))),f195(f937(x103633,a925)))+~P107(f866(f66(x103632),x103636))+E(f866(f866(f866(f70(x103631,x103632,f87(x103631)),f866(f866(f8(f937(x103633,a925),x103631,x103632),f866(f866(f70(x103631,x103633,f87(x103631)),x103634),f84(x103631))),x103635)),f84(x103631)),x103636),f866(f866(f866(f70(x103631,x103633,f87(x103631)),x103634),f84(x103631)),f866(f866(f44(x103632,f937(x103633,a925)),x103636),x103635)))+~P107(f866(f66(x103633),f866(x103635,f821(x103634,x103635,x103633,x103636,x103632,x103631))))
% 157.76/157.53 [8736]~P119(x87361)+~P124(x87361)+~P57(x87361,x87362,x87365)+~P57(x87361,x87362,f866(f866(f86(x87361),x87363),x87366))+P57(x87361,x87362,f866(f866(f86(x87361),f866(f866(f23(x87361),x87363),f866(f866(f87(x87361),x87364),x87365))),x87366))
% 157.76/157.53 [9102]~P119(x91021)+~P124(x91021)+~P57(x91021,x91022,x91025)+P57(x91021,x91022,f866(f866(f86(x91021),x91023),x91024))+~P57(x91021,x91022,f866(f866(f86(x91021),f866(f866(f23(x91021),x91023),f866(f866(f87(x91021),x91026),x91025))),x91024))
% 157.76/157.53 [9042]E(x90421,x90422)+~P58(x90424,x90425,x90426,x90423,x90427)+~E(f866(x90423,x90421),f866(x90423,x90422))+~P107(f866(f866(f336(x90425),x90422),x90427))+~P107(f866(f866(f336(x90425),x90421),x90427))
% 157.76/157.53 [10330]~P107(f866(x103302,x103304))+~E(x103305,f866(f143(x103301,x103302),x103307))+E(f866(f143(x103301,x103302),x103303),f866(f866(f158(x103301),x103304),x103305))+~E(x103303,f866(f866(f141(x103301),x103306),f866(f866(f158(x103301),x103304),x103307)))+P107(f866(x103302,f756(x103305,x103304,x103303,x103302,x103301,x103306,x103307)))
% 157.76/157.53 [10331]~P107(f866(x103314,x103312))+~E(x103313,f866(f143(x103311,x103314),x103317))+E(f866(f866(f158(x103311),x103312),x103313),f866(f143(x103311,x103314),x103315))+~E(x103315,f866(f866(f141(x103311),x103316),f866(f866(f158(x103311),x103312),x103317)))+P107(f866(x103314,f755(x103315,x103314,x103313,x103312,x103311,x103316,x103317)))
% 157.76/157.53 [10375]~P107(f866(x103752,x103754))+~E(x103755,f866(f143(x103751,x103752),x103757))+E(f866(f143(x103751,x103752),x103753),f866(f866(f158(x103751),x103754),x103755))+~E(x103753,f866(f866(f141(x103751),x103756),f866(f866(f158(x103751),x103754),x103757)))+P107(f866(f866(f336(x103751),f756(x103755,x103754,x103753,x103752,x103751,x103756,x103757)),f866(f179(x103751),x103756)))
% 157.76/157.53 [10376]~P107(f866(x103764,x103762))+~E(x103763,f866(f143(x103761,x103764),x103767))+E(f866(f866(f158(x103761),x103762),x103763),f866(f143(x103761,x103764),x103765))+~E(x103765,f866(f866(f141(x103761),x103766),f866(f866(f158(x103761),x103762),x103767)))+P107(f866(f866(f336(x103761),f755(x103765,x103764,x103763,x103762,x103761,x103766,x103767)),f866(f179(x103761),x103766)))
% 157.76/157.53 [10380]~P8(x103801,x103807,x103806)+~P11(x103801,f937(x103805,a925),x103806,x103804)+P107(f866(f866(f336(x103801),f509(x103802,x103803,x103804,x103805,x103806,x103807,x103801)),x103807))+~P107(f866(f866(f336(f937(x103801,a925)),x103803),f866(f866(f65(x103801),x103807),x103806)))+P107(f866(f866(f336(f937(x103805,a925)),f866(f866(f44(x103801,f937(x103805,a925)),x103803),x103804)),x103802))
% 157.76/157.53 [10439]~P8(x104392,x104396,x104397)+~P11(x104392,f937(x104391,a925),x104397,x104394)+~P107(f866(f866(f336(f937(x104392,a925)),x104393),f866(f866(f65(x104392),x104396),x104397)))+~P107(f866(f866(f336(f937(x104391,a925)),f866(x104394,f509(x104395,x104393,x104394,x104391,x104397,x104396,x104392))),x104395))+P107(f866(f866(f336(f937(x104391,a925)),f866(f866(f44(x104392,f937(x104391,a925)),x104393),x104394)),x104395))
% 157.76/157.53 [8628]~P71(x86282)+~P25(x86281,x86285,x86288,x86284)+~E(x86283,f866(f78(x86285,x86282,x86281,x86286),x86288))+~E(x86287,f866(f317(x86281,x86285,x86288),x86284))+E(f866(f866(f9(x86281,x86282),x86283),x86284),f866(f866(f9(x86285,x86282),x86286),x86287))
% 157.76/157.53 [10443]~P71(x104432)+~P25(x104435,x104431,x104438,x104437)+~E(f866(x104436,f349(x104433,x104436,x104434,x104437,x104438,x104431,x104435,x104432)),f866(f866(f78(x104431,x104432,x104435,x104433),x104438),f349(x104433,x104436,x104434,x104437,x104438,x104431,x104435,x104432)))+~E(x104434,f866(f317(x104435,x104431,x104438),x104437))+E(f866(f866(f9(x104431,x104432),x104433),x104434),f866(f866(f9(x104435,x104432),x104436),x104437))
% 157.76/157.53 [10446]~P71(x104462)+~P25(x104461,x104465,x104468,x104464)+~E(x104467,f866(f317(x104461,x104465,x104468),x104464))+E(f866(f866(f9(x104461,x104462),x104463),x104464),f866(f866(f9(x104465,x104462),x104466),x104467))+P107(f866(f866(f336(x104461),f349(x104466,x104463,x104467,x104464,x104468,x104465,x104461,x104462)),x104464))
% 157.76/157.53 [10447]~P72(x104472)+~P25(x104471,x104475,x104478,x104474)+~E(x104477,f866(f317(x104471,x104475,x104478),x104474))+E(f866(f866(f6(x104471,x104472),x104473),x104474),f866(f866(f6(x104475,x104472),x104476),x104477))+P107(f866(f866(f336(x104471),f580(x104476,x104473,x104477,x104474,x104478,x104475,x104471,x104472)),x104474))
% 157.76/157.53 [10452]~P72(x104522)+~P25(x104525,x104521,x104528,x104527)+~E(x104524,f866(f317(x104525,x104521,x104528),x104527))+~E(f866(x104526,f580(x104523,x104526,x104524,x104527,x104528,x104521,x104525,x104522)),f866(x104523,f866(x104528,f580(x104523,x104526,x104524,x104527,x104528,x104521,x104525,x104522))))+E(f866(f866(f6(x104521,x104522),x104523),x104524),f866(f866(f6(x104525,x104522),x104526),x104527))
% 157.76/157.53 [9922]~P23(x99226,x99222,x99225,x99227,x99228,x99221)+~P107(f866(f66(x99222),x99224))+~P107(f866(f66(x99222),x99223))+~E(f866(f866(f108(f937(x99222,a925)),x99223),x99224),f195(f937(x99222,a925)))+E(f866(x99221,f866(f866(f117(f937(x99222,a925)),x99223),x99224)),f866(f866(x99225,f866(x99221,x99223)),f866(x99221,x99224)))
% 157.76/157.53 [10314]~P23(x103148,x103142,x103145,x103147,x103146,x103141)+~E(f866(x103146,f362(x103144,x103143,x103141,x103146,x103147,x103145,x103142)),x103147)+~P107(f866(f66(x103142),x103143))+~P107(f866(f66(x103142),x103144))+E(f866(x103141,f866(f866(f117(f937(x103142,a925)),x103143),x103144)),f866(f866(x103145,f866(x103141,x103143)),f866(x103141,x103144)))
% 157.76/157.53 [10387]~P23(x103878,x103872,x103875,x103877,x103876,x103871)+~P107(f866(f66(x103872),x103873))+~P107(f866(f66(x103872),x103874))+E(f866(x103871,f866(f866(f117(f937(x103872,a925)),x103873),x103874)),f866(f866(x103875,f866(x103871,x103873)),f866(x103871,x103874)))+P107(f866(f866(f336(x103872),f362(x103874,x103873,x103871,x103876,x103877,x103875,x103872)),f866(f866(f108(f937(x103872,a925)),x103873),x103874)))
% 157.76/157.53 [10078]~P8(x100784,x100788,x100785)+~P8(x100781,x100789,x100783)+~P12(x100781,x100784,f937(x100782,a925),x100783,x100785,x100787)+P11(x100781,f937(x100782,a925),x100783,f866(f866(f8(f937(x100784,f937(x100782,a925)),f937(x100782,a925),x100781),f866(f44(x100784,f937(x100782,a925)),f866(f293(x100784,x100784,x100785),f866(f866(f316(x100784),x100786),f195(f937(x100784,a925)))))),x100787))+~P107(f866(f866(f336(x100784),x100786),x100788))
% 157.76/157.53 [5667]~P110(x56673)+~P13(x56673,x56671)+E(x56671,f733(x56672,x56673))+~E(f866(f179(x56673),x56671),x56672)+~P107(f866(f66(x56673),x56672))+~P107(f866(f144(x56673),x56671))
% 157.76/157.53 [7496]P15(x74961,x74962)+~E(f866(x74962,f817(x74962)),f866(x74962,f818(x74962)))+~P107(f866(f866(x74962,f817(x74962)),f817(x74962)))+~P107(f866(f866(x74962,f817(x74962)),f818(x74962)))+~P107(f866(f866(x74962,f818(x74962)),f818(x74962)))+~P107(f866(f866(x74962,x74963),x74963))
% 157.76/157.53 [5291]~P129(x52912)+~P135(x52912)+~P146(x52912)+~P116(x52912)+E(x52911,f2(x52912))+~E(f866(f866(f252(x52912),x52911),x52913),f2(x52912))
% 157.76/157.53 [5292]~P129(x52922)+~P135(x52922)+~P146(x52922)+~P116(x52922)+~E(x52921,f2(a930))+~E(f866(f866(f252(x52922),x52923),x52921),f2(x52922))
% 157.76/157.53 [6749]~P86(x67491)+~E(x67493,f2(x67491))+~E(x67492,f2(x67491))+E(f866(f866(f86(x67491),x67492),x67493),f2(x67491))+~P107(f866(f866(f243(x67491),f2(x67491)),x67493))+~P107(f866(f866(f243(x67491),f2(x67491)),x67492))
% 157.76/157.53 [9112]~E(f866(f259(a930,a930),x91123),f2(a930))+~E(x91121,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x91123)),x91122)),f866(f264(a930,a930),x91123)))+P107(f866(f53(x91121,x91122),x91123))+~P107(f866(f866(f243(a930),f866(f264(a930,a930),x91123)),f2(a930)))+P107(f866(f866(f244(a930),f2(a930)),x91122))+~P107(f866(f866(f244(a930),x91122),f866(f264(a930,a930),x91123)))
% 157.76/157.53 [9120]E(x91201,f2(a930))+~E(x91202,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x91203)),x91201)),f866(f264(a930,a930),x91203)))+P107(f866(f53(x91202,x91201),x91203))+~P107(f866(f866(f244(a930),f2(a930)),x91201))+~P107(f866(f866(f243(a930),f2(a930)),f866(f264(a930,a930),x91203)))+~P107(f866(f866(f244(a930),f866(f264(a930,a930),x91203)),x91201))
% 157.76/157.53 [9138]~E(f866(f259(a930,a930),x91383),f2(a930))+~E(x91381,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x91383)),x91382)),f866(f264(a930,a930),x91383)))+P107(f866(f53(x91381,x91382),x91383))+~P107(f866(f866(f244(a930),f2(a930)),x91382))+~P107(f866(f866(f243(a930),f2(a930)),f866(f264(a930,a930),x91383)))+~P107(f866(f866(f244(a930),f866(f264(a930,a930),x91383)),x91382))
% 157.76/157.53 [7128]~P83(x71282)+E(x71281,f195(f937(x71282,a925)))+E(x71283,f195(f937(x71282,a925)))+~P107(f866(f66(x71282),x71281))+~P107(f866(f66(x71282),x71283))+E(f13(x71282,f866(f866(f117(f937(x71282,a925)),x71283),x71281)),f866(f866(f117(x71282),f13(x71282,x71283)),f13(x71282,x71281)))
% 157.76/157.53 [7129]~P83(x71292)+E(x71291,f195(f937(x71292,a925)))+E(x71293,f195(f937(x71292,a925)))+~P107(f866(f66(x71292),x71291))+~P107(f866(f66(x71292),x71293))+E(f10(x71292,f866(f866(f117(f937(x71292,a925)),x71293),x71291)),f866(f866(f108(x71292),f10(x71292,x71293)),f10(x71292,x71291)))
% 157.76/157.53 [7130]~P110(x71302)+E(x71301,f195(f937(x71302,a925)))+E(x71303,f195(f937(x71302,a925)))+~P107(f866(f66(x71302),x71301))+~P107(f866(f66(x71302),x71303))+E(f14(x71302,f866(f866(f117(f937(x71302,a925)),x71303),x71301)),f866(f866(f242(x71302),f14(x71302,x71303)),f14(x71302,x71301)))
% 157.76/157.53 [7131]~P110(x71312)+E(x71311,f195(f937(x71312,a925)))+E(x71313,f195(f937(x71312,a925)))+~P107(f866(f66(x71312),x71311))+~P107(f866(f66(x71312),x71313))+E(f15(x71312,f866(f866(f117(f937(x71312,a925)),x71313),x71311)),f866(f866(f241(x71312),f15(x71312,x71313)),f15(x71312,x71311)))
% 157.76/157.53 [7763]~P99(x77632)+E(x77631,f195(f937(x77632,a925)))+E(x77633,f195(f937(x77632,a925)))+~P107(f866(f66(x77632),x77631))+~P107(f866(f66(x77632),x77633))+E(f866(f866(f87(x77632),f866(f68(x77632,f87(x77632)),x77633)),f866(f68(x77632,f87(x77632)),x77631)),f866(f68(x77632,f87(x77632)),f866(f866(f117(f937(x77632,a925)),x77633),x77631)))
% 157.76/157.53 [7920]~P110(x79202)+E(x79201,f195(f937(x79202,a925)))+E(x79203,f195(f937(x79202,a925)))+~P107(f866(f66(x79202),x79201))+~P107(f866(f66(x79202),x79203))+E(f866(f866(f241(x79202),f11(x79202,f241(x79202),x79203)),f11(x79202,f241(x79202),x79201)),f11(x79202,f241(x79202),f866(f866(f117(f937(x79202,a925)),x79203),x79201)))
% 157.76/157.53 [7921]~P110(x79212)+E(x79211,f195(f937(x79212,a925)))+E(x79213,f195(f937(x79212,a925)))+~P107(f866(f66(x79212),x79211))+~P107(f866(f66(x79212),x79213))+E(f866(f866(f242(x79212),f12(x79212,f242(x79212),x79213)),f12(x79212,f242(x79212),x79211)),f12(x79212,f242(x79212),f866(f866(f117(f937(x79212,a925)),x79213),x79211)))
% 157.76/157.53 [8943]~P107(f866(x89431,x89433))+P107(f866(x89431,f462(x89431,x89432)))+P107(f866(x89431,f454(x89431,x89432)))+~P107(f866(f866(f244(a1),f2(a1)),x89432))+~P107(f866(f866(f336(a1),x89433),f310(a1,f84(a1),x89432)))+P107(f866(x89431,f866(f866(f23(a1),f454(x89431,x89432)),f866(f866(f87(a1),f461(x89431,x89432)),x89432))))
% 157.76/157.53 [9250]~P107(f866(x92501,x92503))+~P107(f866(x92501,f454(x92501,x92502)))+P107(f866(x92501,f462(x92501,x92502)))+~P107(f866(f866(f244(a1),f2(a1)),x92502))+~P107(f866(f866(f336(a1),x92503),f310(a1,f84(a1),x92502)))+~P107(f866(x92501,f866(f866(f23(a1),f454(x92501,x92502)),f866(f866(f87(a1),f461(x92501,x92502)),x92502))))
% 157.76/157.53 [10479]~P101(x104792)+E(x104791,f195(f937(x104792,a925)))+E(x104793,f195(f937(x104792,a925)))+~P107(f866(f66(x104792),x104791))+~P107(f866(f66(x104792),x104793))+E(f10(x104792,f866(f270(x104792),f866(f866(f8(f937(x104792,a925),a925,x104792),f93(x104792)),f866(f866(f8(f937(x104792,f937(x104792,a925)),f937(x104792,a925),x104792),f866(f8(f937(x104792,a925),a925,x104792),f93(x104792))),f866(f866(f7(x104792,f937(x104792,f937(x104792,a925)),f937(x104792,f937(x104792,a925))),f866(f866(f8(f937(x104792,f937(f937(x104792,a925),f937(x104792,a925))),f937(f937(x104792,f937(x104792,a925)),f937(x104792,f937(x104792,a925))),x104792),f18(x104792,f937(x104792,a925),f937(x104792,a925))),f866(f866(f8(f937(x104792,f937(x104792,f937(a925,a925))),f937(x104792,f937(f937(x104792,a925),f937(x104792,a925))),x104792),f866(f8(f937(x104792,f937(a925,a925)),f937(f937(x104792,a925),f937(x104792,a925)),x104792),f18(x104792,a925,a925))),f866(f866(f8(f937(x104792,f937(x104792,a925)),f937(x104792,f937(x104792,f937(a925,a925))),x104792),f866(f8(f937(x104792,a925),f937(x104792,f937(a925,a925)),x104792),f866(f8(a925,f937(a925,a925),x104792),a333))),f866(f866(f7(x104792,f937(x104792,f937(x104792,x104792)),f937(x104792,f937(x104792,a925))),f866(f866(f8(f937(f937(x104792,x104792),f937(x104792,a925)),f937(f937(x104792,f937(x104792,x104792)),f937(x104792,f937(x104792,a925))),x104792),f8(f937(x104792,x104792),f937(x104792,a925),x104792)),f866(f866(f8(f937(x104792,a925),f937(f937(x104792,x104792),f937(x104792,a925)),x104792),f8(x104792,a925,x104792)),a332))),f117(x104792)))))),f866(f866(f7(x104792,f937(x104792,a925),f937(x104792,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x104792,a925),f937(x104792,a925)),x104792),f8(a925,a925,x104792)),f866(f866(f8(a925,f937(a925,a925),x104792),a333),f866(f866(f7(x104792,f937(x104792,a925),a925),f336(x104792)),x104793)))),f866(f866(f7(x104792,f937(x104792,a925),a925),f336(x104792)),x104791))))))),f866(f866(f117(x104792),f10(x104792,x104793)),f10(x104792,x104791)))
% 157.76/157.53 [10480]~P101(x104802)+E(x104801,f195(f937(x104802,a925)))+E(x104803,f195(f937(x104802,a925)))+~P107(f866(f66(x104802),x104801))+~P107(f866(f66(x104802),x104803))+E(f13(x104802,f866(f270(x104802),f866(f866(f8(f937(x104802,a925),a925,x104802),f93(x104802)),f866(f866(f8(f937(x104802,f937(x104802,a925)),f937(x104802,a925),x104802),f866(f8(f937(x104802,a925),a925,x104802),f93(x104802))),f866(f866(f7(x104802,f937(x104802,f937(x104802,a925)),f937(x104802,f937(x104802,a925))),f866(f866(f8(f937(x104802,f937(f937(x104802,a925),f937(x104802,a925))),f937(f937(x104802,f937(x104802,a925)),f937(x104802,f937(x104802,a925))),x104802),f18(x104802,f937(x104802,a925),f937(x104802,a925))),f866(f866(f8(f937(x104802,f937(x104802,f937(a925,a925))),f937(x104802,f937(f937(x104802,a925),f937(x104802,a925))),x104802),f866(f8(f937(x104802,f937(a925,a925)),f937(f937(x104802,a925),f937(x104802,a925)),x104802),f18(x104802,a925,a925))),f866(f866(f8(f937(x104802,f937(x104802,a925)),f937(x104802,f937(x104802,f937(a925,a925))),x104802),f866(f8(f937(x104802,a925),f937(x104802,f937(a925,a925)),x104802),f866(f8(a925,f937(a925,a925),x104802),a333))),f866(f866(f7(x104802,f937(x104802,f937(x104802,x104802)),f937(x104802,f937(x104802,a925))),f866(f866(f8(f937(f937(x104802,x104802),f937(x104802,a925)),f937(f937(x104802,f937(x104802,x104802)),f937(x104802,f937(x104802,a925))),x104802),f8(f937(x104802,x104802),f937(x104802,a925),x104802)),f866(f866(f8(f937(x104802,a925),f937(f937(x104802,x104802),f937(x104802,a925)),x104802),f8(x104802,a925,x104802)),a332))),f108(x104802)))))),f866(f866(f7(x104802,f937(x104802,a925),f937(x104802,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x104802,a925),f937(x104802,a925)),x104802),f8(a925,a925,x104802)),f866(f866(f8(a925,f937(a925,a925),x104802),a333),f866(f866(f7(x104802,f937(x104802,a925),a925),f336(x104802)),x104803)))),f866(f866(f7(x104802,f937(x104802,a925),a925),f336(x104802)),x104801))))))),f866(f866(f108(x104802),f13(x104802,x104803)),f13(x104802,x104801)))
% 157.76/157.53 [10481]~P110(x104812)+E(x104811,f195(f937(x104812,a925)))+E(x104813,f195(f937(x104812,a925)))+~P107(f866(f66(x104812),x104811))+~P107(f866(f66(x104812),x104813))+E(f12(x104812,f242(x104812),f866(f270(x104812),f866(f866(f8(f937(x104812,a925),a925,x104812),f93(x104812)),f866(f866(f8(f937(x104812,f937(x104812,a925)),f937(x104812,a925),x104812),f866(f8(f937(x104812,a925),a925,x104812),f93(x104812))),f866(f866(f7(x104812,f937(x104812,f937(x104812,a925)),f937(x104812,f937(x104812,a925))),f866(f866(f8(f937(x104812,f937(f937(x104812,a925),f937(x104812,a925))),f937(f937(x104812,f937(x104812,a925)),f937(x104812,f937(x104812,a925))),x104812),f18(x104812,f937(x104812,a925),f937(x104812,a925))),f866(f866(f8(f937(x104812,f937(x104812,f937(a925,a925))),f937(x104812,f937(f937(x104812,a925),f937(x104812,a925))),x104812),f866(f8(f937(x104812,f937(a925,a925)),f937(f937(x104812,a925),f937(x104812,a925)),x104812),f18(x104812,a925,a925))),f866(f866(f8(f937(x104812,f937(x104812,a925)),f937(x104812,f937(x104812,f937(a925,a925))),x104812),f866(f8(f937(x104812,a925),f937(x104812,f937(a925,a925)),x104812),f866(f8(a925,f937(a925,a925),x104812),a333))),f866(f866(f7(x104812,f937(x104812,f937(x104812,x104812)),f937(x104812,f937(x104812,a925))),f866(f866(f8(f937(f937(x104812,x104812),f937(x104812,a925)),f937(f937(x104812,f937(x104812,x104812)),f937(x104812,f937(x104812,a925))),x104812),f8(f937(x104812,x104812),f937(x104812,a925),x104812)),f866(f866(f8(f937(x104812,a925),f937(f937(x104812,x104812),f937(x104812,a925)),x104812),f8(x104812,a925,x104812)),a332))),f241(x104812)))))),f866(f866(f7(x104812,f937(x104812,a925),f937(x104812,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x104812,a925),f937(x104812,a925)),x104812),f8(a925,a925,x104812)),f866(f866(f8(a925,f937(a925,a925),x104812),a333),f866(f866(f7(x104812,f937(x104812,a925),a925),f336(x104812)),x104813)))),f866(f866(f7(x104812,f937(x104812,a925),a925),f336(x104812)),x104811))))))),f866(f866(f241(x104812),f12(x104812,f242(x104812),x104813)),f12(x104812,f242(x104812),x104811)))
% 157.76/157.53 [10482]~P110(x104822)+E(x104821,f195(f937(x104822,a925)))+E(x104823,f195(f937(x104822,a925)))+~P107(f866(f66(x104822),x104821))+~P107(f866(f66(x104822),x104823))+E(f11(x104822,f241(x104822),f866(f270(x104822),f866(f866(f8(f937(x104822,a925),a925,x104822),f93(x104822)),f866(f866(f8(f937(x104822,f937(x104822,a925)),f937(x104822,a925),x104822),f866(f8(f937(x104822,a925),a925,x104822),f93(x104822))),f866(f866(f7(x104822,f937(x104822,f937(x104822,a925)),f937(x104822,f937(x104822,a925))),f866(f866(f8(f937(x104822,f937(f937(x104822,a925),f937(x104822,a925))),f937(f937(x104822,f937(x104822,a925)),f937(x104822,f937(x104822,a925))),x104822),f18(x104822,f937(x104822,a925),f937(x104822,a925))),f866(f866(f8(f937(x104822,f937(x104822,f937(a925,a925))),f937(x104822,f937(f937(x104822,a925),f937(x104822,a925))),x104822),f866(f8(f937(x104822,f937(a925,a925)),f937(f937(x104822,a925),f937(x104822,a925)),x104822),f18(x104822,a925,a925))),f866(f866(f8(f937(x104822,f937(x104822,a925)),f937(x104822,f937(x104822,f937(a925,a925))),x104822),f866(f8(f937(x104822,a925),f937(x104822,f937(a925,a925)),x104822),f866(f8(a925,f937(a925,a925),x104822),a333))),f866(f866(f7(x104822,f937(x104822,f937(x104822,x104822)),f937(x104822,f937(x104822,a925))),f866(f866(f8(f937(f937(x104822,x104822),f937(x104822,a925)),f937(f937(x104822,f937(x104822,x104822)),f937(x104822,f937(x104822,a925))),x104822),f8(f937(x104822,x104822),f937(x104822,a925),x104822)),f866(f866(f8(f937(x104822,a925),f937(f937(x104822,x104822),f937(x104822,a925)),x104822),f8(x104822,a925,x104822)),a332))),f242(x104822)))))),f866(f866(f7(x104822,f937(x104822,a925),f937(x104822,a925)),f866(f866(f8(f937(a925,a925),f937(f937(x104822,a925),f937(x104822,a925)),x104822),f8(a925,a925,x104822)),f866(f866(f8(a925,f937(a925,a925),x104822),a333),f866(f866(f7(x104822,f937(x104822,a925),a925),f336(x104822)),x104823)))),f866(f866(f7(x104822,f937(x104822,a925),a925),f336(x104822)),x104821))))))),f866(f866(f242(x104822),f11(x104822,f241(x104822),x104823)),f11(x104822,f241(x104822),x104821)))
% 157.76/157.53 [7452]~P113(x74523)+E(x74521,x74522)+~E(f866(f866(f252(x74523),x74521),x74524),f866(f866(f252(x74523),x74522),x74524))+~P107(f866(f866(f243(x74523),f2(x74523)),x74522))+~P107(f866(f866(f243(x74523),f2(x74523)),x74521))+~P107(f866(f866(f244(a930),f2(a930)),x74524))
% 157.76/157.53 [7724]~P110(x77242)+E(x77241,f195(f937(x77242,a925)))+~P107(f866(f66(x77242),x77241))+~P107(f866(f866(f336(x77242),x77244),x77241))+P107(f866(f866(f243(x77242),x77243),x77244))+~P107(f866(f866(f243(x77242),x77243),f866(f68(x77242,f241(x77242)),x77241)))
% 157.76/157.53 [7725]~P103(x77252)+E(x77251,f195(f937(x77252,a925)))+~P107(f866(f66(x77252),x77251))+~P107(f866(f866(f336(x77252),x77254),x77251))+P107(f866(f866(f243(x77252),x77253),x77254))+~P107(f866(f866(f243(x77252),x77253),f866(f68(x77252,f108(x77252)),x77251)))
% 157.76/157.53 [7726]~P110(x77262)+E(x77261,f195(f937(x77262,a925)))+~P107(f866(f66(x77262),x77261))+~P107(f866(f866(f336(x77262),x77264),x77261))+P107(f866(f866(f244(x77262),x77263),x77264))+~P107(f866(f866(f244(x77262),x77263),f866(f68(x77262,f241(x77262)),x77261)))
% 157.76/157.53 [7630]E(x76301,f2(a1))+E(f866(f866(f41(a1),x76302),x76301),x76303)+~P107(f866(f866(f243(a1),x76304),f2(a1)))+~E(x76302,f866(f866(f86(a1),f866(f866(f87(a1),x76301),x76303)),x76304))+P107(f866(f866(f244(a1),f2(a1)),x76301))+~P107(f866(f866(f244(a1),x76301),x76304))
% 157.76/157.53 [7646]E(f50(a1,x76462,x76461),x76463)+E(x76461,f2(a1))+~P107(f866(f866(f243(a1),x76463),f2(a1)))+~E(x76462,f866(f866(f86(a1),f866(f866(f87(a1),x76461),x76464)),x76463))+P107(f866(f866(f244(a1),f2(a1)),x76461))+~P107(f866(f866(f244(a1),x76461),x76463))
% 157.76/157.53 [7762]E(x77621,f2(a1))+E(f866(f866(f41(a1),x77622),x77621),x77623)+~E(x77622,f866(f866(f86(a1),f866(f866(f87(a1),x77621),x77623)),x77624))+~P107(f866(f866(f243(a1),f2(a1)),x77624))+~P107(f866(f866(f244(a1),f2(a1)),x77621))+~P107(f866(f866(f244(a1),x77624),x77621))
% 157.76/157.53 [7783]E(f50(a1,x77832,x77831),x77833)+E(x77831,f2(a1))+~E(x77832,f866(f866(f86(a1),f866(f866(f87(a1),x77831),x77834)),x77833))+~P107(f866(f866(f243(a1),f2(a1)),x77833))+~P107(f866(f866(f244(a1),f2(a1)),x77831))+~P107(f866(f866(f244(a1),x77833),x77831))
% 157.76/157.53 [7924]~P110(x79242)+E(x79241,f195(f937(x79242,a925)))+~P107(f866(f66(x79242),x79241))+~P107(f866(f866(f336(x79242),x79244),x79241))+~P107(f866(f866(f243(x79242),x79244),x79243))+P107(f866(f866(f243(x79242),f866(f68(x79242,f241(x79242)),x79241)),x79243))
% 157.76/157.53 [7925]~P110(x79252)+E(x79251,f195(f937(x79252,a925)))+~P107(f866(f66(x79252),x79251))+~P107(f866(f866(f244(x79252),x79254),x79253))+~P107(f866(f866(f336(x79252),x79254),x79251))+P107(f866(f866(f244(x79252),f866(f68(x79252,f241(x79252)),x79251)),x79253))
% 157.76/157.53 [8479]~P107(f866(f866(f243(a1),x84794),f2(a1)))+~E(x84791,f866(f866(f86(a1),f866(f866(f87(a1),x84792),x84793)),x84794))+~P107(f866(f866(f243(a1),f2(a1)),x84794))+~P107(f866(f866(f244(a1),x84794),x84792))+~P107(f866(f866(f244(a1),x84792),x84794))+P107(f866(f54(x84791,x84792),f866(f866(f260(a1,a1),x84793),x84794)))
% 157.76/157.53 [8646]~P111(x86461)+P107(f866(f866(f244(f937(x86461,a925)),f310(x86461,x86462,x86463)),f310(x86461,x86464,x86465)))+~P107(f866(f866(f243(x86461),x86464),x86462))+~P107(f866(f866(f243(x86461),x86464),x86465))+~P107(f866(f866(f243(x86461),x86463),x86465))+~P107(f866(f866(f244(x86461),x86463),x86465))
% 157.76/157.53 [8647]~P111(x86471)+P107(f866(f866(f244(f937(x86471,a925)),f310(x86471,x86472,x86473)),f310(x86471,x86474,x86475)))+~P107(f866(f866(f243(x86471),x86473),x86475))+~P107(f866(f866(f243(x86471),x86474),x86475))+~P107(f866(f866(f243(x86471),x86474),x86472))+~P107(f866(f866(f244(x86471),x86474),x86472))
% 157.76/157.53 [9510]P60(x95102,x95103,x95104,x95101)+E(x95101,f195(f937(x95102,a925)))+~P107(f866(f66(x95102),x95104))+~P107(f866(f66(x95102),x95101))+~P107(f866(f866(x95103,f520(x95101,x95104,x95103,x95102)),x95105))+~P107(f866(f866(f336(x95102),x95105),x95101))
% 157.76/157.53 [9511]P60(x95112,x95113,x95114,x95111)+E(x95111,f195(f937(x95112,a925)))+~P107(f866(f66(x95112),x95114))+~P107(f866(f66(x95112),x95111))+~P107(f866(f866(x95113,f808(x95113,x95111,x95114,x95112)),x95115))+~P107(f866(f866(f336(x95112),x95115),x95111))
% 157.76/157.53 [9512]P60(x95122,x95123,x95124,x95121)+E(x95121,f195(f937(x95122,a925)))+~P107(f866(f66(x95122),x95124))+~P107(f866(f66(x95122),x95121))+~P107(f866(f866(x95123,f809(x95121,x95124,x95123,x95122)),x95125))+~P107(f866(f866(f336(x95122),x95125),x95121))
% 157.76/157.53 [9658]~E(x96583,x96585)+~P71(x96581)+~P72(x96581)+~P40(x96583)+E(f866(f866(f9(a1,x96581),x96582),x96583),f866(f866(f9(a1,x96581),x96584),x96585))+P107(f866(f866(f243(a1),f2(a1)),f476(x96582,x96584,x96583,x96585,x96581)))
% 157.76/157.53 [9659]~E(x96593,x96595)+~P71(x96591)+~P72(x96591)+~P40(x96593)+E(f866(f866(f6(a1,x96591),x96592),x96593),f866(f866(f6(a1,x96591),x96594),x96595))+P107(f866(f866(f243(a1),f2(a1)),f478(x96592,x96594,x96593,x96595,x96591)))
% 157.76/157.53 [9831]~E(x98315,x98313)+~P71(x98311)+~P72(x98311)+~P40(x98315)+~E(f866(x98312,f476(x98314,x98312,x98315,x98313,x98311)),f866(x98314,f476(x98314,x98312,x98315,x98313,x98311)))+E(f866(f866(f9(a1,x98311),x98312),x98313),f866(f866(f9(a1,x98311),x98314),x98315))
% 157.76/157.53 [9832]~E(x98325,x98323)+~P71(x98321)+~P72(x98321)+~P40(x98325)+~E(f866(x98322,f478(x98324,x98322,x98325,x98323,x98321)),f866(x98324,f478(x98324,x98322,x98325,x98323,x98321)))+E(f866(f866(f6(a1,x98321),x98322),x98323),f866(f866(f6(a1,x98321),x98324),x98325))
% 157.76/157.53 [9920]~P79(x99203)+E(f866(x99201,x99202),f2(x99203))+~E(f866(f866(f6(x99204,x99203),x99201),x99205),f2(x99203))+~P107(f866(f66(x99204),x99205))+P107(f866(f866(f336(x99204),f401(x99202,x99201,x99205,x99204,x99203)),x99205))+~P107(f866(f866(f336(x99204),x99202),x99205))
% 157.76/157.53 [10049]~P79(x100493)+E(f866(x100491,x100492),f2(x100493))+~E(f866(f866(f6(x100494,x100493),x100491),x100495),f2(x100493))+~P107(f866(f66(x100494),x100495))+~P107(f866(f866(f336(x100494),x100492),x100495))+~P107(f866(f866(f243(x100493),f2(x100493)),f866(x100491,f401(x100492,x100491,x100495,x100494,x100493))))
% 157.76/157.53 [8565]~P140(x85651)+~P107(f866(f866(f243(x85651),x85653),x85655))+~P107(f866(f866(f243(x85651),x85652),x85654))+~P107(f866(f866(f243(x85651),f2(x85651)),x85653))+~P107(f866(f866(f243(x85651),f2(x85651)),x85654))+P107(f866(f866(f243(x85651),f866(f866(f87(x85651),x85652),x85653)),f866(f866(f87(x85651),x85654),x85655)))
% 157.76/157.53 [8566]~P140(x85661)+~P107(f866(f866(f243(x85661),x85663),x85665))+~P107(f866(f866(f243(x85661),x85662),x85664))+~P107(f866(f866(f243(x85661),f2(x85661)),x85663))+~P107(f866(f866(f243(x85661),f2(x85661)),x85662))+P107(f866(f866(f243(x85661),f866(f866(f87(x85661),x85662),x85663)),f866(f866(f87(x85661),x85664),x85665)))
% 157.76/157.53 [8567]~P68(x85671)+~P107(f866(f866(f244(x85671),f2(x85671)),x85675))+~P107(f866(f866(f243(x85671),x85675),x85673))+~P107(f866(f866(f243(x85671),x85672),x85674))+~P107(f866(f866(f243(x85671),f2(x85671)),x85672))+P107(f866(f866(f243(x85671),f866(f866(f297(x85671),x85672),x85673)),f866(f866(f297(x85671),x85674),x85675)))
% 157.76/157.53 [8568]~P132(x85681)+~P107(f866(f866(f243(x85681),x85683),x85685))+~P107(f866(f866(f243(x85681),f2(x85681)),x85682))+~P107(f866(f866(f244(x85681),x85682),x85684))+~P107(f866(f866(f244(x85681),f2(x85681)),x85683))+P107(f866(f866(f244(x85681),f866(f866(f87(x85681),x85682),x85683)),f866(f866(f87(x85681),x85684),x85685)))
% 157.76/157.53 [8569]~P132(x85691)+~P107(f866(f866(f243(x85691),x85692),x85694))+~P107(f866(f866(f243(x85691),f2(x85691)),x85693))+~P107(f866(f866(f244(x85691),x85693),x85695))+~P107(f866(f866(f244(x85691),f2(x85691)),x85692))+P107(f866(f866(f244(x85691),f866(f866(f87(x85691),x85692),x85693)),f866(f866(f87(x85691),x85694),x85695)))
% 157.76/157.53 [8570]~P132(x85701)+~P107(f866(f866(f243(x85701),f2(x85701)),x85703))+~P107(f866(f866(f243(x85701),f2(x85701)),x85702))+~P107(f866(f866(f244(x85701),x85703),x85705))+~P107(f866(f866(f244(x85701),x85702),x85704))+P107(f866(f866(f244(x85701),f866(f866(f87(x85701),x85702),x85703)),f866(f866(f87(x85701),x85704),x85705)))
% 157.76/157.53 [8571]~P132(x85711)+~P107(f866(f866(f243(x85711),f2(x85711)),x85713))+~P107(f866(f866(f244(x85711),x85713),x85715))+~P107(f866(f866(f244(x85711),x85712),x85714))+~P107(f866(f866(f244(x85711),f2(x85711)),x85714))+P107(f866(f866(f244(x85711),f866(f866(f87(x85711),x85712),x85713)),f866(f866(f87(x85711),x85714),x85715)))
% 157.76/157.53 [8572]~P68(x85721)+~P107(f866(f866(f243(x85721),x85725),x85723))+~P107(f866(f866(f243(x85721),f2(x85721)),x85722))+~P107(f866(f866(f244(x85721),x85722),x85724))+~P107(f866(f866(f244(x85721),f2(x85721)),x85725))+P107(f866(f866(f244(x85721),f866(f866(f297(x85721),x85722),x85723)),f866(f866(f297(x85721),x85724),x85725)))
% 157.76/157.53 [8573]~P68(x85731)+~P107(f866(f866(f243(x85731),x85732),x85734))+~P107(f866(f866(f244(x85731),x85735),x85733))+~P107(f866(f866(f244(x85731),f2(x85731)),x85735))+~P107(f866(f866(f244(x85731),f2(x85731)),x85732))+P107(f866(f866(f244(x85731),f866(f866(f297(x85731),x85732),x85733)),f866(f866(f297(x85731),x85734),x85735)))
% 157.76/157.53 [9964]~P72(x99645)+~P90(x99645)+E(x99641,f195(f937(x99642,a925)))+~P107(f866(f66(x99642),x99641))+P107(f866(f866(f336(x99642),f477(x99643,x99644,x99641,x99642,x99645)),x99641))+P107(f866(f866(f244(x99645),f866(f866(f6(x99642,x99645),x99644),x99641)),f866(f866(f6(x99642,x99645),x99643),x99641)))
% 157.76/157.53 [10074]~P72(x100741)+~P88(x100741)+~P107(f866(f66(x100742),x100745))+~P107(f866(f866(f243(x100741),f2(x100741)),f866(x100743,f402(x100743,x100744,x100745,x100742,x100741))))+P107(f866(f866(f243(x100741),f866(f866(f6(x100742,x100741),x100743),x100744)),f866(f866(f6(x100742,x100741),x100743),x100745)))+~P107(f866(f866(f243(f937(x100742,a925)),x100744),x100745))
% 157.76/157.53 [10235]~P72(x102353)+~P90(x102353)+E(x102351,f195(f937(x102352,a925)))+~P107(f866(f66(x102352),x102351))+~P107(f866(f866(f244(x102353),f866(x102354,f477(x102355,x102354,x102351,x102352,x102353))),f866(x102355,f477(x102355,x102354,x102351,x102352,x102353))))+P107(f866(f866(f244(x102353),f866(f866(f6(x102352,x102353),x102354),x102351)),f866(f866(f6(x102352,x102353),x102355),x102351)))
% 157.76/157.53 [7309]~P17(x73092,x73095,x73094)+E(x73091,f195(f937(x73092,a925)))+E(x73093,f195(f937(x73092,a925)))+~P107(f866(f66(x73092),x73091))+~P107(f866(f66(x73092),x73093))+E(f866(x73094,f866(f866(f117(f937(x73092,a925)),x73093),x73091)),f866(f866(x73095,f866(x73094,x73093)),f866(x73094,x73091)))
% 157.76/157.53 [7891]~P150(x78911,x78913,x78914)+P107(f866(x78911,x78912))+~P107(f866(f866(f244(a1),x78914),f2(a1)))+~P107(f866(f866(f243(a1),x78915),f2(a1)))+~E(x78913,f866(f866(f86(a1),f866(f866(f87(a1),x78914),x78912)),x78915))+~P107(f866(f866(f244(a1),x78914),x78915))
% 157.76/157.53 [7892]~P149(x78921,x78923,x78924)+P107(f866(x78921,x78922))+~P107(f866(f866(f244(a1),x78924),f2(a1)))+~P107(f866(f866(f243(a1),x78922),f2(a1)))+~E(x78923,f866(f866(f86(a1),f866(f866(f87(a1),x78924),x78925)),x78922))+~P107(f866(f866(f244(a1),x78924),x78922))
% 157.76/157.53 [7933]~P150(x79331,x79333,x79334)+P107(f866(x79331,x79332))+~E(x79333,f866(f866(f86(a1),f866(f866(f87(a1),x79334),x79332)),x79335))+~P107(f866(f866(f243(a1),f2(a1)),x79335))+~P107(f866(f866(f244(a1),f2(a1)),x79334))+~P107(f866(f866(f244(a1),x79335),x79334))
% 157.76/157.53 [7934]~P149(x79341,x79343,x79344)+P107(f866(x79341,x79342))+~E(x79343,f866(f866(f86(a1),f866(f866(f87(a1),x79344),x79345)),x79342))+~P107(f866(f866(f243(a1),f2(a1)),x79342))+~P107(f866(f866(f244(a1),f2(a1)),x79344))+~P107(f866(f866(f244(a1),x79342),x79344))
% 157.76/157.53 [8856]P107(f866(f866(x88561,x88562),x88563))+~P107(f866(f866(x88561,f866(f866(f41(a1),x88564),x88565)),f50(a1,x88564,x88565)))+~P107(f866(f866(f244(a1),x88565),f2(a1)))+~P107(f866(f866(f243(a1),x88563),f2(a1)))+~E(x88564,f866(f866(f86(a1),f866(f866(f87(a1),x88565),x88562)),x88563))+~P107(f866(f866(f244(a1),x88565),x88563))
% 157.76/157.53 [8865]P107(f866(f866(x88651,x88652),x88653))+~P107(f866(f866(x88651,f866(f866(f41(a1),x88654),x88655)),f50(a1,x88654,x88655)))+~E(x88654,f866(f866(f86(a1),f866(f866(f87(a1),x88655),x88652)),x88653))+~P107(f866(f866(f243(a1),f2(a1)),x88653))+~P107(f866(f866(f244(a1),f2(a1)),x88655))+~P107(f866(f866(f244(a1),x88653),x88655))
% 157.76/157.53 [9128]E(x91281,x91282)+~P56(x91283,x91285,x91284)+~P107(f866(f866(f336(x91283),x91282),x91285))+~P107(f866(f866(f336(x91283),x91281),x91285))+P107(f866(f866(f336(f936(x91283,x91283)),f866(f866(f260(x91283,x91283),x91281),x91282)),x91284))+P107(f866(f866(f336(f936(x91283,x91283)),f866(f866(f260(x91283,x91283),x91282),x91281)),x91284))
% 157.76/157.53 [9991]~P72(x99915)+~P88(x99915)+~P107(f866(f66(x99911),x99914))+P107(f866(f866(f243(x99915),f866(f866(f6(x99911,x99915),x99912),x99913)),f866(f866(f6(x99911,x99915),x99912),x99914)))+~P107(f866(f866(f243(f937(x99911,a925)),x99913),x99914))+P107(f866(f866(f336(x99911),f402(x99912,x99913,x99914,x99911,x99915)),f866(f866(f23(f937(x99911,a925)),x99914),x99913)))
% 157.76/157.53 [10082]E(x100821,f195(f937(x100822,a925)))+~P107(f866(f66(x100822),x100823))+~P107(f866(f66(x100822),x100821))+P107(f866(f866(f336(f936(f937(x100822,a925),f937(x100822,a925))),f866(f866(f260(f937(x100822,a925),f937(x100822,a925)),x100823),x100821)),f325(x100822,x100824)))+~P107(f866(f866(f336(x100822),x100825),x100821))+~P107(f866(f866(f336(f936(x100822,x100822)),f866(f866(f260(x100822,x100822),f522(x100824,x100821,x100823,x100822)),x100825)),x100824))
% 157.76/157.53 [10083]E(x100831,f195(f937(x100832,a925)))+~P107(f866(f66(x100832),x100833))+~P107(f866(f66(x100832),x100831))+P107(f866(f866(f336(f936(f937(x100832,a925),f937(x100832,a925))),f866(f866(f260(f937(x100832,a925),f937(x100832,a925)),x100833),x100831)),f325(x100832,x100834)))+~P107(f866(f866(f336(x100832),x100835),x100831))+~P107(f866(f866(f336(f936(x100832,x100832)),f866(f866(f260(x100832,x100832),f575(x100834,x100831,x100833,x100832)),x100835)),x100834))
% 157.76/157.53 [10239]~P79(x102391)+~E(f866(f866(f6(x102395,x102391),x102392),x102396),x102394)+~P107(f866(f66(x102395),x102396))+P107(f866(f866(f336(x102395),f413(x102393,x102394,x102392,x102396,x102395,x102391)),x102396))+P107(f866(f866(f243(x102391),f866(x102392,x102393)),x102394))+~P107(f866(f866(f336(x102395),x102393),x102396))
% 157.76/157.53 [10282]~P79(x102821)+~E(f866(f866(f6(x102825,x102821),x102822),x102826),x102824)+~P107(f866(f66(x102825),x102826))+~P107(f866(f866(f336(x102825),x102823),x102826))+~P107(f866(f866(f243(x102821),f2(x102821)),f866(x102822,f413(x102823,x102824,x102822,x102826,x102825,x102821))))+P107(f866(f866(f243(x102821),f866(x102822,x102823)),x102824))
% 157.76/157.53 [10426]~E(x104265,x104268)+~E(x104264,x104267)+~P109(x104261)+~P72(x104262)+E(f866(f866(f6(x104261,x104262),x104263),f866(f309(x104261,x104264),x104265)),f866(f866(f6(x104261,x104262),x104266),f866(f309(x104261,x104267),x104268)))+P107(f866(f866(f243(x104261),x104264),f579(x104263,x104266,x104265,x104268,x104264,x104267,x104261,x104262)))
% 157.76/157.53 [10442]~E(x104427,x104424)+~E(x104428,x104425)+~P109(x104421)+~P72(x104422)+~E(f866(x104423,f579(x104426,x104423,x104428,x104425,x104427,x104424,x104421,x104422)),f866(x104426,f579(x104426,x104423,x104428,x104425,x104427,x104424,x104421,x104422)))+E(f866(f866(f6(x104421,x104422),x104423),f866(f309(x104421,x104424),x104425)),f866(f866(f6(x104421,x104422),x104426),f866(f309(x104421,x104427),x104428)))
% 157.76/157.53 [10445]~E(x104454,x104457)+~E(x104455,x104458)+~P109(x104451)+~P72(x104452)+E(f866(f866(f6(x104451,x104452),x104453),f866(f309(x104451,x104454),x104455)),f866(f866(f6(x104451,x104452),x104456),f866(f309(x104451,x104457),x104458)))+P107(f866(f866(f244(x104451),f579(x104453,x104456,x104455,x104458,x104454,x104457,x104451,x104452)),x104455))
% 157.76/157.53 [10089]~P8(x100895,x100899,x100896)+~P8(x100891,x1008910,x100893)+~P12(x100891,x100895,f937(x100892,a925),x100893,x100896,x100898)+~P107(f866(f866(f336(x100895),x100897),x100899))+~P107(f866(f866(f336(x100891),x100894),x1008910))+E(f866(f866(f44(x100891,f937(x100892,a925)),f866(f293(x100891,x100891,x100893),f866(f866(f316(x100891),x100894),f195(f937(x100891,a925))))),f866(f866(f8(f937(x100895,f937(x100892,a925)),f937(x100892,a925),x100891),f866(f44(x100895,f937(x100892,a925)),f866(f293(x100895,x100895,x100896),f866(f866(f316(x100895),x100897),f195(f937(x100895,a925)))))),x100898)),f866(f866(x100898,x100894),x100897))
% 157.76/157.53 [5845]~P110(x58453)+~P13(x58453,x58452)+~P13(x58453,x58451)+E(x58451,x58452)+~E(f866(f179(x58453),x58451),f866(f179(x58453),x58452))+~P107(f866(f144(x58453),x58452))+~P107(f866(f144(x58453),x58451))
% 157.76/157.53 [5171]~P129(x51712)+~P135(x51712)+~P146(x51712)+~P116(x51712)+~E(x51713,f2(x51712))+E(x51711,f2(a930))+E(f866(f866(f252(x51712),x51713),x51711),f2(x51712))
% 157.76/157.53 [9388]E(x93881,f2(a930))+~E(x93882,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x93883)),x93881)),f866(f264(a930,a930),x93883)))+P107(f866(f53(x93882,x93881),x93883))+~P107(f866(f866(f243(a930),f866(f264(a930,a930),x93883)),f2(a930)))+~P107(f866(f866(f243(a930),f2(a930)),f866(f264(a930,a930),x93883)))+~P107(f866(f866(f244(a930),x93881),f866(f264(a930,a930),x93883)))+~P107(f866(f866(f244(a930),f866(f264(a930,a930),x93883)),x93881))
% 157.76/157.53 [9396]~E(f866(f259(a930,a930),x93963),f2(a930))+~E(x93961,f866(f866(f86(a930),f866(f866(f87(a930),f866(f259(a930,a930),x93963)),x93962)),f866(f264(a930,a930),x93963)))+P107(f866(f53(x93961,x93962),x93963))+~P107(f866(f866(f243(a930),f866(f264(a930,a930),x93963)),f2(a930)))+~P107(f866(f866(f243(a930),f2(a930)),f866(f264(a930,a930),x93963)))+~P107(f866(f866(f244(a930),x93962),f866(f264(a930,a930),x93963)))+~P107(f866(f866(f244(a930),f866(f264(a930,a930),x93963)),x93962))
% 157.76/157.53 [8241]~P69(x82412)+E(x82411,f195(f937(x82412,a925)))+E(x82413,f195(f937(x82412,a925)))+~P107(f866(f66(x82412),x82411))+~P107(f866(f66(x82412),x82413))+~E(f866(f866(f108(f937(x82412,a925)),x82413),x82411),f195(f937(x82412,a925)))+E(f866(f866(f87(x82412),f866(f68(x82412,f87(x82412)),x82413)),f866(f68(x82412,f87(x82412)),x82411)),f866(f68(x82412,f87(x82412)),f866(f866(f117(f937(x82412,a925)),x82413),x82411)))
% 157.76/157.53 [8029]E(x80291,f2(a1))+E(f866(f866(f41(a1),x80292),x80291),x80293)+~P107(f866(f866(f243(a1),x80294),f2(a1)))+~E(x80292,f866(f866(f86(a1),f866(f866(f87(a1),x80291),x80293)),x80294))+~P107(f866(f866(f243(a1),f2(a1)),x80294))+~P107(f866(f866(f244(a1),x80294),x80291))+~P107(f866(f866(f244(a1),x80291),x80294))
% 157.76/157.53 [8037]E(f50(a1,x80372,x80371),x80373)+E(x80371,f2(a1))+~P107(f866(f866(f243(a1),x80373),f2(a1)))+~E(x80372,f866(f866(f86(a1),f866(f866(f87(a1),x80371),x80374)),x80373))+~P107(f866(f866(f243(a1),f2(a1)),x80373))+~P107(f866(f866(f244(a1),x80373),x80371))+~P107(f866(f866(f244(a1),x80371),x80373))
% 157.76/157.53 [6641]~P62(x66412)+~P57(x66412,x66411,x66415)+~P57(x66412,x66413,x66414)+E(x66411,f2(x66412))+E(x66413,f2(x66412))+~E(f866(f866(f41(x66412),x66414),x66413),f866(f866(f41(x66412),x66415),x66411))+E(f866(f866(f87(x66412),x66414),x66411),f866(f866(f87(x66412),x66413),x66415))
% 157.76/157.53 [6642]~P62(x66422)+~P57(x66422,x66421,x66424)+~P57(x66422,x66423,x66425)+E(x66421,f2(x66422))+E(x66423,f2(x66422))+~E(f866(f866(f87(x66422),x66424),x66423),f866(f866(f87(x66422),x66421),x66425))+E(f866(f866(f41(x66422),x66424),x66421),f866(f866(f41(x66422),x66425),x66423))
% 157.76/157.53 [7942]~P18(x79422,x79425,x79424)+E(x79421,f195(f937(x79422,a925)))+E(x79423,f195(f937(x79422,a925)))+~P107(f866(f66(x79422),x79421))+~P107(f866(f66(x79422),x79423))+~E(f866(f866(f108(f937(x79422,a925)),x79423),x79421),f195(f937(x79422,a925)))+E(f866(x79424,f866(f866(f117(f937(x79422,a925)),x79423),x79421)),f866(f866(x79425,f866(x79424,x79423)),f866(x79424,x79421)))
% 157.76/157.53 [9631]~P25(x96313,x96311,x96315,x96314)+~P25(x96311,x96313,x96316,x96312)+E(f866(f40(x96311),x96312),f866(f40(x96313),x96314))+~P107(f866(f66(x96313),x96314))+~P107(f866(f66(x96311),x96312))+~P107(f866(f866(f243(f937(x96313,a925)),f866(f317(x96311,x96313,x96316),x96312)),x96314))+~P107(f866(f866(f243(f937(x96311,a925)),f866(f317(x96313,x96311,x96315),x96314)),x96312))
% 157.76/157.53 [9575]~P107(f866(f866(f244(a1),f866(f866(f86(a1),f866(f866(f87(a1),x95755),x95751)),x95756)),f2(a1)))+~E(f866(f866(f86(a1),f866(f866(f87(a1),x95753),x95752)),x95754),f866(f866(f86(a1),f866(f866(f87(a1),x95755),x95751)),x95756))+~P107(f866(f866(f243(a1),f2(a1)),x95756))+~P107(f866(f866(f244(a1),f2(a1)),x95755))+~P107(f866(f866(f243(a1),x95755),x95753))+~P107(f866(f866(f244(a1),x95754),x95753))+P107(f866(f866(f243(a1),x95751),x95752))
% 157.76/157.53 [9339]~E(f866(f866(f86(a1),f866(f866(f87(a1),x93393),x93391)),x93394),f866(f866(f86(a1),f866(f866(f87(a1),x93395),x93392)),x93396))+~P107(f866(f866(f243(a1),f2(a1)),x93394))+~P107(f866(f866(f244(a1),f2(a1)),x93395))+~P107(f866(f866(f243(a1),x93395),x93393))+~P107(f866(f866(f244(a1),x93396),x93395))+P107(f866(f866(f243(a1),x93391),x93392))+~P107(f866(f866(f243(a1),f2(a1)),f866(f866(f86(a1),f866(f866(f87(a1),x93395),x93392)),x93396)))
% 157.76/157.53 [9515]~P130(x95151)+~E(f866(f866(f86(x95151),x95152),x95154),f84(x95151))+~P107(f866(f866(f243(x95151),x95155),x95156))+~P107(f866(f866(f243(x95151),x95153),x95156))+~P107(f866(f866(f243(x95151),f2(x95151)),x95154))+~P107(f866(f866(f243(x95151),f2(x95151)),x95152))+P107(f866(f866(f243(x95151),f866(f866(f86(x95151),f866(f866(f87(x95151),x95152),x95153)),f866(f866(f87(x95151),x95154),x95155))),x95156))
% 157.76/157.53 [9516]~P133(x95161)+~E(f866(f866(f86(x95161),x95162),x95164),f84(x95161))+~P107(f866(f866(f243(x95161),f2(x95161)),x95164))+~P107(f866(f866(f243(x95161),f2(x95161)),x95162))+~P107(f866(f866(f244(x95161),x95165),x95166))+~P107(f866(f866(f244(x95161),x95163),x95166))+P107(f866(f866(f244(x95161),f866(f866(f86(x95161),f866(f866(f87(x95161),x95162),x95163)),f866(f866(f87(x95161),x95164),x95165))),x95166))
% 157.76/157.53 [10333]~P8(x103337,x103336,x103335)+E(x103331,x103332)+~P11(x103337,f937(x103334,a925),x103335,x103333)+E(f866(x103333,f506(x103331,x103332,x103333,x103334,x103335,x103336,x103337)),f866(x103333,f507(x103331,x103332,x103333,x103334,x103335,x103336,x103337)))+~E(f866(f866(f44(x103337,f937(x103334,a925)),x103331),x103333),f866(f866(f44(x103337,f937(x103334,a925)),x103332),x103333))+~P107(f866(f866(f336(f937(x103337,a925)),x103332),f866(f866(f65(x103337),x103336),x103335)))+~P107(f866(f866(f336(f937(x103337,a925)),x103331),f866(f866(f65(x103337),x103336),x103335)))
% 157.76/157.53 [10378]~P8(x103783,x103787,x103786)+E(x103781,x103782)+~P11(x103783,f937(x103785,a925),x103786,x103784)+~E(f866(f866(f44(x103783,f937(x103785,a925)),x103781),x103784),f866(f866(f44(x103783,f937(x103785,a925)),x103782),x103784))+P107(f866(f866(f336(x103783),f507(x103781,x103782,x103784,x103785,x103786,x103787,x103783)),x103787))+~P107(f866(f866(f336(f937(x103783,a925)),x103782),f866(f866(f65(x103783),x103787),x103786)))+~P107(f866(f866(f336(f937(x103783,a925)),x103781),f866(f866(f65(x103783),x103787),x103786)))
% 157.76/157.53 [10379]~P8(x103793,x103797,x103796)+E(x103791,x103792)+~P11(x103793,f937(x103795,a925),x103796,x103794)+~E(f866(f866(f44(x103793,f937(x103795,a925)),x103791),x103794),f866(f866(f44(x103793,f937(x103795,a925)),x103792),x103794))+P107(f866(f866(f336(x103793),f506(x103791,x103792,x103794,x103795,x103796,x103797,x103793)),x103797))+~P107(f866(f866(f336(f937(x103793,a925)),x103792),f866(f866(f65(x103793),x103797),x103796)))+~P107(f866(f866(f336(f937(x103793,a925)),x103791),f866(f866(f65(x103793),x103797),x103796)))
% 157.76/157.53 [10461]E(x104611,x104612)+~P8(x104613,x104616,x104617)+~P11(x104613,f937(x104614,a925),x104617,x104615)+~E(f866(f866(f44(x104613,f937(x104614,a925)),x104611),x104615),f866(f866(f44(x104613,f937(x104614,a925)),x104612),x104615))+~P107(f866(f866(f336(f936(x104613,x104613)),f866(f866(f260(x104613,x104613),f507(x104611,x104612,x104615,x104614,x104617,x104616,x104613)),f506(x104611,x104612,x104615,x104614,x104617,x104616,x104613))),x104617))+~P107(f866(f866(f336(f937(x104613,a925)),x104612),f866(f866(f65(x104613),x104616),x104617)))+~P107(f866(f866(f336(f937(x104613,a925)),x104611),f866(f866(f65(x104613),x104616),x104617)))
% 157.76/157.53 [9338]~P8(x93381,x93387,x93384)+~E(x93385,x93386)+~P107(f866(f866(f336(x93381),x93383),x93386))+~P107(f866(f866(f336(x93381),x93382),x93385))+~P107(f866(f866(f336(f937(x93381,a925)),x93386),f866(f866(f65(x93381),x93387),x93384)))+~P107(f866(f866(f336(f937(x93381,a925)),x93385),f866(f866(f65(x93381),x93387),x93384)))+P107(f866(f866(f336(f936(x93381,x93381)),f866(f866(f260(x93381,x93381),x93382),x93383)),x93384))
% 157.76/157.53 [9472]E(x94721,x94722)+~P8(x94723,x94724,x94725)+~P107(f866(f866(f336(x94723),x94726),x94722))+~P107(f866(f866(f336(x94723),x94727),x94721))+~P107(f866(f866(f336(f937(x94723,a925)),x94722),f866(f866(f65(x94723),x94724),x94725)))+~P107(f866(f866(f336(f937(x94723,a925)),x94721),f866(f866(f65(x94723),x94724),x94725)))+~P107(f866(f866(f336(f936(x94723,x94723)),f866(f866(f260(x94723,x94723),x94727),x94726)),x94725))
% 157.76/157.53 [10488]~P8(x104889,x104888,x104887)+~P8(x104881,x1048811,x1048810)+~P12(x104881,x104889,f937(x104886,a925),x1048810,x104887,x104885)+P107(f866(f866(f336(x104881),f510(x104882,x104883,x104884,x104885,x104886,x104887,x104888,x104889,x1048810,x1048811,x104881)),x1048811))+~P107(f866(f866(f336(f937(x104889,a925)),x104883),f866(f866(f65(x104889),x104888),x104887)))+~P107(f866(f866(f336(f937(x104881,a925)),x104884),f866(f866(f65(x104881),x1048811),x1048810)))+P107(f866(f866(f336(f937(x104886,a925)),f866(f866(f44(x104881,f937(x104886,a925)),x104884),f866(f866(f8(f937(x104889,f937(x104886,a925)),f937(x104886,a925),x104881),f866(f44(x104889,f937(x104886,a925)),x104883)),x104885))),x104882))
% 157.76/157.53 [10489]~P8(x1048911,x1048910,x104899)+~P8(x104891,x104898,x104897)+~P12(x1048911,x104891,f937(x104896,a925),x104899,x104897,x104895)+P107(f866(f866(f336(x104891),f511(x104892,x104893,x104894,x104895,x104896,x104897,x104898,x104891,x104899,x1048910,x1048911)),x104898))+~P107(f866(f866(f336(f937(x1048911,a925)),x104894),f866(f866(f65(x1048911),x1048910),x104899)))+~P107(f866(f866(f336(f937(x104891,a925)),x104893),f866(f866(f65(x104891),x104898),x104897)))+P107(f866(f866(f336(f937(x104896,a925)),f866(f866(f44(x1048911,f937(x104896,a925)),x104894),f866(f866(f8(f937(x104891,f937(x104896,a925)),f937(x104896,a925),x1048911),f866(f44(x104891,f937(x104896,a925)),x104893)),x104895))),x104892))
% 157.76/157.53 [10490]~P8(x104902,x104908,x104909)+~P8(x104904,x1049010,x1049011)+~P12(x104902,x104904,f937(x104901,a925),x104909,x1049011,x104906)+~P107(f866(f866(f336(f937(x104902,a925)),x104903),f866(f866(f65(x104902),x104908),x104909)))+~P107(f866(f866(f336(f937(x104904,a925)),x104905),f866(f866(f65(x104904),x1049010),x1049011)))+~P107(f866(f866(f336(f937(x104901,a925)),f866(f866(x104906,f510(x104907,x104905,x104903,x104906,x104901,x1049011,x1049010,x104904,x104909,x104908,x104902)),f511(x104907,x104905,x104903,x104906,x104901,x1049011,x1049010,x104904,x104909,x104908,x104902))),x104907))+P107(f866(f866(f336(f937(x104901,a925)),f866(f866(f44(x104902,f937(x104901,a925)),x104903),f866(f866(f8(f937(x104904,f937(x104901,a925)),f937(x104901,a925),x104902),f866(f44(x104904,f937(x104901,a925)),x104905)),x104906))),x104907))
% 157.76/157.53 [9374]E(x93741,x93742)+~P110(x93744)+~P25(x93743,x93744,x93745,f866(f866(f117(f937(x93743,a925)),f866(f179(x93743),x93741)),f866(f179(x93743),x93742)))+~E(f866(f179(x93743),x93741),f866(f179(x93743),x93742))+~P13(x93744,f866(f866(f161(x93743,x93744),x93745),x93742))+~P13(x93744,f866(f866(f161(x93743,x93744),x93745),x93741))+~P107(f866(f144(x93744),f866(f866(f161(x93743,x93744),x93745),x93742)))+~P107(f866(f144(x93744),f866(f866(f161(x93743,x93744),x93745),x93741)))
% 157.76/157.53 %EqnAxiom
% 157.76/157.53 [1]E(x11,x11)
% 157.76/157.53 [2]E(x22,x21)+~E(x21,x22)
% 157.76/157.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 157.76/157.53 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 157.76/157.53 [5]~E(x51,x52)+E(f107(x51),f107(x52))
% 157.76/157.53 [6]~E(x61,x62)+E(f23(x61),f23(x62))
% 157.76/157.53 [7]~E(x71,x72)+E(f195(x71),f195(x72))
% 157.76/157.53 [8]~E(x81,x82)+E(f866(x81,x83),f866(x82,x83))
% 157.76/157.53 [9]~E(x91,x92)+E(f866(x93,x91),f866(x93,x92))
% 157.76/157.53 [10]~E(x101,x102)+E(f29(x101),f29(x102))
% 157.76/157.53 [11]~E(x111,x112)+E(f8(x111,x113,x114),f8(x112,x113,x114))
% 157.76/157.53 [12]~E(x121,x122)+E(f8(x123,x121,x124),f8(x123,x122,x124))
% 157.76/157.53 [13]~E(x131,x132)+E(f8(x133,x134,x131),f8(x133,x134,x132))
% 157.76/157.53 [14]~E(x141,x142)+E(f108(x141),f108(x142))
% 157.76/157.53 [15]~E(x151,x152)+E(f241(x151),f241(x152))
% 157.76/157.53 [16]~E(x161,x162)+E(f117(x161),f117(x162))
% 157.76/157.53 [17]~E(x171,x172)+E(f242(x171),f242(x172))
% 157.76/157.53 [18]~E(x181,x182)+E(f109(x181),f109(x182))
% 157.76/157.53 [19]~E(x191,x192)+E(f32(x191),f32(x192))
% 157.76/157.53 [20]~E(x201,x202)+E(f90(x201),f90(x202))
% 157.76/157.53 [21]~E(x211,x212)+E(f937(x211,x213),f937(x212,x213))
% 157.76/157.53 [22]~E(x221,x222)+E(f937(x223,x221),f937(x223,x222))
% 157.76/157.53 [23]~E(x231,x232)+E(f69(x231,x233,x234),f69(x232,x233,x234))
% 157.76/157.53 [24]~E(x241,x242)+E(f69(x243,x241,x244),f69(x243,x242,x244))
% 157.76/157.53 [25]~E(x251,x252)+E(f69(x253,x254,x251),f69(x253,x254,x252))
% 157.76/157.53 [26]~E(x261,x262)+E(f511(x261,x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612),f511(x262,x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 157.76/157.53 [27]~E(x271,x272)+E(f511(x273,x271,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f511(x273,x272,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712))
% 157.76/157.53 [28]~E(x281,x282)+E(f511(x283,x284,x281,x285,x286,x287,x288,x289,x2810,x2811,x2812),f511(x283,x284,x282,x285,x286,x287,x288,x289,x2810,x2811,x2812))
% 157.76/157.53 [29]~E(x291,x292)+E(f511(x293,x294,x295,x291,x296,x297,x298,x299,x2910,x2911,x2912),f511(x293,x294,x295,x292,x296,x297,x298,x299,x2910,x2911,x2912))
% 157.76/157.53 [30]~E(x301,x302)+E(f511(x303,x304,x305,x306,x301,x307,x308,x309,x3010,x3011,x3012),f511(x303,x304,x305,x306,x302,x307,x308,x309,x3010,x3011,x3012))
% 157.76/157.53 [31]~E(x311,x312)+E(f511(x313,x314,x315,x316,x317,x311,x318,x319,x3110,x3111,x3112),f511(x313,x314,x315,x316,x317,x312,x318,x319,x3110,x3111,x3112))
% 157.76/157.53 [32]~E(x321,x322)+E(f511(x323,x324,x325,x326,x327,x328,x321,x329,x3210,x3211,x3212),f511(x323,x324,x325,x326,x327,x328,x322,x329,x3210,x3211,x3212))
% 157.76/157.53 [33]~E(x331,x332)+E(f511(x333,x334,x335,x336,x337,x338,x339,x331,x3310,x3311,x3312),f511(x333,x334,x335,x336,x337,x338,x339,x332,x3310,x3311,x3312))
% 157.76/157.53 [34]~E(x341,x342)+E(f511(x343,x344,x345,x346,x347,x348,x349,x3410,x341,x3411,x3412),f511(x343,x344,x345,x346,x347,x348,x349,x3410,x342,x3411,x3412))
% 157.76/157.53 [35]~E(x351,x352)+E(f511(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x351,x3512),f511(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x352,x3512))
% 157.76/157.53 [36]~E(x361,x362)+E(f511(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612,x361),f511(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612,x362))
% 157.76/157.53 [37]~E(x371,x372)+E(f84(x371),f84(x372))
% 157.76/157.53 [38]~E(x381,x382)+E(f316(x381),f316(x382))
% 157.76/157.53 [39]~E(x391,x392)+E(f510(x391,x393,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f510(x392,x393,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 157.76/157.53 [40]~E(x401,x402)+E(f510(x403,x401,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f510(x403,x402,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012))
% 157.76/157.53 [41]~E(x411,x412)+E(f510(x413,x414,x411,x415,x416,x417,x418,x419,x4110,x4111,x4112),f510(x413,x414,x412,x415,x416,x417,x418,x419,x4110,x4111,x4112))
% 157.76/157.53 [42]~E(x421,x422)+E(f510(x423,x424,x425,x421,x426,x427,x428,x429,x4210,x4211,x4212),f510(x423,x424,x425,x422,x426,x427,x428,x429,x4210,x4211,x4212))
% 157.76/157.53 [43]~E(x431,x432)+E(f510(x433,x434,x435,x436,x431,x437,x438,x439,x4310,x4311,x4312),f510(x433,x434,x435,x436,x432,x437,x438,x439,x4310,x4311,x4312))
% 157.76/157.53 [44]~E(x441,x442)+E(f510(x443,x444,x445,x446,x447,x441,x448,x449,x4410,x4411,x4412),f510(x443,x444,x445,x446,x447,x442,x448,x449,x4410,x4411,x4412))
% 157.76/157.53 [45]~E(x451,x452)+E(f510(x453,x454,x455,x456,x457,x458,x451,x459,x4510,x4511,x4512),f510(x453,x454,x455,x456,x457,x458,x452,x459,x4510,x4511,x4512))
% 157.76/157.53 [46]~E(x461,x462)+E(f510(x463,x464,x465,x466,x467,x468,x469,x461,x4610,x4611,x4612),f510(x463,x464,x465,x466,x467,x468,x469,x462,x4610,x4611,x4612))
% 157.76/157.53 [47]~E(x471,x472)+E(f510(x473,x474,x475,x476,x477,x478,x479,x4710,x471,x4711,x4712),f510(x473,x474,x475,x476,x477,x478,x479,x4710,x472,x4711,x4712))
% 157.76/157.53 [48]~E(x481,x482)+E(f510(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x481,x4812),f510(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x482,x4812))
% 157.76/157.53 [49]~E(x491,x492)+E(f510(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x4912,x491),f510(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x4912,x492))
% 157.76/157.53 [50]~E(x501,x502)+E(f4(x501),f4(x502))
% 157.76/157.53 [51]~E(x511,x512)+E(f336(x511),f336(x512))
% 157.76/157.53 [52]~E(x521,x522)+E(f86(x521),f86(x522))
% 157.76/157.53 [53]~E(x531,x532)+E(f118(x531),f118(x532))
% 157.76/157.53 [54]~E(x541,x542)+E(f243(x541),f243(x542))
% 157.76/157.53 [55]~E(x551,x552)+E(f929(x551),f929(x552))
% 157.76/157.53 [56]~E(x561,x562)+E(f934(x561),f934(x562))
% 157.76/157.53 [57]~E(x571,x572)+E(f931(x571),f931(x572))
% 157.76/157.53 [58]~E(x581,x582)+E(f932(x581),f932(x582))
% 157.76/157.53 [59]~E(x591,x592)+E(f33(x591),f33(x592))
% 157.76/157.53 [60]~E(x601,x602)+E(f35(x601),f35(x602))
% 157.76/157.53 [61]~E(x611,x612)+E(f110(x611),f110(x612))
% 157.76/157.53 [62]~E(x621,x622)+E(f34(x621),f34(x622))
% 157.76/157.53 [63]~E(x631,x632)+E(f196(x631),f196(x632))
% 157.76/157.53 [64]~E(x641,x642)+E(f7(x641,x643,x644),f7(x642,x643,x644))
% 157.76/157.53 [65]~E(x651,x652)+E(f7(x653,x651,x654),f7(x653,x652,x654))
% 157.76/157.53 [66]~E(x661,x662)+E(f7(x663,x664,x661),f7(x663,x664,x662))
% 157.76/157.53 [67]~E(x671,x672)+E(f85(x671),f85(x672))
% 157.76/157.53 [68]~E(x681,x682)+E(f244(x681),f244(x682))
% 157.76/157.53 [69]~E(x691,x692)+E(f880(x691,x693,x694),f880(x692,x693,x694))
% 157.76/157.53 [70]~E(x701,x702)+E(f880(x703,x701,x704),f880(x703,x702,x704))
% 157.76/157.53 [71]~E(x711,x712)+E(f880(x713,x714,x711),f880(x713,x714,x712))
% 157.76/157.53 [72]~E(x721,x722)+E(f586(x721,x723,x724),f586(x722,x723,x724))
% 157.76/157.53 [73]~E(x731,x732)+E(f586(x733,x731,x734),f586(x733,x732,x734))
% 157.76/157.53 [74]~E(x741,x742)+E(f586(x743,x744,x741),f586(x743,x744,x742))
% 157.76/157.53 [75]~E(x751,x752)+E(f260(x751,x753),f260(x752,x753))
% 157.76/157.53 [76]~E(x761,x762)+E(f260(x763,x761),f260(x763,x762))
% 157.76/157.53 [77]~E(x771,x772)+E(f6(x771,x773),f6(x772,x773))
% 157.76/157.53 [78]~E(x781,x782)+E(f6(x783,x781),f6(x783,x782))
% 157.76/157.53 [79]~E(x791,x792)+E(f65(x791),f65(x792))
% 157.76/157.53 [80]~E(x801,x802)+E(f141(x801),f141(x802))
% 157.76/157.53 [81]~E(x811,x812)+E(f81(x811),f81(x812))
% 157.76/157.53 [82]~E(x821,x822)+E(f87(x821),f87(x822))
% 157.76/157.53 [83]~E(x831,x832)+E(f66(x831),f66(x832))
% 157.76/157.53 [84]~E(x841,x842)+E(f50(x841,x843,x844),f50(x842,x843,x844))
% 157.76/157.53 [85]~E(x851,x852)+E(f50(x853,x851,x854),f50(x853,x852,x854))
% 157.76/157.53 [86]~E(x861,x862)+E(f50(x863,x864,x861),f50(x863,x864,x862))
% 157.76/157.53 [87]~E(x871,x872)+E(f161(x871,x873),f161(x872,x873))
% 157.76/157.53 [88]~E(x881,x882)+E(f161(x883,x881),f161(x883,x882))
% 157.76/157.53 [89]~E(x891,x892)+E(f445(x891,x893,x894,x895),f445(x892,x893,x894,x895))
% 157.76/157.53 [90]~E(x901,x902)+E(f445(x903,x901,x904,x905),f445(x903,x902,x904,x905))
% 157.76/157.53 [91]~E(x911,x912)+E(f445(x913,x914,x911,x915),f445(x913,x914,x912,x915))
% 157.76/157.53 [92]~E(x921,x922)+E(f445(x923,x924,x925,x921),f445(x923,x924,x925,x922))
% 157.76/157.53 [93]~E(x931,x932)+E(f802(x931,x933),f802(x932,x933))
% 157.76/157.53 [94]~E(x941,x942)+E(f802(x943,x941),f802(x943,x942))
% 157.76/157.53 [95]~E(x951,x952)+E(f453(x951,x953,x954,x955),f453(x952,x953,x954,x955))
% 157.76/157.53 [96]~E(x961,x962)+E(f453(x963,x961,x964,x965),f453(x963,x962,x964,x965))
% 157.76/157.53 [97]~E(x971,x972)+E(f453(x973,x974,x971,x975),f453(x973,x974,x972,x975))
% 157.76/157.53 [98]~E(x981,x982)+E(f453(x983,x984,x985,x981),f453(x983,x984,x985,x982))
% 157.76/157.53 [99]~E(x991,x992)+E(f143(x991,x993),f143(x992,x993))
% 157.76/157.53 [100]~E(x1001,x1002)+E(f143(x1003,x1001),f143(x1003,x1002))
% 157.76/157.53 [101]~E(x1011,x1012)+E(f168(x1011,x1013),f168(x1012,x1013))
% 157.76/157.53 [102]~E(x1021,x1022)+E(f168(x1023,x1021),f168(x1023,x1022))
% 157.76/157.53 [103]~E(x1031,x1032)+E(f144(x1031),f144(x1032))
% 157.76/157.53 [104]~E(x1041,x1042)+E(f297(x1041),f297(x1042))
% 157.76/157.53 [105]~E(x1051,x1052)+E(f876(x1051,x1053,x1054),f876(x1052,x1053,x1054))
% 157.76/157.53 [106]~E(x1061,x1062)+E(f876(x1063,x1061,x1064),f876(x1063,x1062,x1064))
% 157.76/157.53 [107]~E(x1071,x1072)+E(f876(x1073,x1074,x1071),f876(x1073,x1074,x1072))
% 157.76/157.53 [108]~E(x1081,x1082)+E(f310(x1081,x1083,x1084),f310(x1082,x1083,x1084))
% 157.76/157.53 [109]~E(x1091,x1092)+E(f310(x1093,x1091,x1094),f310(x1093,x1092,x1094))
% 157.76/157.53 [110]~E(x1101,x1102)+E(f310(x1103,x1104,x1101),f310(x1103,x1104,x1102))
% 157.76/157.53 [111]~E(x1111,x1112)+E(f536(x1111,x1113,x1114,x1115,x1116,x1117),f536(x1112,x1113,x1114,x1115,x1116,x1117))
% 157.76/157.53 [112]~E(x1121,x1122)+E(f536(x1123,x1121,x1124,x1125,x1126,x1127),f536(x1123,x1122,x1124,x1125,x1126,x1127))
% 157.76/157.53 [113]~E(x1131,x1132)+E(f536(x1133,x1134,x1131,x1135,x1136,x1137),f536(x1133,x1134,x1132,x1135,x1136,x1137))
% 157.76/157.53 [114]~E(x1141,x1142)+E(f536(x1143,x1144,x1145,x1141,x1146,x1147),f536(x1143,x1144,x1145,x1142,x1146,x1147))
% 157.76/157.53 [115]~E(x1151,x1152)+E(f536(x1153,x1154,x1155,x1156,x1151,x1157),f536(x1153,x1154,x1155,x1156,x1152,x1157))
% 157.76/157.53 [116]~E(x1161,x1162)+E(f536(x1163,x1164,x1165,x1166,x1167,x1161),f536(x1163,x1164,x1165,x1166,x1167,x1162))
% 157.76/157.53 [117]~E(x1171,x1172)+E(f262(x1171,x1173),f262(x1172,x1173))
% 157.76/157.53 [118]~E(x1181,x1182)+E(f262(x1183,x1181),f262(x1183,x1182))
% 157.76/157.53 [119]~E(x1191,x1192)+E(f16(x1191,x1193),f16(x1192,x1193))
% 157.76/157.53 [120]~E(x1201,x1202)+E(f16(x1203,x1201),f16(x1203,x1202))
% 157.76/157.53 [121]~E(x1211,x1212)+E(f40(x1211),f40(x1212))
% 157.76/157.53 [122]~E(x1221,x1222)+E(f186(x1221,x1223),f186(x1222,x1223))
% 157.76/157.53 [123]~E(x1231,x1232)+E(f186(x1233,x1231),f186(x1233,x1232))
% 157.76/157.53 [124]~E(x1241,x1242)+E(f936(x1241,x1243),f936(x1242,x1243))
% 157.76/157.53 [125]~E(x1251,x1252)+E(f936(x1253,x1251),f936(x1253,x1252))
% 157.76/157.53 [126]~E(x1261,x1262)+E(f78(x1261,x1263,x1264,x1265),f78(x1262,x1263,x1264,x1265))
% 157.76/157.53 [127]~E(x1271,x1272)+E(f78(x1273,x1271,x1274,x1275),f78(x1273,x1272,x1274,x1275))
% 157.76/157.53 [128]~E(x1281,x1282)+E(f78(x1283,x1284,x1281,x1285),f78(x1283,x1284,x1282,x1285))
% 157.76/157.53 [129]~E(x1291,x1292)+E(f78(x1293,x1294,x1295,x1291),f78(x1293,x1294,x1295,x1292))
% 157.76/157.53 [130]~E(x1301,x1302)+E(f12(x1301,x1303,x1304),f12(x1302,x1303,x1304))
% 157.76/157.53 [131]~E(x1311,x1312)+E(f12(x1313,x1311,x1314),f12(x1313,x1312,x1314))
% 157.76/157.53 [132]~E(x1321,x1322)+E(f12(x1323,x1324,x1321),f12(x1323,x1324,x1322))
% 157.76/157.53 [133]~E(x1331,x1332)+E(f265(x1331,x1333,x1334),f265(x1332,x1333,x1334))
% 157.76/157.53 [134]~E(x1341,x1342)+E(f265(x1343,x1341,x1344),f265(x1343,x1342,x1344))
% 157.76/157.53 [135]~E(x1351,x1352)+E(f265(x1353,x1354,x1351),f265(x1353,x1354,x1352))
% 157.76/157.53 [136]~E(x1361,x1362)+E(f70(x1361,x1363,x1364),f70(x1362,x1363,x1364))
% 157.76/157.53 [137]~E(x1371,x1372)+E(f70(x1373,x1371,x1374),f70(x1373,x1372,x1374))
% 157.76/157.53 [138]~E(x1381,x1382)+E(f70(x1383,x1384,x1381),f70(x1383,x1384,x1382))
% 157.76/157.53 [139]~E(x1391,x1392)+E(f68(x1391,x1393),f68(x1392,x1393))
% 157.76/157.53 [140]~E(x1401,x1402)+E(f68(x1403,x1401),f68(x1403,x1402))
% 157.76/157.53 [141]~E(x1411,x1412)+E(f748(x1411,x1413,x1414),f748(x1412,x1413,x1414))
% 157.76/157.53 [142]~E(x1421,x1422)+E(f748(x1423,x1421,x1424),f748(x1423,x1422,x1424))
% 157.76/157.53 [143]~E(x1431,x1432)+E(f748(x1433,x1434,x1431),f748(x1433,x1434,x1432))
% 157.76/157.53 [144]~E(x1441,x1442)+E(f80(x1441,x1443,x1444,x1445,x1446),f80(x1442,x1443,x1444,x1445,x1446))
% 157.76/157.53 [145]~E(x1451,x1452)+E(f80(x1453,x1451,x1454,x1455,x1456),f80(x1453,x1452,x1454,x1455,x1456))
% 157.76/157.53 [146]~E(x1461,x1462)+E(f80(x1463,x1464,x1461,x1465,x1466),f80(x1463,x1464,x1462,x1465,x1466))
% 157.76/157.53 [147]~E(x1471,x1472)+E(f80(x1473,x1474,x1475,x1471,x1476),f80(x1473,x1474,x1475,x1472,x1476))
% 157.76/157.53 [148]~E(x1481,x1482)+E(f80(x1483,x1484,x1485,x1486,x1481),f80(x1483,x1484,x1485,x1486,x1482))
% 157.76/157.53 [149]~E(x1491,x1492)+E(f188(x1491,x1493),f188(x1492,x1493))
% 157.76/157.53 [150]~E(x1501,x1502)+E(f188(x1503,x1501),f188(x1503,x1502))
% 157.76/157.53 [151]~E(x1511,x1512)+E(f320(x1511,x1513,x1514,x1515),f320(x1512,x1513,x1514,x1515))
% 157.76/157.53 [152]~E(x1521,x1522)+E(f320(x1523,x1521,x1524,x1525),f320(x1523,x1522,x1524,x1525))
% 157.76/157.53 [153]~E(x1531,x1532)+E(f320(x1533,x1534,x1531,x1535),f320(x1533,x1534,x1532,x1535))
% 157.76/157.53 [154]~E(x1541,x1542)+E(f320(x1543,x1544,x1545,x1541),f320(x1543,x1544,x1545,x1542))
% 157.76/157.53 [155]~E(x1551,x1552)+E(f596(x1551,x1553,x1554,x1555),f596(x1552,x1553,x1554,x1555))
% 157.76/157.53 [156]~E(x1561,x1562)+E(f596(x1563,x1561,x1564,x1565),f596(x1563,x1562,x1564,x1565))
% 157.76/157.53 [157]~E(x1571,x1572)+E(f596(x1573,x1574,x1571,x1575),f596(x1573,x1574,x1572,x1575))
% 157.76/157.53 [158]~E(x1581,x1582)+E(f596(x1583,x1584,x1585,x1581),f596(x1583,x1584,x1585,x1582))
% 157.76/157.53 [159]~E(x1591,x1592)+E(f252(x1591),f252(x1592))
% 157.76/157.53 [160]~E(x1601,x1602)+E(f158(x1601),f158(x1602))
% 157.76/157.53 [161]~E(x1611,x1612)+E(f325(x1611,x1613),f325(x1612,x1613))
% 157.76/157.53 [162]~E(x1621,x1622)+E(f325(x1623,x1621),f325(x1623,x1622))
% 157.76/157.53 [163]~E(x1631,x1632)+E(f44(x1631,x1633),f44(x1632,x1633))
% 157.76/157.53 [164]~E(x1641,x1642)+E(f44(x1643,x1641),f44(x1643,x1642))
% 157.76/157.53 [165]~E(x1651,x1652)+E(f88(x1651,x1653),f88(x1652,x1653))
% 157.76/157.53 [166]~E(x1661,x1662)+E(f88(x1663,x1661),f88(x1663,x1662))
% 157.76/157.53 [167]~E(x1671,x1672)+E(f309(x1671,x1673),f309(x1672,x1673))
% 157.76/157.53 [168]~E(x1681,x1682)+E(f309(x1683,x1681),f309(x1683,x1682))
% 157.76/157.53 [169]~E(x1691,x1692)+E(f650(x1691,x1693,x1694,x1695),f650(x1692,x1693,x1694,x1695))
% 157.76/157.53 [170]~E(x1701,x1702)+E(f650(x1703,x1701,x1704,x1705),f650(x1703,x1702,x1704,x1705))
% 157.76/157.53 [171]~E(x1711,x1712)+E(f650(x1713,x1714,x1711,x1715),f650(x1713,x1714,x1712,x1715))
% 157.76/157.53 [172]~E(x1721,x1722)+E(f650(x1723,x1724,x1725,x1721),f650(x1723,x1724,x1725,x1722))
% 157.76/157.53 [173]~E(x1731,x1732)+E(f112(x1731),f112(x1732))
% 157.76/157.53 [174]~E(x1741,x1742)+E(f113(x1741),f113(x1742))
% 157.76/157.53 [175]~E(x1751,x1752)+E(f335(x1751),f335(x1752))
% 157.76/157.53 [176]~E(x1761,x1762)+E(f267(x1761,x1763,x1764,x1765),f267(x1762,x1763,x1764,x1765))
% 157.76/157.53 [177]~E(x1771,x1772)+E(f267(x1773,x1771,x1774,x1775),f267(x1773,x1772,x1774,x1775))
% 157.76/157.53 [178]~E(x1781,x1782)+E(f267(x1783,x1784,x1781,x1785),f267(x1783,x1784,x1782,x1785))
% 157.76/157.53 [179]~E(x1791,x1792)+E(f267(x1793,x1794,x1795,x1791),f267(x1793,x1794,x1795,x1792))
% 157.76/157.53 [180]~E(x1801,x1802)+E(f552(x1801),f552(x1802))
% 157.76/157.53 [181]~E(x1811,x1812)+E(f389(x1811,x1813,x1814),f389(x1812,x1813,x1814))
% 157.76/157.53 [182]~E(x1821,x1822)+E(f389(x1823,x1821,x1824),f389(x1823,x1822,x1824))
% 157.76/157.53 [183]~E(x1831,x1832)+E(f389(x1833,x1834,x1831),f389(x1833,x1834,x1832))
% 157.76/157.53 [184]~E(x1841,x1842)+E(f11(x1841,x1843,x1844),f11(x1842,x1843,x1844))
% 157.76/157.53 [185]~E(x1851,x1852)+E(f11(x1853,x1851,x1854),f11(x1853,x1852,x1854))
% 157.76/157.53 [186]~E(x1861,x1862)+E(f11(x1863,x1864,x1861),f11(x1863,x1864,x1862))
% 157.76/157.53 [187]~E(x1871,x1872)+E(f249(x1871,x1873),f249(x1872,x1873))
% 157.76/157.53 [188]~E(x1881,x1882)+E(f249(x1883,x1881),f249(x1883,x1882))
% 157.76/157.53 [189]~E(x1891,x1892)+E(f641(x1891,x1893,x1894,x1895),f641(x1892,x1893,x1894,x1895))
% 157.76/157.53 [190]~E(x1901,x1902)+E(f641(x1903,x1901,x1904,x1905),f641(x1903,x1902,x1904,x1905))
% 157.76/157.53 [191]~E(x1911,x1912)+E(f641(x1913,x1914,x1911,x1915),f641(x1913,x1914,x1912,x1915))
% 157.76/157.53 [192]~E(x1921,x1922)+E(f641(x1923,x1924,x1925,x1921),f641(x1923,x1924,x1925,x1922))
% 157.76/157.53 [193]~E(x1931,x1932)+E(f764(x1931,x1933,x1934),f764(x1932,x1933,x1934))
% 157.76/157.53 [194]~E(x1941,x1942)+E(f764(x1943,x1941,x1944),f764(x1943,x1942,x1944))
% 157.76/157.53 [195]~E(x1951,x1952)+E(f764(x1953,x1954,x1951),f764(x1953,x1954,x1952))
% 157.76/157.53 [196]~E(x1961,x1962)+E(f266(x1961,x1963,x1964,x1965,x1966,x1967),f266(x1962,x1963,x1964,x1965,x1966,x1967))
% 157.76/157.53 [197]~E(x1971,x1972)+E(f266(x1973,x1971,x1974,x1975,x1976,x1977),f266(x1973,x1972,x1974,x1975,x1976,x1977))
% 157.76/157.53 [198]~E(x1981,x1982)+E(f266(x1983,x1984,x1981,x1985,x1986,x1987),f266(x1983,x1984,x1982,x1985,x1986,x1987))
% 157.76/157.53 [199]~E(x1991,x1992)+E(f266(x1993,x1994,x1995,x1991,x1996,x1997),f266(x1993,x1994,x1995,x1992,x1996,x1997))
% 157.76/157.53 [200]~E(x2001,x2002)+E(f266(x2003,x2004,x2005,x2006,x2001,x2007),f266(x2003,x2004,x2005,x2006,x2002,x2007))
% 157.76/157.53 [201]~E(x2011,x2012)+E(f266(x2013,x2014,x2015,x2016,x2017,x2011),f266(x2013,x2014,x2015,x2016,x2017,x2012))
% 157.76/157.53 [202]~E(x2021,x2022)+E(f120(x2021),f120(x2022))
% 157.76/157.53 [203]~E(x2031,x2032)+E(f270(x2031),f270(x2032))
% 157.76/157.53 [204]~E(x2041,x2042)+E(f245(x2041,x2043),f245(x2042,x2043))
% 157.76/157.53 [205]~E(x2051,x2052)+E(f245(x2053,x2051),f245(x2053,x2052))
% 157.76/157.53 [206]~E(x2061,x2062)+E(f5(x2061),f5(x2062))
% 157.76/157.53 [207]~E(x2071,x2072)+E(f561(x2071,x2073,x2074,x2075,x2076),f561(x2072,x2073,x2074,x2075,x2076))
% 157.76/157.53 [208]~E(x2081,x2082)+E(f561(x2083,x2081,x2084,x2085,x2086),f561(x2083,x2082,x2084,x2085,x2086))
% 157.76/157.53 [209]~E(x2091,x2092)+E(f561(x2093,x2094,x2091,x2095,x2096),f561(x2093,x2094,x2092,x2095,x2096))
% 157.76/157.53 [210]~E(x2101,x2102)+E(f561(x2103,x2104,x2105,x2101,x2106),f561(x2103,x2104,x2105,x2102,x2106))
% 157.76/157.53 [211]~E(x2111,x2112)+E(f561(x2113,x2114,x2115,x2116,x2111),f561(x2113,x2114,x2115,x2116,x2112))
% 157.76/157.53 [212]~E(x2121,x2122)+E(f259(x2121,x2123),f259(x2122,x2123))
% 157.76/157.53 [213]~E(x2131,x2132)+E(f259(x2133,x2131),f259(x2133,x2132))
% 157.76/157.53 [214]~E(x2141,x2142)+E(f18(x2141,x2143,x2144),f18(x2142,x2143,x2144))
% 157.76/157.53 [215]~E(x2151,x2152)+E(f18(x2153,x2151,x2154),f18(x2153,x2152,x2154))
% 157.76/157.53 [216]~E(x2161,x2162)+E(f18(x2163,x2164,x2161),f18(x2163,x2164,x2162))
% 157.76/157.53 [217]~E(x2171,x2172)+E(f52(x2171,x2173),f52(x2172,x2173))
% 157.76/157.53 [218]~E(x2181,x2182)+E(f52(x2183,x2181),f52(x2183,x2182))
% 157.76/157.53 [219]~E(x2191,x2192)+E(f184(x2191,x2193,x2194),f184(x2192,x2193,x2194))
% 157.76/157.53 [220]~E(x2201,x2202)+E(f184(x2203,x2201,x2204),f184(x2203,x2202,x2204))
% 157.76/157.53 [221]~E(x2211,x2212)+E(f184(x2213,x2214,x2211),f184(x2213,x2214,x2212))
% 157.76/157.53 [222]~E(x2221,x2222)+E(f190(x2221,x2223),f190(x2222,x2223))
% 157.76/157.53 [223]~E(x2231,x2232)+E(f190(x2233,x2231),f190(x2233,x2232))
% 157.76/157.53 [224]~E(x2241,x2242)+E(f179(x2241),f179(x2242))
% 157.76/157.53 [225]~E(x2251,x2252)+E(f569(x2251,x2253,x2254),f569(x2252,x2253,x2254))
% 157.76/157.53 [226]~E(x2261,x2262)+E(f569(x2263,x2261,x2264),f569(x2263,x2262,x2264))
% 157.76/157.53 [227]~E(x2271,x2272)+E(f569(x2273,x2274,x2271),f569(x2273,x2274,x2272))
% 157.76/157.53 [228]~E(x2281,x2282)+E(f740(x2281,x2283),f740(x2282,x2283))
% 157.76/157.53 [229]~E(x2291,x2292)+E(f740(x2293,x2291),f740(x2293,x2292))
% 157.76/157.53 [230]~E(x2301,x2302)+E(f378(x2301,x2303),f378(x2302,x2303))
% 157.76/157.53 [231]~E(x2311,x2312)+E(f378(x2313,x2311),f378(x2313,x2312))
% 157.76/157.53 [232]~E(x2321,x2322)+E(f701(x2321,x2323,x2324),f701(x2322,x2323,x2324))
% 157.76/157.53 [233]~E(x2331,x2332)+E(f701(x2333,x2331,x2334),f701(x2333,x2332,x2334))
% 157.76/157.53 [234]~E(x2341,x2342)+E(f701(x2343,x2344,x2341),f701(x2343,x2344,x2342))
% 157.76/157.53 [235]~E(x2351,x2352)+E(f171(x2351),f171(x2352))
% 157.76/157.53 [236]~E(x2361,x2362)+E(f547(x2361,x2363,x2364,x2365,x2366,x2367,x2368,x2369),f547(x2362,x2363,x2364,x2365,x2366,x2367,x2368,x2369))
% 157.76/157.53 [237]~E(x2371,x2372)+E(f547(x2373,x2371,x2374,x2375,x2376,x2377,x2378,x2379),f547(x2373,x2372,x2374,x2375,x2376,x2377,x2378,x2379))
% 157.76/157.53 [238]~E(x2381,x2382)+E(f547(x2383,x2384,x2381,x2385,x2386,x2387,x2388,x2389),f547(x2383,x2384,x2382,x2385,x2386,x2387,x2388,x2389))
% 157.76/157.53 [239]~E(x2391,x2392)+E(f547(x2393,x2394,x2395,x2391,x2396,x2397,x2398,x2399),f547(x2393,x2394,x2395,x2392,x2396,x2397,x2398,x2399))
% 157.76/157.53 [240]~E(x2401,x2402)+E(f547(x2403,x2404,x2405,x2406,x2401,x2407,x2408,x2409),f547(x2403,x2404,x2405,x2406,x2402,x2407,x2408,x2409))
% 157.76/157.53 [241]~E(x2411,x2412)+E(f547(x2413,x2414,x2415,x2416,x2417,x2411,x2418,x2419),f547(x2413,x2414,x2415,x2416,x2417,x2412,x2418,x2419))
% 157.76/157.53 [242]~E(x2421,x2422)+E(f547(x2423,x2424,x2425,x2426,x2427,x2428,x2421,x2429),f547(x2423,x2424,x2425,x2426,x2427,x2428,x2422,x2429))
% 157.76/157.53 [243]~E(x2431,x2432)+E(f547(x2433,x2434,x2435,x2436,x2437,x2438,x2439,x2431),f547(x2433,x2434,x2435,x2436,x2437,x2438,x2439,x2432))
% 157.76/157.53 [244]~E(x2441,x2442)+E(f14(x2441,x2443),f14(x2442,x2443))
% 157.76/157.53 [245]~E(x2451,x2452)+E(f14(x2453,x2451),f14(x2453,x2452))
% 157.76/157.53 [246]~E(x2461,x2462)+E(f314(x2461,x2463),f314(x2462,x2463))
% 157.76/157.53 [247]~E(x2471,x2472)+E(f314(x2473,x2471),f314(x2473,x2472))
% 157.76/157.53 [248]~E(x2481,x2482)+E(f73(x2481,x2483,x2484),f73(x2482,x2483,x2484))
% 157.76/157.53 [249]~E(x2491,x2492)+E(f73(x2493,x2491,x2494),f73(x2493,x2492,x2494))
% 157.76/157.53 [250]~E(x2501,x2502)+E(f73(x2503,x2504,x2501),f73(x2503,x2504,x2502))
% 157.76/157.53 [251]~E(x2511,x2512)+E(f145(x2511),f145(x2512))
% 157.76/157.53 [252]~E(x2521,x2522)+E(f172(x2521),f172(x2522))
% 157.76/157.53 [253]~E(x2531,x2532)+E(f317(x2531,x2533,x2534),f317(x2532,x2533,x2534))
% 157.76/157.53 [254]~E(x2541,x2542)+E(f317(x2543,x2541,x2544),f317(x2543,x2542,x2544))
% 157.76/157.53 [255]~E(x2551,x2552)+E(f317(x2553,x2554,x2551),f317(x2553,x2554,x2552))
% 157.76/157.53 [256]~E(x2561,x2562)+E(f818(x2561),f818(x2562))
% 157.76/157.53 [257]~E(x2571,x2572)+E(f15(x2571,x2573),f15(x2572,x2573))
% 157.76/157.53 [258]~E(x2581,x2582)+E(f15(x2583,x2581),f15(x2583,x2582))
% 157.76/157.53 [259]~E(x2591,x2592)+E(f649(x2591,x2593,x2594,x2595),f649(x2592,x2593,x2594,x2595))
% 157.76/157.53 [260]~E(x2601,x2602)+E(f649(x2603,x2601,x2604,x2605),f649(x2603,x2602,x2604,x2605))
% 157.76/157.53 [261]~E(x2611,x2612)+E(f649(x2613,x2614,x2611,x2615),f649(x2613,x2614,x2612,x2615))
% 157.76/157.53 [262]~E(x2621,x2622)+E(f649(x2623,x2624,x2625,x2621),f649(x2623,x2624,x2625,x2622))
% 157.76/157.53 [263]~E(x2631,x2632)+E(f166(x2631,x2633),f166(x2632,x2633))
% 157.76/157.53 [264]~E(x2641,x2642)+E(f166(x2643,x2641),f166(x2643,x2642))
% 157.76/157.53 [265]~E(x2651,x2652)+E(f323(x2651,x2653),f323(x2652,x2653))
% 157.76/157.53 [266]~E(x2661,x2662)+E(f323(x2663,x2661),f323(x2663,x2662))
% 157.76/157.53 [267]~E(x2671,x2672)+E(f176(x2671,x2673,x2674),f176(x2672,x2673,x2674))
% 157.76/157.53 [268]~E(x2681,x2682)+E(f176(x2683,x2681,x2684),f176(x2683,x2682,x2684))
% 157.76/157.53 [269]~E(x2691,x2692)+E(f176(x2693,x2694,x2691),f176(x2693,x2694,x2692))
% 157.76/157.53 [270]~E(x2701,x2702)+E(f167(x2701,x2703),f167(x2702,x2703))
% 157.76/157.53 [271]~E(x2711,x2712)+E(f167(x2713,x2711),f167(x2713,x2712))
% 157.76/157.53 [272]~E(x2721,x2722)+E(f702(x2721,x2723,x2724,x2725,x2726),f702(x2722,x2723,x2724,x2725,x2726))
% 157.76/157.53 [273]~E(x2731,x2732)+E(f702(x2733,x2731,x2734,x2735,x2736),f702(x2733,x2732,x2734,x2735,x2736))
% 157.76/157.53 [274]~E(x2741,x2742)+E(f702(x2743,x2744,x2741,x2745,x2746),f702(x2743,x2744,x2742,x2745,x2746))
% 157.76/157.53 [275]~E(x2751,x2752)+E(f702(x2753,x2754,x2755,x2751,x2756),f702(x2753,x2754,x2755,x2752,x2756))
% 157.76/157.53 [276]~E(x2761,x2762)+E(f702(x2763,x2764,x2765,x2766,x2761),f702(x2763,x2764,x2765,x2766,x2762))
% 157.76/157.53 [277]~E(x2771,x2772)+E(f315(x2771),f315(x2772))
% 157.76/157.53 [278]~E(x2781,x2782)+E(f185(x2781,x2783),f185(x2782,x2783))
% 157.76/157.53 [279]~E(x2791,x2792)+E(f185(x2793,x2791),f185(x2793,x2792))
% 157.76/157.53 [280]~E(x2801,x2802)+E(f293(x2801,x2803,x2804),f293(x2802,x2803,x2804))
% 157.76/157.53 [281]~E(x2811,x2812)+E(f293(x2813,x2811,x2814),f293(x2813,x2812,x2814))
% 157.76/157.53 [282]~E(x2821,x2822)+E(f293(x2823,x2824,x2821),f293(x2823,x2824,x2822))
% 157.76/157.53 [283]~E(x2831,x2832)+E(f296(x2831,x2833,x2834),f296(x2832,x2833,x2834))
% 157.76/157.53 [284]~E(x2841,x2842)+E(f296(x2843,x2841,x2844),f296(x2843,x2842,x2844))
% 157.76/157.53 [285]~E(x2851,x2852)+E(f296(x2853,x2854,x2851),f296(x2853,x2854,x2852))
% 157.76/157.53 [286]~E(x2861,x2862)+E(f646(x2861,x2863),f646(x2862,x2863))
% 157.76/157.53 [287]~E(x2871,x2872)+E(f646(x2873,x2871),f646(x2873,x2872))
% 157.76/157.53 [288]~E(x2881,x2882)+E(f45(x2881,x2883),f45(x2882,x2883))
% 157.76/157.53 [289]~E(x2891,x2892)+E(f45(x2893,x2891),f45(x2893,x2892))
% 157.76/157.53 [290]~E(x2901,x2902)+E(f51(x2901,x2903),f51(x2902,x2903))
% 157.76/157.53 [291]~E(x2911,x2912)+E(f51(x2913,x2911),f51(x2913,x2912))
% 157.76/157.53 [292]~E(x2921,x2922)+E(f121(x2921,x2923),f121(x2922,x2923))
% 157.76/157.53 [293]~E(x2931,x2932)+E(f121(x2933,x2931),f121(x2933,x2932))
% 157.76/157.53 [294]~E(x2941,x2942)+E(f42(x2941,x2943),f42(x2942,x2943))
% 157.76/157.53 [295]~E(x2951,x2952)+E(f42(x2953,x2951),f42(x2953,x2952))
% 157.76/157.53 [296]~E(x2961,x2962)+E(f423(x2961,x2963),f423(x2962,x2963))
% 157.76/157.53 [297]~E(x2971,x2972)+E(f423(x2973,x2971),f423(x2973,x2972))
% 157.76/157.53 [298]~E(x2981,x2982)+E(f159(x2981,x2983),f159(x2982,x2983))
% 157.76/157.53 [299]~E(x2991,x2992)+E(f159(x2993,x2991),f159(x2993,x2992))
% 157.76/157.53 [300]~E(x3001,x3002)+E(f774(x3001,x3003,x3004),f774(x3002,x3003,x3004))
% 157.76/157.53 [301]~E(x3011,x3012)+E(f774(x3013,x3011,x3014),f774(x3013,x3012,x3014))
% 157.76/157.53 [302]~E(x3021,x3022)+E(f774(x3023,x3024,x3021),f774(x3023,x3024,x3022))
% 157.76/157.53 [303]~E(x3031,x3032)+E(f198(x3031),f198(x3032))
% 157.76/157.53 [304]~E(x3041,x3042)+E(f174(x3041),f174(x3042))
% 157.76/157.53 [305]~E(x3051,x3052)+E(f122(x3051),f122(x3052))
% 157.76/157.53 [306]~E(x3061,x3062)+E(f41(x3061),f41(x3062))
% 157.76/157.53 [307]~E(x3071,x3072)+E(f871(x3071,x3073,x3074),f871(x3072,x3073,x3074))
% 157.76/157.53 [308]~E(x3081,x3082)+E(f871(x3083,x3081,x3084),f871(x3083,x3082,x3084))
% 157.76/157.53 [309]~E(x3091,x3092)+E(f871(x3093,x3094,x3091),f871(x3093,x3094,x3092))
% 157.76/157.53 [310]~E(x3101,x3102)+E(f872(x3101,x3103,x3104),f872(x3102,x3103,x3104))
% 157.76/157.53 [311]~E(x3111,x3112)+E(f872(x3113,x3111,x3114),f872(x3113,x3112,x3114))
% 157.76/157.53 [312]~E(x3121,x3122)+E(f872(x3123,x3124,x3121),f872(x3123,x3124,x3122))
% 157.76/157.53 [313]~E(x3131,x3132)+E(f142(x3131),f142(x3132))
% 157.76/157.53 [314]~E(x3141,x3142)+E(f97(x3141,x3143,x3144,x3145),f97(x3142,x3143,x3144,x3145))
% 157.76/157.53 [315]~E(x3151,x3152)+E(f97(x3153,x3151,x3154,x3155),f97(x3153,x3152,x3154,x3155))
% 157.76/157.53 [316]~E(x3161,x3162)+E(f97(x3163,x3164,x3161,x3165),f97(x3163,x3164,x3162,x3165))
% 157.76/157.53 [317]~E(x3171,x3172)+E(f97(x3173,x3174,x3175,x3171),f97(x3173,x3174,x3175,x3172))
% 157.76/157.53 [318]~E(x3181,x3182)+E(f250(x3181),f250(x3182))
% 157.76/157.53 [319]~E(x3191,x3192)+E(f103(x3191),f103(x3192))
% 157.76/157.53 [320]~E(x3201,x3202)+E(f96(x3201,x3203),f96(x3202,x3203))
% 157.76/157.53 [321]~E(x3211,x3212)+E(f96(x3213,x3211),f96(x3213,x3212))
% 157.76/157.53 [322]~E(x3221,x3222)+E(f322(x3221,x3223),f322(x3222,x3223))
% 157.76/157.53 [323]~E(x3231,x3232)+E(f322(x3233,x3231),f322(x3233,x3232))
% 157.76/157.53 [324]~E(x3241,x3242)+E(f938(x3241,x3243),f938(x3242,x3243))
% 157.76/157.53 [325]~E(x3251,x3252)+E(f938(x3253,x3251),f938(x3253,x3252))
% 157.76/157.53 [326]~E(x3261,x3262)+E(f935(x3261,x3263),f935(x3262,x3263))
% 157.76/157.53 [327]~E(x3271,x3272)+E(f935(x3273,x3271),f935(x3273,x3272))
% 157.76/157.53 [328]~E(x3281,x3282)+E(f782(x3281,x3283,x3284),f782(x3282,x3283,x3284))
% 157.76/157.53 [329]~E(x3291,x3292)+E(f782(x3293,x3291,x3294),f782(x3293,x3292,x3294))
% 157.76/157.53 [330]~E(x3301,x3302)+E(f782(x3303,x3304,x3301),f782(x3303,x3304,x3302))
% 157.76/157.53 [331]~E(x3311,x3312)+E(f54(x3311,x3313),f54(x3312,x3313))
% 157.76/157.53 [332]~E(x3321,x3322)+E(f54(x3323,x3321),f54(x3323,x3322))
% 157.76/157.53 [333]~E(x3331,x3332)+E(f570(x3331,x3333,x3334),f570(x3332,x3333,x3334))
% 157.76/157.53 [334]~E(x3341,x3342)+E(f570(x3343,x3341,x3344),f570(x3343,x3342,x3344))
% 157.76/157.53 [335]~E(x3351,x3352)+E(f570(x3353,x3354,x3351),f570(x3353,x3354,x3352))
% 157.76/157.53 [336]~E(x3361,x3362)+E(f183(x3361,x3363,x3364),f183(x3362,x3363,x3364))
% 157.76/157.53 [337]~E(x3371,x3372)+E(f183(x3373,x3371,x3374),f183(x3373,x3372,x3374))
% 157.76/157.53 [338]~E(x3381,x3382)+E(f183(x3383,x3384,x3381),f183(x3383,x3384,x3382))
% 157.76/157.53 [339]~E(x3391,x3392)+E(f178(x3391),f178(x3392))
% 157.76/157.53 [340]~E(x3401,x3402)+E(f175(x3401),f175(x3402))
% 157.76/157.53 [341]~E(x3411,x3412)+E(f154(x3411,x3413),f154(x3412,x3413))
% 157.76/157.53 [342]~E(x3421,x3422)+E(f154(x3423,x3421),f154(x3423,x3422))
% 157.76/157.53 [343]~E(x3431,x3432)+E(f164(x3431,x3433),f164(x3432,x3433))
% 157.76/157.53 [344]~E(x3441,x3442)+E(f164(x3443,x3441),f164(x3443,x3442))
% 157.76/157.53 [345]~E(x3451,x3452)+E(f292(x3451,x3453),f292(x3452,x3453))
% 157.76/157.53 [346]~E(x3461,x3462)+E(f292(x3463,x3461),f292(x3463,x3462))
% 157.76/157.53 [347]~E(x3471,x3472)+E(f272(x3471,x3473),f272(x3472,x3473))
% 157.76/157.53 [348]~E(x3481,x3482)+E(f272(x3483,x3481),f272(x3483,x3482))
% 157.76/157.53 [349]~E(x3491,x3492)+E(f875(x3491,x3493,x3494,x3495,x3496),f875(x3492,x3493,x3494,x3495,x3496))
% 157.76/157.53 [350]~E(x3501,x3502)+E(f875(x3503,x3501,x3504,x3505,x3506),f875(x3503,x3502,x3504,x3505,x3506))
% 157.76/157.53 [351]~E(x3511,x3512)+E(f875(x3513,x3514,x3511,x3515,x3516),f875(x3513,x3514,x3512,x3515,x3516))
% 157.76/157.53 [352]~E(x3521,x3522)+E(f875(x3523,x3524,x3525,x3521,x3526),f875(x3523,x3524,x3525,x3522,x3526))
% 157.76/157.53 [353]~E(x3531,x3532)+E(f875(x3533,x3534,x3535,x3536,x3531),f875(x3533,x3534,x3535,x3536,x3532))
% 157.76/157.53 [354]~E(x3541,x3542)+E(f182(x3541),f182(x3542))
% 157.76/157.53 [355]~E(x3551,x3552)+E(f817(x3551),f817(x3552))
% 157.76/157.53 [356]~E(x3561,x3562)+E(f126(x3561),f126(x3562))
% 157.76/157.53 [357]~E(x3571,x3572)+E(f318(x3571,x3573,x3574),f318(x3572,x3573,x3574))
% 157.76/157.53 [358]~E(x3581,x3582)+E(f318(x3583,x3581,x3584),f318(x3583,x3582,x3584))
% 157.76/157.53 [359]~E(x3591,x3592)+E(f318(x3593,x3594,x3591),f318(x3593,x3594,x3592))
% 157.76/157.53 [360]~E(x3601,x3602)+E(f294(x3601,x3603),f294(x3602,x3603))
% 157.76/157.53 [361]~E(x3611,x3612)+E(f294(x3613,x3611),f294(x3613,x3612))
% 157.76/157.53 [362]~E(x3621,x3622)+E(f26(x3621,x3623),f26(x3622,x3623))
% 157.76/157.53 [363]~E(x3631,x3632)+E(f26(x3633,x3631),f26(x3633,x3632))
% 157.76/157.53 [364]~E(x3641,x3642)+E(f877(x3641,x3643,x3644),f877(x3642,x3643,x3644))
% 157.76/157.53 [365]~E(x3651,x3652)+E(f877(x3653,x3651,x3654),f877(x3653,x3652,x3654))
% 157.76/157.53 [366]~E(x3661,x3662)+E(f877(x3663,x3664,x3661),f877(x3663,x3664,x3662))
% 157.76/157.53 [367]~E(x3671,x3672)+E(f13(x3671,x3673),f13(x3672,x3673))
% 157.76/157.53 [368]~E(x3681,x3682)+E(f13(x3683,x3681),f13(x3683,x3682))
% 157.76/157.53 [369]~E(x3691,x3692)+E(f521(x3691,x3693,x3694,x3695,x3696),f521(x3692,x3693,x3694,x3695,x3696))
% 157.76/157.53 [370]~E(x3701,x3702)+E(f521(x3703,x3701,x3704,x3705,x3706),f521(x3703,x3702,x3704,x3705,x3706))
% 157.76/157.53 [371]~E(x3711,x3712)+E(f521(x3713,x3714,x3711,x3715,x3716),f521(x3713,x3714,x3712,x3715,x3716))
% 157.76/157.53 [372]~E(x3721,x3722)+E(f521(x3723,x3724,x3725,x3721,x3726),f521(x3723,x3724,x3725,x3722,x3726))
% 157.76/157.53 [373]~E(x3731,x3732)+E(f521(x3733,x3734,x3735,x3736,x3731),f521(x3733,x3734,x3735,x3736,x3732))
% 157.76/157.53 [374]~E(x3741,x3742)+E(f9(x3741,x3743),f9(x3742,x3743))
% 157.76/157.53 [375]~E(x3751,x3752)+E(f9(x3753,x3751),f9(x3753,x3752))
% 157.76/157.53 [376]~E(x3761,x3762)+E(f149(x3761,x3763,x3764,x3765),f149(x3762,x3763,x3764,x3765))
% 157.76/157.53 [377]~E(x3771,x3772)+E(f149(x3773,x3771,x3774,x3775),f149(x3773,x3772,x3774,x3775))
% 157.76/157.53 [378]~E(x3781,x3782)+E(f149(x3783,x3784,x3781,x3785),f149(x3783,x3784,x3782,x3785))
% 157.76/157.53 [379]~E(x3791,x3792)+E(f149(x3793,x3794,x3795,x3791),f149(x3793,x3794,x3795,x3792))
% 157.76/157.53 [380]~E(x3801,x3802)+E(f327(x3801,x3803),f327(x3802,x3803))
% 157.76/157.53 [381]~E(x3811,x3812)+E(f327(x3813,x3811),f327(x3813,x3812))
% 157.76/157.53 [382]~E(x3821,x3822)+E(f92(x3821,x3823),f92(x3822,x3823))
% 157.76/157.53 [383]~E(x3831,x3832)+E(f92(x3833,x3831),f92(x3833,x3832))
% 157.76/157.53 [384]~E(x3841,x3842)+E(f91(x3841,x3843),f91(x3842,x3843))
% 157.76/157.53 [385]~E(x3851,x3852)+E(f91(x3853,x3851),f91(x3853,x3852))
% 157.76/157.53 [386]~E(x3861,x3862)+E(f264(x3861,x3863),f264(x3862,x3863))
% 157.76/157.53 [387]~E(x3871,x3872)+E(f264(x3873,x3871),f264(x3873,x3872))
% 157.76/157.53 [388]~E(x3881,x3882)+E(f221(x3881),f221(x3882))
% 157.76/157.53 [389]~E(x3891,x3892)+E(f31(x3891,x3893),f31(x3892,x3893))
% 157.76/157.53 [390]~E(x3901,x3902)+E(f31(x3903,x3901),f31(x3903,x3902))
% 157.76/157.53 [391]~E(x3911,x3912)+E(f30(x3911,x3913),f30(x3912,x3913))
% 157.76/157.53 [392]~E(x3921,x3922)+E(f30(x3923,x3921),f30(x3923,x3922))
% 157.76/157.53 [393]~E(x3931,x3932)+E(f402(x3931,x3933,x3934,x3935,x3936),f402(x3932,x3933,x3934,x3935,x3936))
% 157.76/157.53 [394]~E(x3941,x3942)+E(f402(x3943,x3941,x3944,x3945,x3946),f402(x3943,x3942,x3944,x3945,x3946))
% 157.76/157.53 [395]~E(x3951,x3952)+E(f402(x3953,x3954,x3951,x3955,x3956),f402(x3953,x3954,x3952,x3955,x3956))
% 157.76/157.53 [396]~E(x3961,x3962)+E(f402(x3963,x3964,x3965,x3961,x3966),f402(x3963,x3964,x3965,x3962,x3966))
% 157.76/157.53 [397]~E(x3971,x3972)+E(f402(x3973,x3974,x3975,x3976,x3971),f402(x3973,x3974,x3975,x3976,x3972))
% 157.76/157.53 [398]~E(x3981,x3982)+E(f67(x3981,x3983,x3984),f67(x3982,x3983,x3984))
% 157.76/157.53 [399]~E(x3991,x3992)+E(f67(x3993,x3991,x3994),f67(x3993,x3992,x3994))
% 157.76/157.53 [400]~E(x4001,x4002)+E(f67(x4003,x4004,x4001),f67(x4003,x4004,x4002))
% 157.76/157.53 [401]~E(x4011,x4012)+E(f426(x4011),f426(x4012))
% 157.76/157.53 [402]~E(x4021,x4022)+E(f344(x4021,x4023,x4024),f344(x4022,x4023,x4024))
% 157.76/157.53 [403]~E(x4031,x4032)+E(f344(x4033,x4031,x4034),f344(x4033,x4032,x4034))
% 157.76/157.53 [404]~E(x4041,x4042)+E(f344(x4043,x4044,x4041),f344(x4043,x4044,x4042))
% 157.76/157.53 [405]~E(x4051,x4052)+E(f457(x4051,x4053,x4054,x4055),f457(x4052,x4053,x4054,x4055))
% 157.76/157.53 [406]~E(x4061,x4062)+E(f457(x4063,x4061,x4064,x4065),f457(x4063,x4062,x4064,x4065))
% 157.76/157.53 [407]~E(x4071,x4072)+E(f457(x4073,x4074,x4071,x4075),f457(x4073,x4074,x4072,x4075))
% 157.76/157.53 [408]~E(x4081,x4082)+E(f457(x4083,x4084,x4085,x4081),f457(x4083,x4084,x4085,x4082))
% 157.76/157.53 [409]~E(x4091,x4092)+E(f55(x4091,x4093),f55(x4092,x4093))
% 157.76/157.53 [410]~E(x4101,x4102)+E(f55(x4103,x4101),f55(x4103,x4102))
% 157.76/157.53 [411]~E(x4111,x4112)+E(f767(x4111,x4113,x4114),f767(x4112,x4113,x4114))
% 157.76/157.53 [412]~E(x4121,x4122)+E(f767(x4123,x4121,x4124),f767(x4123,x4122,x4124))
% 157.76/157.53 [413]~E(x4131,x4132)+E(f767(x4133,x4134,x4131),f767(x4133,x4134,x4132))
% 157.76/157.53 [414]~E(x4141,x4142)+E(f146(x4141,x4143),f146(x4142,x4143))
% 157.76/157.53 [415]~E(x4151,x4152)+E(f146(x4153,x4151),f146(x4153,x4152))
% 157.76/157.53 [416]~E(x4161,x4162)+E(f616(x4161,x4163,x4164,x4165,x4166),f616(x4162,x4163,x4164,x4165,x4166))
% 157.76/157.53 [417]~E(x4171,x4172)+E(f616(x4173,x4171,x4174,x4175,x4176),f616(x4173,x4172,x4174,x4175,x4176))
% 157.76/157.53 [418]~E(x4181,x4182)+E(f616(x4183,x4184,x4181,x4185,x4186),f616(x4183,x4184,x4182,x4185,x4186))
% 157.76/157.53 [419]~E(x4191,x4192)+E(f616(x4193,x4194,x4195,x4191,x4196),f616(x4193,x4194,x4195,x4192,x4196))
% 157.76/157.53 [420]~E(x4201,x4202)+E(f616(x4203,x4204,x4205,x4206,x4201),f616(x4203,x4204,x4205,x4206,x4202))
% 157.76/157.53 [421]~E(x4211,x4212)+E(f127(x4211,x4213),f127(x4212,x4213))
% 157.76/157.53 [422]~E(x4221,x4222)+E(f127(x4223,x4221),f127(x4223,x4222))
% 157.76/157.53 [423]~E(x4231,x4232)+E(f308(x4231),f308(x4232))
% 157.76/157.53 [424]~E(x4241,x4242)+E(f53(x4241,x4243),f53(x4242,x4243))
% 157.76/157.53 [425]~E(x4251,x4252)+E(f53(x4253,x4251),f53(x4253,x4252))
% 157.76/157.53 [426]~E(x4261,x4262)+E(f192(x4261,x4263,x4264,x4265),f192(x4262,x4263,x4264,x4265))
% 157.76/157.53 [427]~E(x4271,x4272)+E(f192(x4273,x4271,x4274,x4275),f192(x4273,x4272,x4274,x4275))
% 157.76/157.53 [428]~E(x4281,x4282)+E(f192(x4283,x4284,x4281,x4285),f192(x4283,x4284,x4282,x4285))
% 157.76/157.53 [429]~E(x4291,x4292)+E(f192(x4293,x4294,x4295,x4291),f192(x4293,x4294,x4295,x4292))
% 157.76/157.53 [430]~E(x4301,x4302)+E(f256(x4301,x4303),f256(x4302,x4303))
% 157.76/157.53 [431]~E(x4311,x4312)+E(f256(x4313,x4311),f256(x4313,x4312))
% 157.76/157.53 [432]~E(x4321,x4322)+E(f151(x4321,x4323),f151(x4322,x4323))
% 157.76/157.53 [433]~E(x4331,x4332)+E(f151(x4333,x4331),f151(x4333,x4332))
% 157.76/157.53 [434]~E(x4341,x4342)+E(f28(x4341,x4343,x4344),f28(x4342,x4343,x4344))
% 157.76/157.53 [435]~E(x4351,x4352)+E(f28(x4353,x4351,x4354),f28(x4353,x4352,x4354))
% 157.76/157.53 [436]~E(x4361,x4362)+E(f28(x4363,x4364,x4361),f28(x4363,x4364,x4362))
% 157.76/157.53 [437]~E(x4371,x4372)+E(f301(x4371,x4373,x4374),f301(x4372,x4373,x4374))
% 157.76/157.53 [438]~E(x4381,x4382)+E(f301(x4383,x4381,x4384),f301(x4383,x4382,x4384))
% 157.76/157.53 [439]~E(x4391,x4392)+E(f301(x4393,x4394,x4391),f301(x4393,x4394,x4392))
% 157.76/157.53 [440]~E(x4401,x4402)+E(f512(x4401),f512(x4402))
% 157.76/157.53 [441]~E(x4411,x4412)+E(f160(x4411,x4413),f160(x4412,x4413))
% 157.76/157.53 [442]~E(x4421,x4422)+E(f160(x4423,x4421),f160(x4423,x4422))
% 157.76/157.53 [443]~E(x4431,x4432)+E(f271(x4431,x4433),f271(x4432,x4433))
% 157.76/157.53 [444]~E(x4441,x4442)+E(f271(x4443,x4441),f271(x4443,x4442))
% 157.76/157.53 [445]~E(x4451,x4452)+E(f177(x4451,x4453,x4454),f177(x4452,x4453,x4454))
% 157.76/157.53 [446]~E(x4461,x4462)+E(f177(x4463,x4461,x4464),f177(x4463,x4462,x4464))
% 157.76/157.53 [447]~E(x4471,x4472)+E(f177(x4473,x4474,x4471),f177(x4473,x4474,x4472))
% 157.76/157.53 [448]~E(x4481,x4482)+E(f299(x4481,x4483),f299(x4482,x4483))
% 157.76/157.53 [449]~E(x4491,x4492)+E(f299(x4493,x4491),f299(x4493,x4492))
% 157.76/157.53 [450]~E(x4501,x4502)+E(f424(x4501,x4503),f424(x4502,x4503))
% 157.76/157.53 [451]~E(x4511,x4512)+E(f424(x4513,x4511),f424(x4513,x4512))
% 157.76/157.53 [452]~E(x4521,x4522)+E(f279(x4521,x4523,x4524,x4525),f279(x4522,x4523,x4524,x4525))
% 157.76/157.53 [453]~E(x4531,x4532)+E(f279(x4533,x4531,x4534,x4535),f279(x4533,x4532,x4534,x4535))
% 157.76/157.53 [454]~E(x4541,x4542)+E(f279(x4543,x4544,x4541,x4545),f279(x4543,x4544,x4542,x4545))
% 157.76/157.53 [455]~E(x4551,x4552)+E(f279(x4553,x4554,x4555,x4551),f279(x4553,x4554,x4555,x4552))
% 157.76/157.53 [456]~E(x4561,x4562)+E(f290(x4561),f290(x4562))
% 157.76/157.53 [457]~E(x4571,x4572)+E(f10(x4571,x4573),f10(x4572,x4573))
% 157.76/157.53 [458]~E(x4581,x4582)+E(f10(x4583,x4581),f10(x4583,x4582))
% 157.76/157.53 [459]~E(x4591,x4592)+E(f814(x4591,x4593),f814(x4592,x4593))
% 157.76/157.53 [460]~E(x4601,x4602)+E(f814(x4603,x4601),f814(x4603,x4602))
% 157.76/157.53 [461]~E(x4611,x4612)+E(f471(x4611,x4613,x4614),f471(x4612,x4613,x4614))
% 157.76/157.53 [462]~E(x4621,x4622)+E(f471(x4623,x4621,x4624),f471(x4623,x4622,x4624))
% 157.76/157.53 [463]~E(x4631,x4632)+E(f471(x4633,x4634,x4631),f471(x4633,x4634,x4632))
% 157.76/157.53 [464]~E(x4641,x4642)+E(f600(x4641,x4643,x4644,x4645,x4646),f600(x4642,x4643,x4644,x4645,x4646))
% 157.76/157.53 [465]~E(x4651,x4652)+E(f600(x4653,x4651,x4654,x4655,x4656),f600(x4653,x4652,x4654,x4655,x4656))
% 157.76/157.53 [466]~E(x4661,x4662)+E(f600(x4663,x4664,x4661,x4665,x4666),f600(x4663,x4664,x4662,x4665,x4666))
% 157.76/157.53 [467]~E(x4671,x4672)+E(f600(x4673,x4674,x4675,x4671,x4676),f600(x4673,x4674,x4675,x4672,x4676))
% 157.76/157.53 [468]~E(x4681,x4682)+E(f600(x4683,x4684,x4685,x4686,x4681),f600(x4683,x4684,x4685,x4686,x4682))
% 157.76/157.53 [469]~E(x4691,x4692)+E(f71(x4691,x4693,x4694,x4695,x4696),f71(x4692,x4693,x4694,x4695,x4696))
% 157.76/157.53 [470]~E(x4701,x4702)+E(f71(x4703,x4701,x4704,x4705,x4706),f71(x4703,x4702,x4704,x4705,x4706))
% 157.76/157.53 [471]~E(x4711,x4712)+E(f71(x4713,x4714,x4711,x4715,x4716),f71(x4713,x4714,x4712,x4715,x4716))
% 157.76/157.53 [472]~E(x4721,x4722)+E(f71(x4723,x4724,x4725,x4721,x4726),f71(x4723,x4724,x4725,x4722,x4726))
% 157.76/157.53 [473]~E(x4731,x4732)+E(f71(x4733,x4734,x4735,x4736,x4731),f71(x4733,x4734,x4735,x4736,x4732))
% 157.76/157.53 [474]~E(x4741,x4742)+E(f519(x4741,x4743,x4744),f519(x4742,x4743,x4744))
% 157.76/157.53 [475]~E(x4751,x4752)+E(f519(x4753,x4751,x4754),f519(x4753,x4752,x4754))
% 157.76/157.53 [476]~E(x4761,x4762)+E(f519(x4763,x4764,x4761),f519(x4763,x4764,x4762))
% 157.76/157.53 [477]~E(x4771,x4772)+E(f894(x4771,x4773),f894(x4772,x4773))
% 157.76/157.53 [478]~E(x4781,x4782)+E(f894(x4783,x4781),f894(x4783,x4782))
% 157.76/157.53 [479]~E(x4791,x4792)+E(f721(x4791,x4793,x4794),f721(x4792,x4793,x4794))
% 157.76/157.53 [480]~E(x4801,x4802)+E(f721(x4803,x4801,x4804),f721(x4803,x4802,x4804))
% 157.76/157.53 [481]~E(x4811,x4812)+E(f721(x4813,x4814,x4811),f721(x4813,x4814,x4812))
% 157.76/157.53 [482]~E(x4821,x4822)+E(f610(x4821,x4823,x4824,x4825,x4826),f610(x4822,x4823,x4824,x4825,x4826))
% 157.76/157.53 [483]~E(x4831,x4832)+E(f610(x4833,x4831,x4834,x4835,x4836),f610(x4833,x4832,x4834,x4835,x4836))
% 157.76/157.53 [484]~E(x4841,x4842)+E(f610(x4843,x4844,x4841,x4845,x4846),f610(x4843,x4844,x4842,x4845,x4846))
% 157.76/157.53 [485]~E(x4851,x4852)+E(f610(x4853,x4854,x4855,x4851,x4856),f610(x4853,x4854,x4855,x4852,x4856))
% 157.76/157.53 [486]~E(x4861,x4862)+E(f610(x4863,x4864,x4865,x4866,x4861),f610(x4863,x4864,x4865,x4866,x4862))
% 157.76/157.53 [487]~E(x4871,x4872)+E(f618(x4871,x4873,x4874,x4875,x4876),f618(x4872,x4873,x4874,x4875,x4876))
% 157.76/157.53 [488]~E(x4881,x4882)+E(f618(x4883,x4881,x4884,x4885,x4886),f618(x4883,x4882,x4884,x4885,x4886))
% 157.76/157.53 [489]~E(x4891,x4892)+E(f618(x4893,x4894,x4891,x4895,x4896),f618(x4893,x4894,x4892,x4895,x4896))
% 157.76/157.53 [490]~E(x4901,x4902)+E(f618(x4903,x4904,x4905,x4901,x4906),f618(x4903,x4904,x4905,x4902,x4906))
% 157.76/157.53 [491]~E(x4911,x4912)+E(f618(x4913,x4914,x4915,x4916,x4911),f618(x4913,x4914,x4915,x4916,x4912))
% 157.76/157.53 [492]~E(x4921,x4922)+E(f878(x4921,x4923,x4924),f878(x4922,x4923,x4924))
% 157.76/157.53 [493]~E(x4931,x4932)+E(f878(x4933,x4931,x4934),f878(x4933,x4932,x4934))
% 157.76/157.53 [494]~E(x4941,x4942)+E(f878(x4943,x4944,x4941),f878(x4943,x4944,x4942))
% 157.76/157.53 [495]~E(x4951,x4952)+E(f851(x4951,x4953,x4954,x4955,x4956,x4957,x4958,x4959),f851(x4952,x4953,x4954,x4955,x4956,x4957,x4958,x4959))
% 157.76/157.53 [496]~E(x4961,x4962)+E(f851(x4963,x4961,x4964,x4965,x4966,x4967,x4968,x4969),f851(x4963,x4962,x4964,x4965,x4966,x4967,x4968,x4969))
% 157.76/157.53 [497]~E(x4971,x4972)+E(f851(x4973,x4974,x4971,x4975,x4976,x4977,x4978,x4979),f851(x4973,x4974,x4972,x4975,x4976,x4977,x4978,x4979))
% 157.76/157.53 [498]~E(x4981,x4982)+E(f851(x4983,x4984,x4985,x4981,x4986,x4987,x4988,x4989),f851(x4983,x4984,x4985,x4982,x4986,x4987,x4988,x4989))
% 157.76/157.53 [499]~E(x4991,x4992)+E(f851(x4993,x4994,x4995,x4996,x4991,x4997,x4998,x4999),f851(x4993,x4994,x4995,x4996,x4992,x4997,x4998,x4999))
% 157.76/157.53 [500]~E(x5001,x5002)+E(f851(x5003,x5004,x5005,x5006,x5007,x5001,x5008,x5009),f851(x5003,x5004,x5005,x5006,x5007,x5002,x5008,x5009))
% 157.76/157.53 [501]~E(x5011,x5012)+E(f851(x5013,x5014,x5015,x5016,x5017,x5018,x5011,x5019),f851(x5013,x5014,x5015,x5016,x5017,x5018,x5012,x5019))
% 157.76/157.53 [502]~E(x5021,x5022)+E(f851(x5023,x5024,x5025,x5026,x5027,x5028,x5029,x5021),f851(x5023,x5024,x5025,x5026,x5027,x5028,x5029,x5022))
% 157.76/157.53 [503]~E(x5031,x5032)+E(f82(x5031,x5033,x5034,x5035,x5036),f82(x5032,x5033,x5034,x5035,x5036))
% 157.76/157.53 [504]~E(x5041,x5042)+E(f82(x5043,x5041,x5044,x5045,x5046),f82(x5043,x5042,x5044,x5045,x5046))
% 157.76/157.53 [505]~E(x5051,x5052)+E(f82(x5053,x5054,x5051,x5055,x5056),f82(x5053,x5054,x5052,x5055,x5056))
% 157.76/157.53 [506]~E(x5061,x5062)+E(f82(x5063,x5064,x5065,x5061,x5066),f82(x5063,x5064,x5065,x5062,x5066))
% 157.76/157.53 [507]~E(x5071,x5072)+E(f82(x5073,x5074,x5075,x5076,x5071),f82(x5073,x5074,x5075,x5076,x5072))
% 157.76/157.53 [508]~E(x5081,x5082)+E(f116(x5081),f116(x5082))
% 157.76/157.53 [509]~E(x5091,x5092)+E(f456(x5091,x5093,x5094,x5095),f456(x5092,x5093,x5094,x5095))
% 157.76/157.53 [510]~E(x5101,x5102)+E(f456(x5103,x5101,x5104,x5105),f456(x5103,x5102,x5104,x5105))
% 157.76/157.53 [511]~E(x5111,x5112)+E(f456(x5113,x5114,x5111,x5115),f456(x5113,x5114,x5112,x5115))
% 157.76/157.53 [512]~E(x5121,x5122)+E(f456(x5123,x5124,x5125,x5121),f456(x5123,x5124,x5125,x5122))
% 157.76/157.53 [513]~E(x5131,x5132)+E(f123(x5131,x5133,x5134),f123(x5132,x5133,x5134))
% 157.76/157.53 [514]~E(x5141,x5142)+E(f123(x5143,x5141,x5144),f123(x5143,x5142,x5144))
% 157.76/157.53 [515]~E(x5151,x5152)+E(f123(x5153,x5154,x5151),f123(x5153,x5154,x5152))
% 157.76/157.53 [516]~E(x5161,x5162)+E(f328(x5161,x5163,x5164),f328(x5162,x5163,x5164))
% 157.76/157.53 [517]~E(x5171,x5172)+E(f328(x5173,x5171,x5174),f328(x5173,x5172,x5174))
% 157.76/157.53 [518]~E(x5181,x5182)+E(f328(x5183,x5184,x5181),f328(x5183,x5184,x5182))
% 157.76/157.53 [519]~E(x5191,x5192)+E(f762(x5191,x5193,x5194),f762(x5192,x5193,x5194))
% 157.76/157.53 [520]~E(x5201,x5202)+E(f762(x5203,x5201,x5204),f762(x5203,x5202,x5204))
% 157.76/157.53 [521]~E(x5211,x5212)+E(f762(x5213,x5214,x5211),f762(x5213,x5214,x5212))
% 157.76/157.53 [522]~E(x5221,x5222)+E(f744(x5221,x5223,x5224,x5225,x5226),f744(x5222,x5223,x5224,x5225,x5226))
% 157.76/157.53 [523]~E(x5231,x5232)+E(f744(x5233,x5231,x5234,x5235,x5236),f744(x5233,x5232,x5234,x5235,x5236))
% 157.76/157.53 [524]~E(x5241,x5242)+E(f744(x5243,x5244,x5241,x5245,x5246),f744(x5243,x5244,x5242,x5245,x5246))
% 157.76/157.53 [525]~E(x5251,x5252)+E(f744(x5253,x5254,x5255,x5251,x5256),f744(x5253,x5254,x5255,x5252,x5256))
% 157.76/157.53 [526]~E(x5261,x5262)+E(f744(x5263,x5264,x5265,x5266,x5261),f744(x5263,x5264,x5265,x5266,x5262))
% 157.76/157.53 [527]~E(x5271,x5272)+E(f62(x5271),f62(x5272))
% 157.76/157.53 [528]~E(x5281,x5282)+E(f810(x5281,x5283,x5284,x5285,x5286),f810(x5282,x5283,x5284,x5285,x5286))
% 157.76/157.53 [529]~E(x5291,x5292)+E(f810(x5293,x5291,x5294,x5295,x5296),f810(x5293,x5292,x5294,x5295,x5296))
% 157.76/157.53 [530]~E(x5301,x5302)+E(f810(x5303,x5304,x5301,x5305,x5306),f810(x5303,x5304,x5302,x5305,x5306))
% 157.76/157.53 [531]~E(x5311,x5312)+E(f810(x5313,x5314,x5315,x5311,x5316),f810(x5313,x5314,x5315,x5312,x5316))
% 157.76/157.53 [532]~E(x5321,x5322)+E(f810(x5323,x5324,x5325,x5326,x5321),f810(x5323,x5324,x5325,x5326,x5322))
% 157.76/157.53 [533]~E(x5331,x5332)+E(f639(x5331,x5333,x5334,x5335),f639(x5332,x5333,x5334,x5335))
% 157.76/157.53 [534]~E(x5341,x5342)+E(f639(x5343,x5341,x5344,x5345),f639(x5343,x5342,x5344,x5345))
% 157.76/157.53 [535]~E(x5351,x5352)+E(f639(x5353,x5354,x5351,x5355),f639(x5353,x5354,x5352,x5355))
% 157.76/157.53 [536]~E(x5361,x5362)+E(f639(x5363,x5364,x5365,x5361),f639(x5363,x5364,x5365,x5362))
% 157.76/157.53 [537]~E(x5371,x5372)+E(f474(x5371,x5373,x5374,x5375,x5376),f474(x5372,x5373,x5374,x5375,x5376))
% 157.76/157.53 [538]~E(x5381,x5382)+E(f474(x5383,x5381,x5384,x5385,x5386),f474(x5383,x5382,x5384,x5385,x5386))
% 157.76/157.53 [539]~E(x5391,x5392)+E(f474(x5393,x5394,x5391,x5395,x5396),f474(x5393,x5394,x5392,x5395,x5396))
% 157.76/157.53 [540]~E(x5401,x5402)+E(f474(x5403,x5404,x5405,x5401,x5406),f474(x5403,x5404,x5405,x5402,x5406))
% 157.76/157.53 [541]~E(x5411,x5412)+E(f474(x5413,x5414,x5415,x5416,x5411),f474(x5413,x5414,x5415,x5416,x5412))
% 157.76/157.53 [542]~E(x5421,x5422)+E(f321(x5421),f321(x5422))
% 157.76/157.53 [543]~E(x5431,x5432)+E(f345(x5431,x5433,x5434),f345(x5432,x5433,x5434))
% 157.76/157.53 [544]~E(x5441,x5442)+E(f345(x5443,x5441,x5444),f345(x5443,x5442,x5444))
% 157.76/157.53 [545]~E(x5451,x5452)+E(f345(x5453,x5454,x5451),f345(x5453,x5454,x5452))
% 157.76/157.53 [546]~E(x5461,x5462)+E(f507(x5461,x5463,x5464,x5465,x5466,x5467,x5468),f507(x5462,x5463,x5464,x5465,x5466,x5467,x5468))
% 157.76/157.53 [547]~E(x5471,x5472)+E(f507(x5473,x5471,x5474,x5475,x5476,x5477,x5478),f507(x5473,x5472,x5474,x5475,x5476,x5477,x5478))
% 157.76/157.53 [548]~E(x5481,x5482)+E(f507(x5483,x5484,x5481,x5485,x5486,x5487,x5488),f507(x5483,x5484,x5482,x5485,x5486,x5487,x5488))
% 157.76/157.53 [549]~E(x5491,x5492)+E(f507(x5493,x5494,x5495,x5491,x5496,x5497,x5498),f507(x5493,x5494,x5495,x5492,x5496,x5497,x5498))
% 157.76/157.53 [550]~E(x5501,x5502)+E(f507(x5503,x5504,x5505,x5506,x5501,x5507,x5508),f507(x5503,x5504,x5505,x5506,x5502,x5507,x5508))
% 157.76/157.53 [551]~E(x5511,x5512)+E(f507(x5513,x5514,x5515,x5516,x5517,x5511,x5518),f507(x5513,x5514,x5515,x5516,x5517,x5512,x5518))
% 157.76/157.53 [552]~E(x5521,x5522)+E(f507(x5523,x5524,x5525,x5526,x5527,x5528,x5521),f507(x5523,x5524,x5525,x5526,x5527,x5528,x5522))
% 157.76/157.53 [553]~E(x5531,x5532)+E(f191(x5531,x5533,x5534),f191(x5532,x5533,x5534))
% 157.76/157.53 [554]~E(x5541,x5542)+E(f191(x5543,x5541,x5544),f191(x5543,x5542,x5544))
% 157.76/157.53 [555]~E(x5551,x5552)+E(f191(x5553,x5554,x5551),f191(x5553,x5554,x5552))
% 157.76/157.53 [556]~E(x5561,x5562)+E(f688(x5561,x5563,x5564,x5565,x5566),f688(x5562,x5563,x5564,x5565,x5566))
% 157.76/157.53 [557]~E(x5571,x5572)+E(f688(x5573,x5571,x5574,x5575,x5576),f688(x5573,x5572,x5574,x5575,x5576))
% 157.76/157.53 [558]~E(x5581,x5582)+E(f688(x5583,x5584,x5581,x5585,x5586),f688(x5583,x5584,x5582,x5585,x5586))
% 157.76/157.53 [559]~E(x5591,x5592)+E(f688(x5593,x5594,x5595,x5591,x5596),f688(x5593,x5594,x5595,x5592,x5596))
% 157.76/157.53 [560]~E(x5601,x5602)+E(f688(x5603,x5604,x5605,x5606,x5601),f688(x5603,x5604,x5605,x5606,x5602))
% 157.76/157.53 [561]~E(x5611,x5612)+E(f414(x5611,x5613),f414(x5612,x5613))
% 157.76/157.53 [562]~E(x5621,x5622)+E(f414(x5623,x5621),f414(x5623,x5622))
% 157.76/157.53 [563]~E(x5631,x5632)+E(f157(x5631,x5633,x5634,x5635),f157(x5632,x5633,x5634,x5635))
% 157.76/157.53 [564]~E(x5641,x5642)+E(f157(x5643,x5641,x5644,x5645),f157(x5643,x5642,x5644,x5645))
% 157.76/157.53 [565]~E(x5651,x5652)+E(f157(x5653,x5654,x5651,x5655),f157(x5653,x5654,x5652,x5655))
% 157.76/157.53 [566]~E(x5661,x5662)+E(f157(x5663,x5664,x5665,x5661),f157(x5663,x5664,x5665,x5662))
% 157.76/157.53 [567]~E(x5671,x5672)+E(f690(x5671,x5673,x5674,x5675),f690(x5672,x5673,x5674,x5675))
% 157.76/157.53 [568]~E(x5681,x5682)+E(f690(x5683,x5681,x5684,x5685),f690(x5683,x5682,x5684,x5685))
% 157.76/157.53 [569]~E(x5691,x5692)+E(f690(x5693,x5694,x5691,x5695),f690(x5693,x5694,x5692,x5695))
% 157.76/157.53 [570]~E(x5701,x5702)+E(f690(x5703,x5704,x5705,x5701),f690(x5703,x5704,x5705,x5702))
% 157.76/157.53 [571]~E(x5711,x5712)+E(f442(x5711,x5713,x5714,x5715),f442(x5712,x5713,x5714,x5715))
% 157.76/157.53 [572]~E(x5721,x5722)+E(f442(x5723,x5721,x5724,x5725),f442(x5723,x5722,x5724,x5725))
% 157.76/157.53 [573]~E(x5731,x5732)+E(f442(x5733,x5734,x5731,x5735),f442(x5733,x5734,x5732,x5735))
% 157.76/157.53 [574]~E(x5741,x5742)+E(f442(x5743,x5744,x5745,x5741),f442(x5743,x5744,x5745,x5742))
% 157.76/157.53 [575]~E(x5751,x5752)+E(f461(x5751,x5753),f461(x5752,x5753))
% 157.76/157.53 [576]~E(x5761,x5762)+E(f461(x5763,x5761),f461(x5763,x5762))
% 157.76/157.53 [577]~E(x5771,x5772)+E(f567(x5771,x5773),f567(x5772,x5773))
% 157.76/157.53 [578]~E(x5781,x5782)+E(f567(x5783,x5781),f567(x5783,x5782))
% 157.76/157.53 [579]~E(x5791,x5792)+E(f225(x5791,x5793),f225(x5792,x5793))
% 157.76/157.53 [580]~E(x5801,x5802)+E(f225(x5803,x5801),f225(x5803,x5802))
% 157.76/157.53 [581]~E(x5811,x5812)+E(f350(x5811,x5813,x5814),f350(x5812,x5813,x5814))
% 157.76/157.53 [582]~E(x5821,x5822)+E(f350(x5823,x5821,x5824),f350(x5823,x5822,x5824))
% 157.76/157.53 [583]~E(x5831,x5832)+E(f350(x5833,x5834,x5831),f350(x5833,x5834,x5832))
% 157.76/157.53 [584]~E(x5841,x5842)+E(f578(x5841,x5843,x5844),f578(x5842,x5843,x5844))
% 157.76/157.53 [585]~E(x5851,x5852)+E(f578(x5853,x5851,x5854),f578(x5853,x5852,x5854))
% 157.76/157.53 [586]~E(x5861,x5862)+E(f578(x5863,x5864,x5861),f578(x5863,x5864,x5862))
% 157.76/157.53 [587]~E(x5871,x5872)+E(f291(x5871),f291(x5872))
% 157.76/157.53 [588]~E(x5881,x5882)+E(f808(x5881,x5883,x5884,x5885),f808(x5882,x5883,x5884,x5885))
% 157.76/157.53 [589]~E(x5891,x5892)+E(f808(x5893,x5891,x5894,x5895),f808(x5893,x5892,x5894,x5895))
% 157.76/157.53 [590]~E(x5901,x5902)+E(f808(x5903,x5904,x5901,x5905),f808(x5903,x5904,x5902,x5905))
% 157.76/157.53 [591]~E(x5911,x5912)+E(f808(x5913,x5914,x5915,x5911),f808(x5913,x5914,x5915,x5912))
% 157.76/157.53 [592]~E(x5921,x5922)+E(f852(x5921,x5923,x5924,x5925,x5926,x5927,x5928,x5929),f852(x5922,x5923,x5924,x5925,x5926,x5927,x5928,x5929))
% 157.76/157.53 [593]~E(x5931,x5932)+E(f852(x5933,x5931,x5934,x5935,x5936,x5937,x5938,x5939),f852(x5933,x5932,x5934,x5935,x5936,x5937,x5938,x5939))
% 157.76/157.53 [594]~E(x5941,x5942)+E(f852(x5943,x5944,x5941,x5945,x5946,x5947,x5948,x5949),f852(x5943,x5944,x5942,x5945,x5946,x5947,x5948,x5949))
% 157.76/157.53 [595]~E(x5951,x5952)+E(f852(x5953,x5954,x5955,x5951,x5956,x5957,x5958,x5959),f852(x5953,x5954,x5955,x5952,x5956,x5957,x5958,x5959))
% 157.76/157.53 [596]~E(x5961,x5962)+E(f852(x5963,x5964,x5965,x5966,x5961,x5967,x5968,x5969),f852(x5963,x5964,x5965,x5966,x5962,x5967,x5968,x5969))
% 157.76/157.53 [597]~E(x5971,x5972)+E(f852(x5973,x5974,x5975,x5976,x5977,x5971,x5978,x5979),f852(x5973,x5974,x5975,x5976,x5977,x5972,x5978,x5979))
% 157.76/157.53 [598]~E(x5981,x5982)+E(f852(x5983,x5984,x5985,x5986,x5987,x5988,x5981,x5989),f852(x5983,x5984,x5985,x5986,x5987,x5988,x5982,x5989))
% 157.76/157.53 [599]~E(x5991,x5992)+E(f852(x5993,x5994,x5995,x5996,x5997,x5998,x5999,x5991),f852(x5993,x5994,x5995,x5996,x5997,x5998,x5999,x5992))
% 157.76/157.53 [600]~E(x6001,x6002)+E(f712(x6001,x6003,x6004),f712(x6002,x6003,x6004))
% 157.76/157.53 [601]~E(x6011,x6012)+E(f712(x6013,x6011,x6014),f712(x6013,x6012,x6014))
% 157.76/157.53 [602]~E(x6021,x6022)+E(f712(x6023,x6024,x6021),f712(x6023,x6024,x6022))
% 157.76/157.53 [603]~E(x6031,x6032)+E(f302(x6031,x6033,x6034),f302(x6032,x6033,x6034))
% 157.76/157.53 [604]~E(x6041,x6042)+E(f302(x6043,x6041,x6044),f302(x6043,x6042,x6044))
% 157.76/157.53 [605]~E(x6051,x6052)+E(f302(x6053,x6054,x6051),f302(x6053,x6054,x6052))
% 157.76/157.53 [606]~E(x6061,x6062)+E(f346(x6061,x6063,x6064),f346(x6062,x6063,x6064))
% 157.76/157.53 [607]~E(x6071,x6072)+E(f346(x6073,x6071,x6074),f346(x6073,x6072,x6074))
% 157.76/157.53 [608]~E(x6081,x6082)+E(f346(x6083,x6084,x6081),f346(x6083,x6084,x6082))
% 157.76/157.53 [609]~E(x6091,x6092)+E(f725(x6091,x6093,x6094),f725(x6092,x6093,x6094))
% 157.76/157.53 [610]~E(x6101,x6102)+E(f725(x6103,x6101,x6104),f725(x6103,x6102,x6104))
% 157.76/157.53 [611]~E(x6111,x6112)+E(f725(x6113,x6114,x6111),f725(x6113,x6114,x6112))
% 157.76/157.53 [612]~E(x6121,x6122)+E(f727(x6121,x6123,x6124,x6125,x6126),f727(x6122,x6123,x6124,x6125,x6126))
% 157.76/157.53 [613]~E(x6131,x6132)+E(f727(x6133,x6131,x6134,x6135,x6136),f727(x6133,x6132,x6134,x6135,x6136))
% 157.76/157.53 [614]~E(x6141,x6142)+E(f727(x6143,x6144,x6141,x6145,x6146),f727(x6143,x6144,x6142,x6145,x6146))
% 157.76/157.53 [615]~E(x6151,x6152)+E(f727(x6153,x6154,x6155,x6151,x6156),f727(x6153,x6154,x6155,x6152,x6156))
% 157.76/157.53 [616]~E(x6161,x6162)+E(f727(x6163,x6164,x6165,x6166,x6161),f727(x6163,x6164,x6165,x6166,x6162))
% 157.76/157.53 [617]~E(x6171,x6172)+E(f587(x6171,x6173),f587(x6172,x6173))
% 157.76/157.53 [618]~E(x6181,x6182)+E(f587(x6183,x6181),f587(x6183,x6182))
% 157.76/157.53 [619]~E(x6191,x6192)+E(f879(x6191,x6193,x6194),f879(x6192,x6193,x6194))
% 157.76/157.53 [620]~E(x6201,x6202)+E(f879(x6203,x6201,x6204),f879(x6203,x6202,x6204))
% 157.76/157.53 [621]~E(x6211,x6212)+E(f879(x6213,x6214,x6211),f879(x6213,x6214,x6212))
% 157.76/157.53 [622]~E(x6221,x6222)+E(f625(x6221,x6223,x6224),f625(x6222,x6223,x6224))
% 157.76/157.53 [623]~E(x6231,x6232)+E(f625(x6233,x6231,x6234),f625(x6233,x6232,x6234))
% 157.76/157.53 [624]~E(x6241,x6242)+E(f625(x6243,x6244,x6241),f625(x6243,x6244,x6242))
% 157.76/157.53 [625]~E(x6251,x6252)+E(f800(x6251,x6253,x6254,x6255,x6256,x6257,x6258),f800(x6252,x6253,x6254,x6255,x6256,x6257,x6258))
% 157.76/157.53 [626]~E(x6261,x6262)+E(f800(x6263,x6261,x6264,x6265,x6266,x6267,x6268),f800(x6263,x6262,x6264,x6265,x6266,x6267,x6268))
% 157.76/157.53 [627]~E(x6271,x6272)+E(f800(x6273,x6274,x6271,x6275,x6276,x6277,x6278),f800(x6273,x6274,x6272,x6275,x6276,x6277,x6278))
% 157.76/157.53 [628]~E(x6281,x6282)+E(f800(x6283,x6284,x6285,x6281,x6286,x6287,x6288),f800(x6283,x6284,x6285,x6282,x6286,x6287,x6288))
% 157.76/157.53 [629]~E(x6291,x6292)+E(f800(x6293,x6294,x6295,x6296,x6291,x6297,x6298),f800(x6293,x6294,x6295,x6296,x6292,x6297,x6298))
% 157.76/157.53 [630]~E(x6301,x6302)+E(f800(x6303,x6304,x6305,x6306,x6307,x6301,x6308),f800(x6303,x6304,x6305,x6306,x6307,x6302,x6308))
% 157.76/157.53 [631]~E(x6311,x6312)+E(f800(x6313,x6314,x6315,x6316,x6317,x6318,x6311),f800(x6313,x6314,x6315,x6316,x6317,x6318,x6312))
% 157.76/157.53 [632]~E(x6321,x6322)+E(f72(x6321,x6323,x6324),f72(x6322,x6323,x6324))
% 157.76/157.53 [633]~E(x6331,x6332)+E(f72(x6333,x6331,x6334),f72(x6333,x6332,x6334))
% 157.76/157.53 [634]~E(x6341,x6342)+E(f72(x6343,x6344,x6341),f72(x6343,x6344,x6342))
% 157.76/157.53 [635]~E(x6351,x6352)+E(f155(x6351,x6353,x6354),f155(x6352,x6353,x6354))
% 157.76/157.53 [636]~E(x6361,x6362)+E(f155(x6363,x6361,x6364),f155(x6363,x6362,x6364))
% 157.76/157.53 [637]~E(x6371,x6372)+E(f155(x6373,x6374,x6371),f155(x6373,x6374,x6372))
% 157.76/157.53 [638]~E(x6381,x6382)+E(f352(x6381,x6383,x6384,x6385,x6386),f352(x6382,x6383,x6384,x6385,x6386))
% 157.76/157.53 [639]~E(x6391,x6392)+E(f352(x6393,x6391,x6394,x6395,x6396),f352(x6393,x6392,x6394,x6395,x6396))
% 157.76/157.53 [640]~E(x6401,x6402)+E(f352(x6403,x6404,x6401,x6405,x6406),f352(x6403,x6404,x6402,x6405,x6406))
% 157.76/157.53 [641]~E(x6411,x6412)+E(f352(x6413,x6414,x6415,x6411,x6416),f352(x6413,x6414,x6415,x6412,x6416))
% 157.76/157.53 [642]~E(x6421,x6422)+E(f352(x6423,x6424,x6425,x6426,x6421),f352(x6423,x6424,x6425,x6426,x6422))
% 157.76/157.53 [643]~E(x6431,x6432)+E(f548(x6431,x6433,x6434),f548(x6432,x6433,x6434))
% 157.76/157.53 [644]~E(x6441,x6442)+E(f548(x6443,x6441,x6444),f548(x6443,x6442,x6444))
% 157.76/157.53 [645]~E(x6451,x6452)+E(f548(x6453,x6454,x6451),f548(x6453,x6454,x6452))
% 157.76/157.53 [646]~E(x6461,x6462)+E(f251(x6461,x6463,x6464),f251(x6462,x6463,x6464))
% 157.76/157.53 [647]~E(x6471,x6472)+E(f251(x6473,x6471,x6474),f251(x6473,x6472,x6474))
% 157.76/157.53 [648]~E(x6481,x6482)+E(f251(x6483,x6484,x6481),f251(x6483,x6484,x6482))
% 157.76/157.53 [649]~E(x6491,x6492)+E(f825(x6491,x6493),f825(x6492,x6493))
% 157.76/157.53 [650]~E(x6501,x6502)+E(f825(x6503,x6501),f825(x6503,x6502))
% 157.76/157.53 [651]~E(x6511,x6512)+E(f132(x6511,x6513),f132(x6512,x6513))
% 157.76/157.53 [652]~E(x6521,x6522)+E(f132(x6523,x6521),f132(x6523,x6522))
% 157.76/157.53 [653]~E(x6531,x6532)+E(f675(x6531,x6533),f675(x6532,x6533))
% 157.76/157.53 [654]~E(x6541,x6542)+E(f675(x6543,x6541),f675(x6543,x6542))
% 157.76/157.53 [655]~E(x6551,x6552)+E(f795(x6551,x6553,x6554,x6555),f795(x6552,x6553,x6554,x6555))
% 157.76/157.53 [656]~E(x6561,x6562)+E(f795(x6563,x6561,x6564,x6565),f795(x6563,x6562,x6564,x6565))
% 157.76/157.53 [657]~E(x6571,x6572)+E(f795(x6573,x6574,x6571,x6575),f795(x6573,x6574,x6572,x6575))
% 157.76/157.53 [658]~E(x6581,x6582)+E(f795(x6583,x6584,x6585,x6581),f795(x6583,x6584,x6585,x6582))
% 157.76/157.53 [659]~E(x6591,x6592)+E(f496(x6591,x6593,x6594),f496(x6592,x6593,x6594))
% 157.76/157.53 [660]~E(x6601,x6602)+E(f496(x6603,x6601,x6604),f496(x6603,x6602,x6604))
% 157.76/157.53 [661]~E(x6611,x6612)+E(f496(x6613,x6614,x6611),f496(x6613,x6614,x6612))
% 157.76/157.53 [662]~E(x6621,x6622)+E(f393(x6621,x6623,x6624),f393(x6622,x6623,x6624))
% 157.76/157.53 [663]~E(x6631,x6632)+E(f393(x6633,x6631,x6634),f393(x6633,x6632,x6634))
% 157.76/157.53 [664]~E(x6641,x6642)+E(f393(x6643,x6644,x6641),f393(x6643,x6644,x6642))
% 157.76/157.53 [665]~E(x6651,x6652)+E(f685(x6651,x6653,x6654,x6655),f685(x6652,x6653,x6654,x6655))
% 157.76/157.53 [666]~E(x6661,x6662)+E(f685(x6663,x6661,x6664,x6665),f685(x6663,x6662,x6664,x6665))
% 157.76/157.53 [667]~E(x6671,x6672)+E(f685(x6673,x6674,x6671,x6675),f685(x6673,x6674,x6672,x6675))
% 157.76/157.53 [668]~E(x6681,x6682)+E(f685(x6683,x6684,x6685,x6681),f685(x6683,x6684,x6685,x6682))
% 157.76/157.53 [669]~E(x6691,x6692)+E(f821(x6691,x6693,x6694,x6695,x6696,x6697),f821(x6692,x6693,x6694,x6695,x6696,x6697))
% 157.76/157.53 [670]~E(x6701,x6702)+E(f821(x6703,x6701,x6704,x6705,x6706,x6707),f821(x6703,x6702,x6704,x6705,x6706,x6707))
% 157.76/157.53 [671]~E(x6711,x6712)+E(f821(x6713,x6714,x6711,x6715,x6716,x6717),f821(x6713,x6714,x6712,x6715,x6716,x6717))
% 157.76/157.53 [672]~E(x6721,x6722)+E(f821(x6723,x6724,x6725,x6721,x6726,x6727),f821(x6723,x6724,x6725,x6722,x6726,x6727))
% 157.76/157.53 [673]~E(x6731,x6732)+E(f821(x6733,x6734,x6735,x6736,x6731,x6737),f821(x6733,x6734,x6735,x6736,x6732,x6737))
% 157.76/157.53 [674]~E(x6741,x6742)+E(f821(x6743,x6744,x6745,x6746,x6747,x6741),f821(x6743,x6744,x6745,x6746,x6747,x6742))
% 157.76/157.53 [675]~E(x6751,x6752)+E(f313(x6751,x6753,x6754),f313(x6752,x6753,x6754))
% 157.76/157.53 [676]~E(x6761,x6762)+E(f313(x6763,x6761,x6764),f313(x6763,x6762,x6764))
% 157.76/157.53 [677]~E(x6771,x6772)+E(f313(x6773,x6774,x6771),f313(x6773,x6774,x6772))
% 157.76/157.53 [678]~E(x6781,x6782)+E(f556(x6781,x6783,x6784),f556(x6782,x6783,x6784))
% 157.76/157.53 [679]~E(x6791,x6792)+E(f556(x6793,x6791,x6794),f556(x6793,x6792,x6794))
% 157.76/157.53 [680]~E(x6801,x6802)+E(f556(x6803,x6804,x6801),f556(x6803,x6804,x6802))
% 157.76/157.53 [681]~E(x6811,x6812)+E(f83(x6811,x6813,x6814,x6815),f83(x6812,x6813,x6814,x6815))
% 157.76/157.53 [682]~E(x6821,x6822)+E(f83(x6823,x6821,x6824,x6825),f83(x6823,x6822,x6824,x6825))
% 157.76/157.53 [683]~E(x6831,x6832)+E(f83(x6833,x6834,x6831,x6835),f83(x6833,x6834,x6832,x6835))
% 157.76/157.53 [684]~E(x6841,x6842)+E(f83(x6843,x6844,x6845,x6841),f83(x6843,x6844,x6845,x6842))
% 157.76/157.53 [685]~E(x6851,x6852)+E(f479(x6851,x6853,x6854),f479(x6852,x6853,x6854))
% 157.76/157.53 [686]~E(x6861,x6862)+E(f479(x6863,x6861,x6864),f479(x6863,x6862,x6864))
% 157.76/157.53 [687]~E(x6871,x6872)+E(f479(x6873,x6874,x6871),f479(x6873,x6874,x6872))
% 157.76/157.53 [688]~E(x6881,x6882)+E(f839(x6881,x6883,x6884,x6885,x6886),f839(x6882,x6883,x6884,x6885,x6886))
% 157.76/157.53 [689]~E(x6891,x6892)+E(f839(x6893,x6891,x6894,x6895,x6896),f839(x6893,x6892,x6894,x6895,x6896))
% 157.76/157.53 [690]~E(x6901,x6902)+E(f839(x6903,x6904,x6901,x6905,x6906),f839(x6903,x6904,x6902,x6905,x6906))
% 157.76/157.53 [691]~E(x6911,x6912)+E(f839(x6913,x6914,x6915,x6911,x6916),f839(x6913,x6914,x6915,x6912,x6916))
% 157.76/157.53 [692]~E(x6921,x6922)+E(f839(x6923,x6924,x6925,x6926,x6921),f839(x6923,x6924,x6925,x6926,x6922))
% 157.76/157.53 [693]~E(x6931,x6932)+E(f500(x6931,x6933,x6934),f500(x6932,x6933,x6934))
% 157.76/157.53 [694]~E(x6941,x6942)+E(f500(x6943,x6941,x6944),f500(x6943,x6942,x6944))
% 157.76/157.53 [695]~E(x6951,x6952)+E(f500(x6953,x6954,x6951),f500(x6953,x6954,x6952))
% 157.76/157.53 [696]~E(x6961,x6962)+E(f358(x6961,x6963,x6964),f358(x6962,x6963,x6964))
% 157.76/157.53 [697]~E(x6971,x6972)+E(f358(x6973,x6971,x6974),f358(x6973,x6972,x6974))
% 157.76/157.53 [698]~E(x6981,x6982)+E(f358(x6983,x6984,x6981),f358(x6983,x6984,x6982))
% 157.76/157.53 [699]~E(x6991,x6992)+E(f434(x6991,x6993,x6994,x6995),f434(x6992,x6993,x6994,x6995))
% 157.76/157.53 [700]~E(x7001,x7002)+E(f434(x7003,x7001,x7004,x7005),f434(x7003,x7002,x7004,x7005))
% 157.76/157.53 [701]~E(x7011,x7012)+E(f434(x7013,x7014,x7011,x7015),f434(x7013,x7014,x7012,x7015))
% 157.76/157.53 [702]~E(x7021,x7022)+E(f434(x7023,x7024,x7025,x7021),f434(x7023,x7024,x7025,x7022))
% 157.76/157.53 [703]~E(x7031,x7032)+E(f630(x7031,x7033,x7034,x7035),f630(x7032,x7033,x7034,x7035))
% 157.76/157.53 [704]~E(x7041,x7042)+E(f630(x7043,x7041,x7044,x7045),f630(x7043,x7042,x7044,x7045))
% 157.76/157.53 [705]~E(x7051,x7052)+E(f630(x7053,x7054,x7051,x7055),f630(x7053,x7054,x7052,x7055))
% 157.76/157.53 [706]~E(x7061,x7062)+E(f630(x7063,x7064,x7065,x7061),f630(x7063,x7064,x7065,x7062))
% 157.76/157.53 [707]~E(x7071,x7072)+E(f653(x7071,x7073,x7074,x7075,x7076,x7077),f653(x7072,x7073,x7074,x7075,x7076,x7077))
% 157.76/157.53 [708]~E(x7081,x7082)+E(f653(x7083,x7081,x7084,x7085,x7086,x7087),f653(x7083,x7082,x7084,x7085,x7086,x7087))
% 157.76/157.53 [709]~E(x7091,x7092)+E(f653(x7093,x7094,x7091,x7095,x7096,x7097),f653(x7093,x7094,x7092,x7095,x7096,x7097))
% 157.76/157.53 [710]~E(x7101,x7102)+E(f653(x7103,x7104,x7105,x7101,x7106,x7107),f653(x7103,x7104,x7105,x7102,x7106,x7107))
% 157.76/157.53 [711]~E(x7111,x7112)+E(f653(x7113,x7114,x7115,x7116,x7111,x7117),f653(x7113,x7114,x7115,x7116,x7112,x7117))
% 157.76/157.53 [712]~E(x7121,x7122)+E(f653(x7123,x7124,x7125,x7126,x7127,x7121),f653(x7123,x7124,x7125,x7126,x7127,x7122))
% 157.76/157.53 [713]~E(x7131,x7132)+E(f312(x7131,x7133,x7134),f312(x7132,x7133,x7134))
% 157.76/157.53 [714]~E(x7141,x7142)+E(f312(x7143,x7141,x7144),f312(x7143,x7142,x7144))
% 157.76/157.53 [715]~E(x7151,x7152)+E(f312(x7153,x7154,x7151),f312(x7153,x7154,x7152))
% 157.76/157.53 [716]~E(x7161,x7162)+E(f915(x7161,x7163,x7164),f915(x7162,x7163,x7164))
% 157.76/157.53 [717]~E(x7171,x7172)+E(f915(x7173,x7171,x7174),f915(x7173,x7172,x7174))
% 157.76/157.53 [718]~E(x7181,x7182)+E(f915(x7183,x7184,x7181),f915(x7183,x7184,x7182))
% 157.76/157.53 [719]~E(x7191,x7192)+E(f43(x7191,x7193),f43(x7192,x7193))
% 157.76/157.53 [720]~E(x7201,x7202)+E(f43(x7203,x7201),f43(x7203,x7202))
% 157.76/157.53 [721]~E(x7211,x7212)+E(f626(x7211,x7213,x7214),f626(x7212,x7213,x7214))
% 157.76/157.53 [722]~E(x7221,x7222)+E(f626(x7223,x7221,x7224),f626(x7223,x7222,x7224))
% 157.76/157.53 [723]~E(x7231,x7232)+E(f626(x7233,x7234,x7231),f626(x7233,x7234,x7232))
% 157.76/157.53 [724]~E(x7241,x7242)+E(f462(x7241,x7243),f462(x7242,x7243))
% 157.76/157.53 [725]~E(x7251,x7252)+E(f462(x7253,x7251),f462(x7253,x7252))
% 157.76/157.53 [726]~E(x7261,x7262)+E(f133(x7261,x7263,x7264),f133(x7262,x7263,x7264))
% 157.76/157.53 [727]~E(x7271,x7272)+E(f133(x7273,x7271,x7274),f133(x7273,x7272,x7274))
% 157.76/157.53 [728]~E(x7281,x7282)+E(f133(x7283,x7284,x7281),f133(x7283,x7284,x7282))
% 157.76/157.53 [729]~E(x7291,x7292)+E(f887(x7291,x7293,x7294,x7295),f887(x7292,x7293,x7294,x7295))
% 157.76/157.53 [730]~E(x7301,x7302)+E(f887(x7303,x7301,x7304,x7305),f887(x7303,x7302,x7304,x7305))
% 157.76/157.53 [731]~E(x7311,x7312)+E(f887(x7313,x7314,x7311,x7315),f887(x7313,x7314,x7312,x7315))
% 157.76/157.53 [732]~E(x7321,x7322)+E(f887(x7323,x7324,x7325,x7321),f887(x7323,x7324,x7325,x7322))
% 157.76/157.53 [733]~E(x7331,x7332)+E(f660(x7331,x7333,x7334,x7335,x7336),f660(x7332,x7333,x7334,x7335,x7336))
% 157.76/157.53 [734]~E(x7341,x7342)+E(f660(x7343,x7341,x7344,x7345,x7346),f660(x7343,x7342,x7344,x7345,x7346))
% 157.76/157.53 [735]~E(x7351,x7352)+E(f660(x7353,x7354,x7351,x7355,x7356),f660(x7353,x7354,x7352,x7355,x7356))
% 157.76/157.53 [736]~E(x7361,x7362)+E(f660(x7363,x7364,x7365,x7361,x7366),f660(x7363,x7364,x7365,x7362,x7366))
% 157.76/157.53 [737]~E(x7371,x7372)+E(f660(x7373,x7374,x7375,x7376,x7371),f660(x7373,x7374,x7375,x7376,x7372))
% 157.76/157.53 [738]~E(x7381,x7382)+E(f554(x7381,x7383),f554(x7382,x7383))
% 157.76/157.53 [739]~E(x7391,x7392)+E(f554(x7393,x7391),f554(x7393,x7392))
% 157.76/157.53 [740]~E(x7401,x7402)+E(f732(x7401,x7403,x7404,x7405),f732(x7402,x7403,x7404,x7405))
% 157.76/157.53 [741]~E(x7411,x7412)+E(f732(x7413,x7411,x7414,x7415),f732(x7413,x7412,x7414,x7415))
% 157.76/157.53 [742]~E(x7421,x7422)+E(f732(x7423,x7424,x7421,x7425),f732(x7423,x7424,x7422,x7425))
% 157.76/157.53 [743]~E(x7431,x7432)+E(f732(x7433,x7434,x7435,x7431),f732(x7433,x7434,x7435,x7432))
% 157.76/157.53 [744]~E(x7441,x7442)+E(f900(x7441,x7443,x7444),f900(x7442,x7443,x7444))
% 157.76/157.53 [745]~E(x7451,x7452)+E(f900(x7453,x7451,x7454),f900(x7453,x7452,x7454))
% 157.76/157.53 [746]~E(x7461,x7462)+E(f900(x7463,x7464,x7461),f900(x7463,x7464,x7462))
% 157.76/157.53 [747]~E(x7471,x7472)+E(f873(x7471,x7473,x7474),f873(x7472,x7473,x7474))
% 157.76/157.53 [748]~E(x7481,x7482)+E(f873(x7483,x7481,x7484),f873(x7483,x7482,x7484))
% 157.76/157.53 [749]~E(x7491,x7492)+E(f873(x7493,x7494,x7491),f873(x7493,x7494,x7492))
% 157.76/157.53 [750]~E(x7501,x7502)+E(f459(x7501,x7503,x7504),f459(x7502,x7503,x7504))
% 157.76/157.53 [751]~E(x7511,x7512)+E(f459(x7513,x7511,x7514),f459(x7513,x7512,x7514))
% 157.76/157.53 [752]~E(x7521,x7522)+E(f459(x7523,x7524,x7521),f459(x7523,x7524,x7522))
% 157.76/157.53 [753]~E(x7531,x7532)+E(f213(x7531),f213(x7532))
% 157.76/157.53 [754]~E(x7541,x7542)+E(f201(x7541,x7543),f201(x7542,x7543))
% 157.76/157.53 [755]~E(x7551,x7552)+E(f201(x7553,x7551),f201(x7553,x7552))
% 157.76/157.53 [756]~E(x7561,x7562)+E(f769(x7561,x7563,x7564),f769(x7562,x7563,x7564))
% 157.76/157.53 [757]~E(x7571,x7572)+E(f769(x7573,x7571,x7574),f769(x7573,x7572,x7574))
% 157.76/157.53 [758]~E(x7581,x7582)+E(f769(x7583,x7584,x7581),f769(x7583,x7584,x7582))
% 157.76/157.53 [759]~E(x7591,x7592)+E(f558(x7591,x7593,x7594),f558(x7592,x7593,x7594))
% 157.76/157.53 [760]~E(x7601,x7602)+E(f558(x7603,x7601,x7604),f558(x7603,x7602,x7604))
% 157.76/157.53 [761]~E(x7611,x7612)+E(f558(x7613,x7614,x7611),f558(x7613,x7614,x7612))
% 157.76/157.53 [762]~E(x7621,x7622)+E(f295(x7621,x7623),f295(x7622,x7623))
% 157.76/157.53 [763]~E(x7631,x7632)+E(f295(x7633,x7631),f295(x7633,x7632))
% 157.76/157.53 [764]~E(x7641,x7642)+E(f644(x7641,x7643,x7644),f644(x7642,x7643,x7644))
% 157.76/157.53 [765]~E(x7651,x7652)+E(f644(x7653,x7651,x7654),f644(x7653,x7652,x7654))
% 157.76/157.53 [766]~E(x7661,x7662)+E(f644(x7663,x7664,x7661),f644(x7663,x7664,x7662))
% 157.76/157.53 [767]~E(x7671,x7672)+E(f689(x7671,x7673,x7674,x7675,x7676),f689(x7672,x7673,x7674,x7675,x7676))
% 157.76/157.53 [768]~E(x7681,x7682)+E(f689(x7683,x7681,x7684,x7685,x7686),f689(x7683,x7682,x7684,x7685,x7686))
% 157.76/157.53 [769]~E(x7691,x7692)+E(f689(x7693,x7694,x7691,x7695,x7696),f689(x7693,x7694,x7692,x7695,x7696))
% 157.76/157.53 [770]~E(x7701,x7702)+E(f689(x7703,x7704,x7705,x7701,x7706),f689(x7703,x7704,x7705,x7702,x7706))
% 157.76/157.53 [771]~E(x7711,x7712)+E(f689(x7713,x7714,x7715,x7716,x7711),f689(x7713,x7714,x7715,x7716,x7712))
% 157.76/157.53 [772]~E(x7721,x7722)+E(f741(x7721,x7723,x7724,x7725,x7726,x7727,x7728,x7729),f741(x7722,x7723,x7724,x7725,x7726,x7727,x7728,x7729))
% 157.76/157.53 [773]~E(x7731,x7732)+E(f741(x7733,x7731,x7734,x7735,x7736,x7737,x7738,x7739),f741(x7733,x7732,x7734,x7735,x7736,x7737,x7738,x7739))
% 157.76/157.53 [774]~E(x7741,x7742)+E(f741(x7743,x7744,x7741,x7745,x7746,x7747,x7748,x7749),f741(x7743,x7744,x7742,x7745,x7746,x7747,x7748,x7749))
% 157.76/157.53 [775]~E(x7751,x7752)+E(f741(x7753,x7754,x7755,x7751,x7756,x7757,x7758,x7759),f741(x7753,x7754,x7755,x7752,x7756,x7757,x7758,x7759))
% 157.76/157.53 [776]~E(x7761,x7762)+E(f741(x7763,x7764,x7765,x7766,x7761,x7767,x7768,x7769),f741(x7763,x7764,x7765,x7766,x7762,x7767,x7768,x7769))
% 157.76/157.53 [777]~E(x7771,x7772)+E(f741(x7773,x7774,x7775,x7776,x7777,x7771,x7778,x7779),f741(x7773,x7774,x7775,x7776,x7777,x7772,x7778,x7779))
% 157.76/157.53 [778]~E(x7781,x7782)+E(f741(x7783,x7784,x7785,x7786,x7787,x7788,x7781,x7789),f741(x7783,x7784,x7785,x7786,x7787,x7788,x7782,x7789))
% 157.76/157.53 [779]~E(x7791,x7792)+E(f741(x7793,x7794,x7795,x7796,x7797,x7798,x7799,x7791),f741(x7793,x7794,x7795,x7796,x7797,x7798,x7799,x7792))
% 157.76/157.53 [780]~E(x7801,x7802)+E(f326(x7801,x7803,x7804,x7805),f326(x7802,x7803,x7804,x7805))
% 157.76/157.53 [781]~E(x7811,x7812)+E(f326(x7813,x7811,x7814,x7815),f326(x7813,x7812,x7814,x7815))
% 157.76/157.53 [782]~E(x7821,x7822)+E(f326(x7823,x7824,x7821,x7825),f326(x7823,x7824,x7822,x7825))
% 157.76/157.53 [783]~E(x7831,x7832)+E(f326(x7833,x7834,x7835,x7831),f326(x7833,x7834,x7835,x7832))
% 157.76/157.53 [784]~E(x7841,x7842)+E(f611(x7841,x7843,x7844,x7845),f611(x7842,x7843,x7844,x7845))
% 157.76/157.53 [785]~E(x7851,x7852)+E(f611(x7853,x7851,x7854,x7855),f611(x7853,x7852,x7854,x7855))
% 157.76/157.53 [786]~E(x7861,x7862)+E(f611(x7863,x7864,x7861,x7865),f611(x7863,x7864,x7862,x7865))
% 157.76/157.53 [787]~E(x7871,x7872)+E(f611(x7873,x7874,x7875,x7871),f611(x7873,x7874,x7875,x7872))
% 157.76/157.53 [788]~E(x7881,x7882)+E(f209(x7881),f209(x7882))
% 157.76/157.53 [789]~E(x7891,x7892)+E(f403(x7891,x7893,x7894,x7895,x7896,x7897),f403(x7892,x7893,x7894,x7895,x7896,x7897))
% 157.76/157.53 [790]~E(x7901,x7902)+E(f403(x7903,x7901,x7904,x7905,x7906,x7907),f403(x7903,x7902,x7904,x7905,x7906,x7907))
% 157.76/157.53 [791]~E(x7911,x7912)+E(f403(x7913,x7914,x7911,x7915,x7916,x7917),f403(x7913,x7914,x7912,x7915,x7916,x7917))
% 157.76/157.53 [792]~E(x7921,x7922)+E(f403(x7923,x7924,x7925,x7921,x7926,x7927),f403(x7923,x7924,x7925,x7922,x7926,x7927))
% 157.76/157.53 [793]~E(x7931,x7932)+E(f403(x7933,x7934,x7935,x7936,x7931,x7937),f403(x7933,x7934,x7935,x7936,x7932,x7937))
% 157.76/157.53 [794]~E(x7941,x7942)+E(f403(x7943,x7944,x7945,x7946,x7947,x7941),f403(x7943,x7944,x7945,x7946,x7947,x7942))
% 157.76/157.53 [795]~E(x7951,x7952)+E(f391(x7951,x7953,x7954),f391(x7952,x7953,x7954))
% 157.76/157.53 [796]~E(x7961,x7962)+E(f391(x7963,x7961,x7964),f391(x7963,x7962,x7964))
% 157.76/157.53 [797]~E(x7971,x7972)+E(f391(x7973,x7974,x7971),f391(x7973,x7974,x7972))
% 157.76/157.53 [798]~E(x7981,x7982)+E(f258(x7981,x7983,x7984),f258(x7982,x7983,x7984))
% 157.76/157.53 [799]~E(x7991,x7992)+E(f258(x7993,x7991,x7994),f258(x7993,x7992,x7994))
% 157.76/157.53 [800]~E(x8001,x8002)+E(f258(x8003,x8004,x8001),f258(x8003,x8004,x8002))
% 157.76/157.53 [801]~E(x8011,x8012)+E(f840(x8011,x8013,x8014,x8015),f840(x8012,x8013,x8014,x8015))
% 157.76/157.53 [802]~E(x8021,x8022)+E(f840(x8023,x8021,x8024,x8025),f840(x8023,x8022,x8024,x8025))
% 157.76/157.53 [803]~E(x8031,x8032)+E(f840(x8033,x8034,x8031,x8035),f840(x8033,x8034,x8032,x8035))
% 157.76/157.53 [804]~E(x8041,x8042)+E(f840(x8043,x8044,x8045,x8041),f840(x8043,x8044,x8045,x8042))
% 157.76/157.53 [805]~E(x8051,x8052)+E(f148(x8051),f148(x8052))
% 157.76/157.53 [806]~E(x8061,x8062)+E(f655(x8061,x8063,x8064,x8065,x8066,x8067),f655(x8062,x8063,x8064,x8065,x8066,x8067))
% 157.76/157.53 [807]~E(x8071,x8072)+E(f655(x8073,x8071,x8074,x8075,x8076,x8077),f655(x8073,x8072,x8074,x8075,x8076,x8077))
% 157.76/157.53 [808]~E(x8081,x8082)+E(f655(x8083,x8084,x8081,x8085,x8086,x8087),f655(x8083,x8084,x8082,x8085,x8086,x8087))
% 157.76/157.53 [809]~E(x8091,x8092)+E(f655(x8093,x8094,x8095,x8091,x8096,x8097),f655(x8093,x8094,x8095,x8092,x8096,x8097))
% 157.76/157.53 [810]~E(x8101,x8102)+E(f655(x8103,x8104,x8105,x8106,x8101,x8107),f655(x8103,x8104,x8105,x8106,x8102,x8107))
% 157.76/157.53 [811]~E(x8111,x8112)+E(f655(x8113,x8114,x8115,x8116,x8117,x8111),f655(x8113,x8114,x8115,x8116,x8117,x8112))
% 157.76/157.53 [812]~E(x8121,x8122)+E(f530(x8121,x8123),f530(x8122,x8123))
% 157.76/157.53 [813]~E(x8131,x8132)+E(f530(x8133,x8131),f530(x8133,x8132))
% 157.76/157.53 [814]~E(x8141,x8142)+E(f93(x8141),f93(x8142))
% 157.76/157.53 [815]~E(x8151,x8152)+E(f27(x8151,x8153,x8154),f27(x8152,x8153,x8154))
% 157.76/157.53 [816]~E(x8161,x8162)+E(f27(x8163,x8161,x8164),f27(x8163,x8162,x8164))
% 157.76/157.53 [817]~E(x8171,x8172)+E(f27(x8173,x8174,x8171),f27(x8173,x8174,x8172))
% 157.76/157.53 [818]~E(x8181,x8182)+E(f60(x8181,x8183,x8184),f60(x8182,x8183,x8184))
% 157.76/157.53 [819]~E(x8191,x8192)+E(f60(x8193,x8191,x8194),f60(x8193,x8192,x8194))
% 157.76/157.53 [820]~E(x8201,x8202)+E(f60(x8203,x8204,x8201),f60(x8203,x8204,x8202))
% 157.76/157.53 [821]~E(x8211,x8212)+E(f98(x8211,x8213,x8214,x8215),f98(x8212,x8213,x8214,x8215))
% 157.76/157.53 [822]~E(x8221,x8222)+E(f98(x8223,x8221,x8224,x8225),f98(x8223,x8222,x8224,x8225))
% 157.76/157.53 [823]~E(x8231,x8232)+E(f98(x8233,x8234,x8231,x8235),f98(x8233,x8234,x8232,x8235))
% 157.76/157.53 [824]~E(x8241,x8242)+E(f98(x8243,x8244,x8245,x8241),f98(x8243,x8244,x8245,x8242))
% 157.76/157.53 [825]~E(x8251,x8252)+E(f478(x8251,x8253,x8254,x8255,x8256),f478(x8252,x8253,x8254,x8255,x8256))
% 157.76/157.53 [826]~E(x8261,x8262)+E(f478(x8263,x8261,x8264,x8265,x8266),f478(x8263,x8262,x8264,x8265,x8266))
% 157.76/157.53 [827]~E(x8271,x8272)+E(f478(x8273,x8274,x8271,x8275,x8276),f478(x8273,x8274,x8272,x8275,x8276))
% 157.76/157.53 [828]~E(x8281,x8282)+E(f478(x8283,x8284,x8285,x8281,x8286),f478(x8283,x8284,x8285,x8282,x8286))
% 157.76/157.53 [829]~E(x8291,x8292)+E(f478(x8293,x8294,x8295,x8296,x8291),f478(x8293,x8294,x8295,x8296,x8292))
% 157.76/157.53 [830]~E(x8301,x8302)+E(f738(x8301,x8303),f738(x8302,x8303))
% 157.76/157.53 [831]~E(x8311,x8312)+E(f738(x8313,x8311),f738(x8313,x8312))
% 157.76/157.53 [832]~E(x8321,x8322)+E(f483(x8321,x8323,x8324,x8325),f483(x8322,x8323,x8324,x8325))
% 157.76/157.53 [833]~E(x8331,x8332)+E(f483(x8333,x8331,x8334,x8335),f483(x8333,x8332,x8334,x8335))
% 157.76/157.53 [834]~E(x8341,x8342)+E(f483(x8343,x8344,x8341,x8345),f483(x8343,x8344,x8342,x8345))
% 157.76/157.53 [835]~E(x8351,x8352)+E(f483(x8353,x8354,x8355,x8351),f483(x8353,x8354,x8355,x8352))
% 157.76/157.53 [836]~E(x8361,x8362)+E(f874(x8361,x8363),f874(x8362,x8363))
% 157.76/157.53 [837]~E(x8371,x8372)+E(f874(x8373,x8371),f874(x8373,x8372))
% 157.76/157.53 [838]~E(x8381,x8382)+E(f300(x8381,x8383,x8384),f300(x8382,x8383,x8384))
% 157.76/157.53 [839]~E(x8391,x8392)+E(f300(x8393,x8391,x8394),f300(x8393,x8392,x8394))
% 157.76/157.53 [840]~E(x8401,x8402)+E(f300(x8403,x8404,x8401),f300(x8403,x8404,x8402))
% 157.76/157.53 [841]~E(x8411,x8412)+E(f868(x8411),f868(x8412))
% 157.76/157.53 [842]~E(x8421,x8422)+E(f692(x8421,x8423,x8424,x8425,x8426),f692(x8422,x8423,x8424,x8425,x8426))
% 157.76/157.53 [843]~E(x8431,x8432)+E(f692(x8433,x8431,x8434,x8435,x8436),f692(x8433,x8432,x8434,x8435,x8436))
% 157.76/157.53 [844]~E(x8441,x8442)+E(f692(x8443,x8444,x8441,x8445,x8446),f692(x8443,x8444,x8442,x8445,x8446))
% 157.76/157.53 [845]~E(x8451,x8452)+E(f692(x8453,x8454,x8455,x8451,x8456),f692(x8453,x8454,x8455,x8452,x8456))
% 157.76/157.53 [846]~E(x8461,x8462)+E(f692(x8463,x8464,x8465,x8466,x8461),f692(x8463,x8464,x8465,x8466,x8462))
% 157.76/157.53 [847]~E(x8471,x8472)+E(f382(x8471,x8473),f382(x8472,x8473))
% 157.76/157.53 [848]~E(x8481,x8482)+E(f382(x8483,x8481),f382(x8483,x8482))
% 157.76/157.53 [849]~E(x8491,x8492)+E(f895(x8491,x8493,x8494,x8495,x8496,x8497,x8498),f895(x8492,x8493,x8494,x8495,x8496,x8497,x8498))
% 157.76/157.53 [850]~E(x8501,x8502)+E(f895(x8503,x8501,x8504,x8505,x8506,x8507,x8508),f895(x8503,x8502,x8504,x8505,x8506,x8507,x8508))
% 157.76/157.53 [851]~E(x8511,x8512)+E(f895(x8513,x8514,x8511,x8515,x8516,x8517,x8518),f895(x8513,x8514,x8512,x8515,x8516,x8517,x8518))
% 157.76/157.53 [852]~E(x8521,x8522)+E(f895(x8523,x8524,x8525,x8521,x8526,x8527,x8528),f895(x8523,x8524,x8525,x8522,x8526,x8527,x8528))
% 157.76/157.53 [853]~E(x8531,x8532)+E(f895(x8533,x8534,x8535,x8536,x8531,x8537,x8538),f895(x8533,x8534,x8535,x8536,x8532,x8537,x8538))
% 157.76/157.53 [854]~E(x8541,x8542)+E(f895(x8543,x8544,x8545,x8546,x8547,x8541,x8548),f895(x8543,x8544,x8545,x8546,x8547,x8542,x8548))
% 157.76/157.53 [855]~E(x8551,x8552)+E(f895(x8553,x8554,x8555,x8556,x8557,x8558,x8551),f895(x8553,x8554,x8555,x8556,x8557,x8558,x8552))
% 157.76/157.53 [856]~E(x8561,x8562)+E(f709(x8561,x8563,x8564,x8565,x8566),f709(x8562,x8563,x8564,x8565,x8566))
% 157.76/157.53 [857]~E(x8571,x8572)+E(f709(x8573,x8571,x8574,x8575,x8576),f709(x8573,x8572,x8574,x8575,x8576))
% 157.76/157.53 [858]~E(x8581,x8582)+E(f709(x8583,x8584,x8581,x8585,x8586),f709(x8583,x8584,x8582,x8585,x8586))
% 157.76/157.53 [859]~E(x8591,x8592)+E(f709(x8593,x8594,x8595,x8591,x8596),f709(x8593,x8594,x8595,x8592,x8596))
% 157.76/157.53 [860]~E(x8601,x8602)+E(f709(x8603,x8604,x8605,x8606,x8601),f709(x8603,x8604,x8605,x8606,x8602))
% 157.76/157.53 [861]~E(x8611,x8612)+E(f436(x8611,x8613,x8614,x8615),f436(x8612,x8613,x8614,x8615))
% 157.76/157.53 [862]~E(x8621,x8622)+E(f436(x8623,x8621,x8624,x8625),f436(x8623,x8622,x8624,x8625))
% 157.76/157.53 [863]~E(x8631,x8632)+E(f436(x8633,x8634,x8631,x8635),f436(x8633,x8634,x8632,x8635))
% 157.76/157.53 [864]~E(x8641,x8642)+E(f436(x8643,x8644,x8645,x8641),f436(x8643,x8644,x8645,x8642))
% 157.76/157.53 [865]~E(x8651,x8652)+E(f482(x8651,x8653),f482(x8652,x8653))
% 157.76/157.53 [866]~E(x8661,x8662)+E(f482(x8663,x8661),f482(x8663,x8662))
% 157.76/157.53 [867]~E(x8671,x8672)+E(f911(x8671,x8673,x8674),f911(x8672,x8673,x8674))
% 157.76/157.53 [868]~E(x8681,x8682)+E(f911(x8683,x8681,x8684),f911(x8683,x8682,x8684))
% 157.76/157.53 [869]~E(x8691,x8692)+E(f911(x8693,x8694,x8691),f911(x8693,x8694,x8692))
% 157.76/157.53 [870]~E(x8701,x8702)+E(f362(x8701,x8703,x8704,x8705,x8706,x8707,x8708),f362(x8702,x8703,x8704,x8705,x8706,x8707,x8708))
% 157.76/157.53 [871]~E(x8711,x8712)+E(f362(x8713,x8711,x8714,x8715,x8716,x8717,x8718),f362(x8713,x8712,x8714,x8715,x8716,x8717,x8718))
% 157.76/157.53 [872]~E(x8721,x8722)+E(f362(x8723,x8724,x8721,x8725,x8726,x8727,x8728),f362(x8723,x8724,x8722,x8725,x8726,x8727,x8728))
% 157.76/157.53 [873]~E(x8731,x8732)+E(f362(x8733,x8734,x8735,x8731,x8736,x8737,x8738),f362(x8733,x8734,x8735,x8732,x8736,x8737,x8738))
% 157.76/157.53 [874]~E(x8741,x8742)+E(f362(x8743,x8744,x8745,x8746,x8741,x8747,x8748),f362(x8743,x8744,x8745,x8746,x8742,x8747,x8748))
% 157.76/157.53 [875]~E(x8751,x8752)+E(f362(x8753,x8754,x8755,x8756,x8757,x8751,x8758),f362(x8753,x8754,x8755,x8756,x8757,x8752,x8758))
% 157.76/157.53 [876]~E(x8761,x8762)+E(f362(x8763,x8764,x8765,x8766,x8767,x8768,x8761),f362(x8763,x8764,x8765,x8766,x8767,x8768,x8762))
% 157.76/157.53 [877]~E(x8771,x8772)+E(f408(x8771,x8773),f408(x8772,x8773))
% 157.76/157.53 [878]~E(x8781,x8782)+E(f408(x8783,x8781),f408(x8783,x8782))
% 157.76/157.53 [879]~E(x8791,x8792)+E(f909(x8791,x8793),f909(x8792,x8793))
% 157.76/157.53 [880]~E(x8801,x8802)+E(f909(x8803,x8801),f909(x8803,x8802))
% 157.76/157.53 [881]~E(x8811,x8812)+E(f717(x8811,x8813),f717(x8812,x8813))
% 157.76/157.53 [882]~E(x8821,x8822)+E(f717(x8823,x8821),f717(x8823,x8822))
% 157.76/157.53 [883]~E(x8831,x8832)+E(f162(x8831,x8833,x8834),f162(x8832,x8833,x8834))
% 157.76/157.53 [884]~E(x8841,x8842)+E(f162(x8843,x8841,x8844),f162(x8843,x8842,x8844))
% 157.76/157.53 [885]~E(x8851,x8852)+E(f162(x8853,x8854,x8851),f162(x8853,x8854,x8852))
% 157.76/157.53 [886]~E(x8861,x8862)+E(f193(x8861),f193(x8862))
% 157.76/157.53 [887]~E(x8871,x8872)+E(f693(x8871,x8873,x8874,x8875),f693(x8872,x8873,x8874,x8875))
% 157.76/157.53 [888]~E(x8881,x8882)+E(f693(x8883,x8881,x8884,x8885),f693(x8883,x8882,x8884,x8885))
% 157.76/157.53 [889]~E(x8891,x8892)+E(f693(x8893,x8894,x8891,x8895),f693(x8893,x8894,x8892,x8895))
% 157.76/157.53 [890]~E(x8901,x8902)+E(f693(x8903,x8904,x8905,x8901),f693(x8903,x8904,x8905,x8902))
% 157.76/157.53 [891]~E(x8911,x8912)+E(f523(x8911,x8913,x8914,x8915),f523(x8912,x8913,x8914,x8915))
% 157.76/157.53 [892]~E(x8921,x8922)+E(f523(x8923,x8921,x8924,x8925),f523(x8923,x8922,x8924,x8925))
% 157.76/157.53 [893]~E(x8931,x8932)+E(f523(x8933,x8934,x8931,x8935),f523(x8933,x8934,x8932,x8935))
% 157.76/157.53 [894]~E(x8941,x8942)+E(f523(x8943,x8944,x8945,x8941),f523(x8943,x8944,x8945,x8942))
% 157.76/157.53 [895]~E(x8951,x8952)+E(f768(x8951,x8953,x8954),f768(x8952,x8953,x8954))
% 157.76/157.53 [896]~E(x8961,x8962)+E(f768(x8963,x8961,x8964),f768(x8963,x8962,x8964))
% 157.76/157.53 [897]~E(x8971,x8972)+E(f768(x8973,x8974,x8971),f768(x8973,x8974,x8972))
% 157.76/157.53 [898]~E(x8981,x8982)+E(f497(x8981,x8983,x8984,x8985,x8986,x8987,x8988),f497(x8982,x8983,x8984,x8985,x8986,x8987,x8988))
% 157.76/157.53 [899]~E(x8991,x8992)+E(f497(x8993,x8991,x8994,x8995,x8996,x8997,x8998),f497(x8993,x8992,x8994,x8995,x8996,x8997,x8998))
% 157.76/157.53 [900]~E(x9001,x9002)+E(f497(x9003,x9004,x9001,x9005,x9006,x9007,x9008),f497(x9003,x9004,x9002,x9005,x9006,x9007,x9008))
% 157.76/157.53 [901]~E(x9011,x9012)+E(f497(x9013,x9014,x9015,x9011,x9016,x9017,x9018),f497(x9013,x9014,x9015,x9012,x9016,x9017,x9018))
% 157.76/157.53 [902]~E(x9021,x9022)+E(f497(x9023,x9024,x9025,x9026,x9021,x9027,x9028),f497(x9023,x9024,x9025,x9026,x9022,x9027,x9028))
% 157.76/157.53 [903]~E(x9031,x9032)+E(f497(x9033,x9034,x9035,x9036,x9037,x9031,x9038),f497(x9033,x9034,x9035,x9036,x9037,x9032,x9038))
% 157.76/157.53 [904]~E(x9041,x9042)+E(f497(x9043,x9044,x9045,x9046,x9047,x9048,x9041),f497(x9043,x9044,x9045,x9046,x9047,x9048,x9042))
% 157.76/157.53 [905]~E(x9051,x9052)+E(f515(x9051,x9053),f515(x9052,x9053))
% 157.76/157.53 [906]~E(x9061,x9062)+E(f515(x9063,x9061),f515(x9063,x9062))
% 157.76/157.53 [907]~E(x9071,x9072)+E(f406(x9071,x9073,x9074,x9075,x9076,x9077),f406(x9072,x9073,x9074,x9075,x9076,x9077))
% 157.76/157.53 [908]~E(x9081,x9082)+E(f406(x9083,x9081,x9084,x9085,x9086,x9087),f406(x9083,x9082,x9084,x9085,x9086,x9087))
% 157.76/157.53 [909]~E(x9091,x9092)+E(f406(x9093,x9094,x9091,x9095,x9096,x9097),f406(x9093,x9094,x9092,x9095,x9096,x9097))
% 157.76/157.53 [910]~E(x9101,x9102)+E(f406(x9103,x9104,x9105,x9101,x9106,x9107),f406(x9103,x9104,x9105,x9102,x9106,x9107))
% 157.76/157.53 [911]~E(x9111,x9112)+E(f406(x9113,x9114,x9115,x9116,x9111,x9117),f406(x9113,x9114,x9115,x9116,x9112,x9117))
% 157.76/157.53 [912]~E(x9121,x9122)+E(f406(x9123,x9124,x9125,x9126,x9127,x9121),f406(x9123,x9124,x9125,x9126,x9127,x9122))
% 157.76/157.53 [913]~E(x9131,x9132)+E(f165(x9131,x9133),f165(x9132,x9133))
% 157.76/157.53 [914]~E(x9141,x9142)+E(f165(x9143,x9141),f165(x9143,x9142))
% 157.76/157.53 [915]~E(x9151,x9152)+E(f37(x9151,x9153,x9154,x9155),f37(x9152,x9153,x9154,x9155))
% 157.76/157.53 [916]~E(x9161,x9162)+E(f37(x9163,x9161,x9164,x9165),f37(x9163,x9162,x9164,x9165))
% 157.76/157.53 [917]~E(x9171,x9172)+E(f37(x9173,x9174,x9171,x9175),f37(x9173,x9174,x9172,x9175))
% 157.76/157.53 [918]~E(x9181,x9182)+E(f37(x9183,x9184,x9185,x9181),f37(x9183,x9184,x9185,x9182))
% 157.76/157.53 [919]~E(x9191,x9192)+E(f349(x9191,x9193,x9194,x9195,x9196,x9197,x9198,x9199),f349(x9192,x9193,x9194,x9195,x9196,x9197,x9198,x9199))
% 157.76/157.53 [920]~E(x9201,x9202)+E(f349(x9203,x9201,x9204,x9205,x9206,x9207,x9208,x9209),f349(x9203,x9202,x9204,x9205,x9206,x9207,x9208,x9209))
% 157.76/157.53 [921]~E(x9211,x9212)+E(f349(x9213,x9214,x9211,x9215,x9216,x9217,x9218,x9219),f349(x9213,x9214,x9212,x9215,x9216,x9217,x9218,x9219))
% 157.76/157.53 [922]~E(x9221,x9222)+E(f349(x9223,x9224,x9225,x9221,x9226,x9227,x9228,x9229),f349(x9223,x9224,x9225,x9222,x9226,x9227,x9228,x9229))
% 157.76/157.53 [923]~E(x9231,x9232)+E(f349(x9233,x9234,x9235,x9236,x9231,x9237,x9238,x9239),f349(x9233,x9234,x9235,x9236,x9232,x9237,x9238,x9239))
% 157.76/157.53 [924]~E(x9241,x9242)+E(f349(x9243,x9244,x9245,x9246,x9247,x9241,x9248,x9249),f349(x9243,x9244,x9245,x9246,x9247,x9242,x9248,x9249))
% 157.76/157.53 [925]~E(x9251,x9252)+E(f349(x9253,x9254,x9255,x9256,x9257,x9258,x9251,x9259),f349(x9253,x9254,x9255,x9256,x9257,x9258,x9252,x9259))
% 157.76/157.53 [926]~E(x9261,x9262)+E(f349(x9263,x9264,x9265,x9266,x9267,x9268,x9269,x9261),f349(x9263,x9264,x9265,x9266,x9267,x9268,x9269,x9262))
% 157.76/157.53 [927]~E(x9271,x9272)+E(f577(x9271,x9273,x9274,x9275,x9276),f577(x9272,x9273,x9274,x9275,x9276))
% 157.76/157.53 [928]~E(x9281,x9282)+E(f577(x9283,x9281,x9284,x9285,x9286),f577(x9283,x9282,x9284,x9285,x9286))
% 157.76/157.53 [929]~E(x9291,x9292)+E(f577(x9293,x9294,x9291,x9295,x9296),f577(x9293,x9294,x9292,x9295,x9296))
% 157.76/157.53 [930]~E(x9301,x9302)+E(f577(x9303,x9304,x9305,x9301,x9306),f577(x9303,x9304,x9305,x9302,x9306))
% 157.76/157.53 [931]~E(x9311,x9312)+E(f577(x9313,x9314,x9315,x9316,x9311),f577(x9313,x9314,x9315,x9316,x9312))
% 157.76/157.53 [932]~E(x9321,x9322)+E(f838(x9321,x9323,x9324,x9325),f838(x9322,x9323,x9324,x9325))
% 157.76/157.53 [933]~E(x9331,x9332)+E(f838(x9333,x9331,x9334,x9335),f838(x9333,x9332,x9334,x9335))
% 157.76/157.53 [934]~E(x9341,x9342)+E(f838(x9343,x9344,x9341,x9345),f838(x9343,x9344,x9342,x9345))
% 157.76/157.53 [935]~E(x9351,x9352)+E(f838(x9353,x9354,x9355,x9351),f838(x9353,x9354,x9355,x9352))
% 157.76/157.53 [936]~E(x9361,x9362)+E(f274(x9361,x9363),f274(x9362,x9363))
% 157.76/157.53 [937]~E(x9371,x9372)+E(f274(x9373,x9371),f274(x9373,x9372))
% 157.76/157.53 [938]~E(x9381,x9382)+E(f361(x9381,x9383,x9384,x9385),f361(x9382,x9383,x9384,x9385))
% 157.76/157.53 [939]~E(x9391,x9392)+E(f361(x9393,x9391,x9394,x9395),f361(x9393,x9392,x9394,x9395))
% 157.76/157.53 [940]~E(x9401,x9402)+E(f361(x9403,x9404,x9401,x9405),f361(x9403,x9404,x9402,x9405))
% 157.76/157.53 [941]~E(x9411,x9412)+E(f361(x9413,x9414,x9415,x9411),f361(x9413,x9414,x9415,x9412))
% 157.76/157.53 [942]~E(x9421,x9422)+E(f656(x9421,x9423,x9424,x9425),f656(x9422,x9423,x9424,x9425))
% 157.76/157.53 [943]~E(x9431,x9432)+E(f656(x9433,x9431,x9434,x9435),f656(x9433,x9432,x9434,x9435))
% 157.76/157.53 [944]~E(x9441,x9442)+E(f656(x9443,x9444,x9441,x9445),f656(x9443,x9444,x9442,x9445))
% 157.76/157.53 [945]~E(x9451,x9452)+E(f656(x9453,x9454,x9455,x9451),f656(x9453,x9454,x9455,x9452))
% 157.76/157.53 [946]~E(x9461,x9462)+E(f180(x9461,x9463,x9464),f180(x9462,x9463,x9464))
% 157.76/157.53 [947]~E(x9471,x9472)+E(f180(x9473,x9471,x9474),f180(x9473,x9472,x9474))
% 157.76/157.53 [948]~E(x9481,x9482)+E(f180(x9483,x9484,x9481),f180(x9483,x9484,x9482))
% 157.76/157.53 [949]~E(x9491,x9492)+E(f224(x9491,x9493),f224(x9492,x9493))
% 157.76/157.53 [950]~E(x9501,x9502)+E(f224(x9503,x9501),f224(x9503,x9502))
% 157.76/157.53 [951]~E(x9511,x9512)+E(f508(x9511,x9513,x9514,x9515,x9516,x9517,x9518),f508(x9512,x9513,x9514,x9515,x9516,x9517,x9518))
% 157.76/157.54 [952]~E(x9521,x9522)+E(f508(x9523,x9521,x9524,x9525,x9526,x9527,x9528),f508(x9523,x9522,x9524,x9525,x9526,x9527,x9528))
% 157.76/157.54 [953]~E(x9531,x9532)+E(f508(x9533,x9534,x9531,x9535,x9536,x9537,x9538),f508(x9533,x9534,x9532,x9535,x9536,x9537,x9538))
% 157.76/157.54 [954]~E(x9541,x9542)+E(f508(x9543,x9544,x9545,x9541,x9546,x9547,x9548),f508(x9543,x9544,x9545,x9542,x9546,x9547,x9548))
% 157.76/157.54 [955]~E(x9551,x9552)+E(f508(x9553,x9554,x9555,x9556,x9551,x9557,x9558),f508(x9553,x9554,x9555,x9556,x9552,x9557,x9558))
% 157.76/157.54 [956]~E(x9561,x9562)+E(f508(x9563,x9564,x9565,x9566,x9567,x9561,x9568),f508(x9563,x9564,x9565,x9566,x9567,x9562,x9568))
% 157.76/157.54 [957]~E(x9571,x9572)+E(f508(x9573,x9574,x9575,x9576,x9577,x9578,x9571),f508(x9573,x9574,x9575,x9576,x9577,x9578,x9572))
% 157.76/157.54 [958]~E(x9581,x9582)+E(f412(x9581,x9583,x9584,x9585,x9586),f412(x9582,x9583,x9584,x9585,x9586))
% 157.76/157.54 [959]~E(x9591,x9592)+E(f412(x9593,x9591,x9594,x9595,x9596),f412(x9593,x9592,x9594,x9595,x9596))
% 157.76/157.54 [960]~E(x9601,x9602)+E(f412(x9603,x9604,x9601,x9605,x9606),f412(x9603,x9604,x9602,x9605,x9606))
% 157.76/157.54 [961]~E(x9611,x9612)+E(f412(x9613,x9614,x9615,x9611,x9616),f412(x9613,x9614,x9615,x9612,x9616))
% 157.76/157.54 [962]~E(x9621,x9622)+E(f412(x9623,x9624,x9625,x9626,x9621),f412(x9623,x9624,x9625,x9626,x9622))
% 157.76/157.54 [963]~E(x9631,x9632)+E(f798(x9631,x9633,x9634,x9635,x9636,x9637,x9638),f798(x9632,x9633,x9634,x9635,x9636,x9637,x9638))
% 157.76/157.54 [964]~E(x9641,x9642)+E(f798(x9643,x9641,x9644,x9645,x9646,x9647,x9648),f798(x9643,x9642,x9644,x9645,x9646,x9647,x9648))
% 157.76/157.54 [965]~E(x9651,x9652)+E(f798(x9653,x9654,x9651,x9655,x9656,x9657,x9658),f798(x9653,x9654,x9652,x9655,x9656,x9657,x9658))
% 157.76/157.54 [966]~E(x9661,x9662)+E(f798(x9663,x9664,x9665,x9661,x9666,x9667,x9668),f798(x9663,x9664,x9665,x9662,x9666,x9667,x9668))
% 157.76/157.54 [967]~E(x9671,x9672)+E(f798(x9673,x9674,x9675,x9676,x9671,x9677,x9678),f798(x9673,x9674,x9675,x9676,x9672,x9677,x9678))
% 157.76/157.54 [968]~E(x9681,x9682)+E(f798(x9683,x9684,x9685,x9686,x9687,x9681,x9688),f798(x9683,x9684,x9685,x9686,x9687,x9682,x9688))
% 157.76/157.54 [969]~E(x9691,x9692)+E(f798(x9693,x9694,x9695,x9696,x9697,x9698,x9691),f798(x9693,x9694,x9695,x9696,x9697,x9698,x9692))
% 157.76/157.54 [970]~E(x9701,x9702)+E(f623(x9701,x9703,x9704),f623(x9702,x9703,x9704))
% 157.76/157.54 [971]~E(x9711,x9712)+E(f623(x9713,x9711,x9714),f623(x9713,x9712,x9714))
% 157.76/157.54 [972]~E(x9721,x9722)+E(f623(x9723,x9724,x9721),f623(x9723,x9724,x9722))
% 157.76/157.54 [973]~E(x9731,x9732)+E(f575(x9731,x9733,x9734,x9735),f575(x9732,x9733,x9734,x9735))
% 157.76/157.54 [974]~E(x9741,x9742)+E(f575(x9743,x9741,x9744,x9745),f575(x9743,x9742,x9744,x9745))
% 157.76/157.54 [975]~E(x9751,x9752)+E(f575(x9753,x9754,x9751,x9755),f575(x9753,x9754,x9752,x9755))
% 157.76/157.54 [976]~E(x9761,x9762)+E(f575(x9763,x9764,x9765,x9761),f575(x9763,x9764,x9765,x9762))
% 157.76/157.54 [977]~E(x9771,x9772)+E(f757(x9771,x9773),f757(x9772,x9773))
% 157.76/157.54 [978]~E(x9781,x9782)+E(f757(x9783,x9781),f757(x9783,x9782))
% 157.76/157.54 [979]~E(x9791,x9792)+E(f922(x9791,x9793,x9794,x9795),f922(x9792,x9793,x9794,x9795))
% 157.76/157.54 [980]~E(x9801,x9802)+E(f922(x9803,x9801,x9804,x9805),f922(x9803,x9802,x9804,x9805))
% 157.76/157.54 [981]~E(x9811,x9812)+E(f922(x9813,x9814,x9811,x9815),f922(x9813,x9814,x9812,x9815))
% 157.76/157.54 [982]~E(x9821,x9822)+E(f922(x9823,x9824,x9825,x9821),f922(x9823,x9824,x9825,x9822))
% 157.76/157.54 [983]~E(x9831,x9832)+E(f48(x9831),f48(x9832))
% 157.76/157.54 [984]~E(x9841,x9842)+E(f730(x9841,x9843,x9844),f730(x9842,x9843,x9844))
% 157.76/157.54 [985]~E(x9851,x9852)+E(f730(x9853,x9851,x9854),f730(x9853,x9852,x9854))
% 157.76/157.54 [986]~E(x9861,x9862)+E(f730(x9863,x9864,x9861),f730(x9863,x9864,x9862))
% 157.76/157.54 [987]~E(x9871,x9872)+E(f372(x9871,x9873),f372(x9872,x9873))
% 157.76/157.54 [988]~E(x9881,x9882)+E(f372(x9883,x9881),f372(x9883,x9882))
% 157.76/157.54 [989]~E(x9891,x9892)+E(f473(x9891,x9893,x9894,x9895),f473(x9892,x9893,x9894,x9895))
% 157.76/157.54 [990]~E(x9901,x9902)+E(f473(x9903,x9901,x9904,x9905),f473(x9903,x9902,x9904,x9905))
% 157.76/157.54 [991]~E(x9911,x9912)+E(f473(x9913,x9914,x9911,x9915),f473(x9913,x9914,x9912,x9915))
% 157.76/157.54 [992]~E(x9921,x9922)+E(f473(x9923,x9924,x9925,x9921),f473(x9923,x9924,x9925,x9922))
% 157.76/157.54 [993]~E(x9931,x9932)+E(f199(x9931,x9933),f199(x9932,x9933))
% 157.76/157.54 [994]~E(x9941,x9942)+E(f199(x9943,x9941),f199(x9943,x9942))
% 157.76/157.54 [995]~E(x9951,x9952)+E(f667(x9951,x9953,x9954),f667(x9952,x9953,x9954))
% 157.76/157.54 [996]~E(x9961,x9962)+E(f667(x9963,x9961,x9964),f667(x9963,x9962,x9964))
% 157.76/157.54 [997]~E(x9971,x9972)+E(f667(x9973,x9974,x9971),f667(x9973,x9974,x9972))
% 157.76/157.54 [998]~E(x9981,x9982)+E(f128(x9981,x9983),f128(x9982,x9983))
% 157.76/157.54 [999]~E(x9991,x9992)+E(f128(x9993,x9991),f128(x9993,x9992))
% 157.76/157.54 [1000]~E(x10001,x10002)+E(f672(x10001,x10003,x10004,x10005),f672(x10002,x10003,x10004,x10005))
% 157.76/157.54 [1001]~E(x10011,x10012)+E(f672(x10013,x10011,x10014,x10015),f672(x10013,x10012,x10014,x10015))
% 157.76/157.54 [1002]~E(x10021,x10022)+E(f672(x10023,x10024,x10021,x10025),f672(x10023,x10024,x10022,x10025))
% 157.76/157.54 [1003]~E(x10031,x10032)+E(f672(x10033,x10034,x10035,x10031),f672(x10033,x10034,x10035,x10032))
% 157.76/157.54 [1004]~E(x10041,x10042)+E(f356(x10041,x10043,x10044),f356(x10042,x10043,x10044))
% 157.76/157.54 [1005]~E(x10051,x10052)+E(f356(x10053,x10051,x10054),f356(x10053,x10052,x10054))
% 157.76/157.54 [1006]~E(x10061,x10062)+E(f356(x10063,x10064,x10061),f356(x10063,x10064,x10062))
% 157.76/157.54 [1007]~E(x10071,x10072)+E(f778(x10071,x10073,x10074),f778(x10072,x10073,x10074))
% 157.76/157.54 [1008]~E(x10081,x10082)+E(f778(x10083,x10081,x10084),f778(x10083,x10082,x10084))
% 157.76/157.54 [1009]~E(x10091,x10092)+E(f778(x10093,x10094,x10091),f778(x10093,x10094,x10092))
% 157.76/157.54 [1010]~E(x10101,x10102)+E(f686(x10101,x10103,x10104),f686(x10102,x10103,x10104))
% 157.76/157.54 [1011]~E(x10111,x10112)+E(f686(x10113,x10111,x10114),f686(x10113,x10112,x10114))
% 157.76/157.54 [1012]~E(x10121,x10122)+E(f686(x10123,x10124,x10121),f686(x10123,x10124,x10122))
% 157.76/157.54 [1013]~E(x10131,x10132)+E(f439(x10131,x10133,x10134,x10135),f439(x10132,x10133,x10134,x10135))
% 157.76/157.54 [1014]~E(x10141,x10142)+E(f439(x10143,x10141,x10144,x10145),f439(x10143,x10142,x10144,x10145))
% 157.76/157.54 [1015]~E(x10151,x10152)+E(f439(x10153,x10154,x10151,x10155),f439(x10153,x10154,x10152,x10155))
% 157.76/157.54 [1016]~E(x10161,x10162)+E(f439(x10163,x10164,x10165,x10161),f439(x10163,x10164,x10165,x10162))
% 157.76/157.54 [1017]~E(x10171,x10172)+E(f156(x10171,x10173,x10174,x10175,x10176),f156(x10172,x10173,x10174,x10175,x10176))
% 157.76/157.54 [1018]~E(x10181,x10182)+E(f156(x10183,x10181,x10184,x10185,x10186),f156(x10183,x10182,x10184,x10185,x10186))
% 157.76/157.54 [1019]~E(x10191,x10192)+E(f156(x10193,x10194,x10191,x10195,x10196),f156(x10193,x10194,x10192,x10195,x10196))
% 157.76/157.54 [1020]~E(x10201,x10202)+E(f156(x10203,x10204,x10205,x10201,x10206),f156(x10203,x10204,x10205,x10202,x10206))
% 157.76/157.54 [1021]~E(x10211,x10212)+E(f156(x10213,x10214,x10215,x10216,x10211),f156(x10213,x10214,x10215,x10216,x10212))
% 157.76/157.54 [1022]~E(x10221,x10222)+E(f891(x10221,x10223,x10224,x10225,x10226,x10227,x10228),f891(x10222,x10223,x10224,x10225,x10226,x10227,x10228))
% 157.76/157.54 [1023]~E(x10231,x10232)+E(f891(x10233,x10231,x10234,x10235,x10236,x10237,x10238),f891(x10233,x10232,x10234,x10235,x10236,x10237,x10238))
% 157.76/157.54 [1024]~E(x10241,x10242)+E(f891(x10243,x10244,x10241,x10245,x10246,x10247,x10248),f891(x10243,x10244,x10242,x10245,x10246,x10247,x10248))
% 157.76/157.54 [1025]~E(x10251,x10252)+E(f891(x10253,x10254,x10255,x10251,x10256,x10257,x10258),f891(x10253,x10254,x10255,x10252,x10256,x10257,x10258))
% 157.76/157.54 [1026]~E(x10261,x10262)+E(f891(x10263,x10264,x10265,x10266,x10261,x10267,x10268),f891(x10263,x10264,x10265,x10266,x10262,x10267,x10268))
% 157.76/157.54 [1027]~E(x10271,x10272)+E(f891(x10273,x10274,x10275,x10276,x10277,x10271,x10278),f891(x10273,x10274,x10275,x10276,x10277,x10272,x10278))
% 157.76/157.54 [1028]~E(x10281,x10282)+E(f891(x10283,x10284,x10285,x10286,x10287,x10288,x10281),f891(x10283,x10284,x10285,x10286,x10287,x10288,x10282))
% 157.76/157.54 [1029]~E(x10291,x10292)+E(f729(x10291,x10293,x10294,x10295,x10296),f729(x10292,x10293,x10294,x10295,x10296))
% 157.76/157.54 [1030]~E(x10301,x10302)+E(f729(x10303,x10301,x10304,x10305,x10306),f729(x10303,x10302,x10304,x10305,x10306))
% 157.76/157.54 [1031]~E(x10311,x10312)+E(f729(x10313,x10314,x10311,x10315,x10316),f729(x10313,x10314,x10312,x10315,x10316))
% 157.76/157.54 [1032]~E(x10321,x10322)+E(f729(x10323,x10324,x10325,x10321,x10326),f729(x10323,x10324,x10325,x10322,x10326))
% 157.76/157.54 [1033]~E(x10331,x10332)+E(f729(x10333,x10334,x10335,x10336,x10331),f729(x10333,x10334,x10335,x10336,x10332))
% 157.76/157.54 [1034]~E(x10341,x10342)+E(f694(x10341,x10343,x10344,x10345),f694(x10342,x10343,x10344,x10345))
% 157.76/157.54 [1035]~E(x10351,x10352)+E(f694(x10353,x10351,x10354,x10355),f694(x10353,x10352,x10354,x10355))
% 157.76/157.54 [1036]~E(x10361,x10362)+E(f694(x10363,x10364,x10361,x10365),f694(x10363,x10364,x10362,x10365))
% 157.76/157.54 [1037]~E(x10371,x10372)+E(f694(x10373,x10374,x10375,x10371),f694(x10373,x10374,x10375,x10372))
% 157.76/157.54 [1038]~E(x10381,x10382)+E(f505(x10381,x10383,x10384),f505(x10382,x10383,x10384))
% 157.76/157.54 [1039]~E(x10391,x10392)+E(f505(x10393,x10391,x10394),f505(x10393,x10392,x10394))
% 157.76/157.54 [1040]~E(x10401,x10402)+E(f505(x10403,x10404,x10401),f505(x10403,x10404,x10402))
% 157.76/157.54 [1041]~E(x10411,x10412)+E(f846(x10411,x10413,x10414,x10415,x10416,x10417,x10418,x10419),f846(x10412,x10413,x10414,x10415,x10416,x10417,x10418,x10419))
% 157.76/157.54 [1042]~E(x10421,x10422)+E(f846(x10423,x10421,x10424,x10425,x10426,x10427,x10428,x10429),f846(x10423,x10422,x10424,x10425,x10426,x10427,x10428,x10429))
% 157.76/157.54 [1043]~E(x10431,x10432)+E(f846(x10433,x10434,x10431,x10435,x10436,x10437,x10438,x10439),f846(x10433,x10434,x10432,x10435,x10436,x10437,x10438,x10439))
% 157.76/157.54 [1044]~E(x10441,x10442)+E(f846(x10443,x10444,x10445,x10441,x10446,x10447,x10448,x10449),f846(x10443,x10444,x10445,x10442,x10446,x10447,x10448,x10449))
% 157.76/157.54 [1045]~E(x10451,x10452)+E(f846(x10453,x10454,x10455,x10456,x10451,x10457,x10458,x10459),f846(x10453,x10454,x10455,x10456,x10452,x10457,x10458,x10459))
% 157.76/157.54 [1046]~E(x10461,x10462)+E(f846(x10463,x10464,x10465,x10466,x10467,x10461,x10468,x10469),f846(x10463,x10464,x10465,x10466,x10467,x10462,x10468,x10469))
% 157.76/157.54 [1047]~E(x10471,x10472)+E(f846(x10473,x10474,x10475,x10476,x10477,x10478,x10471,x10479),f846(x10473,x10474,x10475,x10476,x10477,x10478,x10472,x10479))
% 157.76/157.54 [1048]~E(x10481,x10482)+E(f846(x10483,x10484,x10485,x10486,x10487,x10488,x10489,x10481),f846(x10483,x10484,x10485,x10486,x10487,x10488,x10489,x10482))
% 157.76/157.54 [1049]~E(x10491,x10492)+E(f893(x10491,x10493),f893(x10492,x10493))
% 157.76/157.54 [1050]~E(x10501,x10502)+E(f893(x10503,x10501),f893(x10503,x10502))
% 157.76/157.54 [1051]~E(x10511,x10512)+E(f484(x10511,x10513,x10514),f484(x10512,x10513,x10514))
% 157.76/157.54 [1052]~E(x10521,x10522)+E(f484(x10523,x10521,x10524),f484(x10523,x10522,x10524))
% 157.76/157.54 [1053]~E(x10531,x10532)+E(f484(x10533,x10534,x10531),f484(x10533,x10534,x10532))
% 157.76/157.54 [1054]~E(x10541,x10542)+E(f376(x10541),f376(x10542))
% 157.76/157.54 [1055]~E(x10551,x10552)+E(f580(x10551,x10553,x10554,x10555,x10556,x10557,x10558,x10559),f580(x10552,x10553,x10554,x10555,x10556,x10557,x10558,x10559))
% 157.76/157.54 [1056]~E(x10561,x10562)+E(f580(x10563,x10561,x10564,x10565,x10566,x10567,x10568,x10569),f580(x10563,x10562,x10564,x10565,x10566,x10567,x10568,x10569))
% 157.76/157.54 [1057]~E(x10571,x10572)+E(f580(x10573,x10574,x10571,x10575,x10576,x10577,x10578,x10579),f580(x10573,x10574,x10572,x10575,x10576,x10577,x10578,x10579))
% 157.76/157.54 [1058]~E(x10581,x10582)+E(f580(x10583,x10584,x10585,x10581,x10586,x10587,x10588,x10589),f580(x10583,x10584,x10585,x10582,x10586,x10587,x10588,x10589))
% 157.76/157.54 [1059]~E(x10591,x10592)+E(f580(x10593,x10594,x10595,x10596,x10591,x10597,x10598,x10599),f580(x10593,x10594,x10595,x10596,x10592,x10597,x10598,x10599))
% 157.76/157.54 [1060]~E(x10601,x10602)+E(f580(x10603,x10604,x10605,x10606,x10607,x10601,x10608,x10609),f580(x10603,x10604,x10605,x10606,x10607,x10602,x10608,x10609))
% 157.76/157.54 [1061]~E(x10611,x10612)+E(f580(x10613,x10614,x10615,x10616,x10617,x10618,x10611,x10619),f580(x10613,x10614,x10615,x10616,x10617,x10618,x10612,x10619))
% 157.76/157.54 [1062]~E(x10621,x10622)+E(f580(x10623,x10624,x10625,x10626,x10627,x10628,x10629,x10621),f580(x10623,x10624,x10625,x10626,x10627,x10628,x10629,x10622))
% 157.76/157.54 [1063]~E(x10631,x10632)+E(f574(x10631,x10633,x10634,x10635),f574(x10632,x10633,x10634,x10635))
% 157.76/157.54 [1064]~E(x10641,x10642)+E(f574(x10643,x10641,x10644,x10645),f574(x10643,x10642,x10644,x10645))
% 157.76/157.54 [1065]~E(x10651,x10652)+E(f574(x10653,x10654,x10651,x10655),f574(x10653,x10654,x10652,x10655))
% 157.76/157.54 [1066]~E(x10661,x10662)+E(f574(x10663,x10664,x10665,x10661),f574(x10663,x10664,x10665,x10662))
% 157.76/157.54 [1067]~E(x10671,x10672)+E(f905(x10671,x10673,x10674),f905(x10672,x10673,x10674))
% 157.76/157.54 [1068]~E(x10681,x10682)+E(f905(x10683,x10681,x10684),f905(x10683,x10682,x10684))
% 157.76/157.54 [1069]~E(x10691,x10692)+E(f905(x10693,x10694,x10691),f905(x10693,x10694,x10692))
% 157.76/157.54 [1070]~E(x10701,x10702)+E(f797(x10701,x10703,x10704,x10705,x10706,x10707,x10708),f797(x10702,x10703,x10704,x10705,x10706,x10707,x10708))
% 157.76/157.54 [1071]~E(x10711,x10712)+E(f797(x10713,x10711,x10714,x10715,x10716,x10717,x10718),f797(x10713,x10712,x10714,x10715,x10716,x10717,x10718))
% 157.76/157.54 [1072]~E(x10721,x10722)+E(f797(x10723,x10724,x10721,x10725,x10726,x10727,x10728),f797(x10723,x10724,x10722,x10725,x10726,x10727,x10728))
% 157.76/157.54 [1073]~E(x10731,x10732)+E(f797(x10733,x10734,x10735,x10731,x10736,x10737,x10738),f797(x10733,x10734,x10735,x10732,x10736,x10737,x10738))
% 157.76/157.54 [1074]~E(x10741,x10742)+E(f797(x10743,x10744,x10745,x10746,x10741,x10747,x10748),f797(x10743,x10744,x10745,x10746,x10742,x10747,x10748))
% 157.76/157.54 [1075]~E(x10751,x10752)+E(f797(x10753,x10754,x10755,x10756,x10757,x10751,x10758),f797(x10753,x10754,x10755,x10756,x10757,x10752,x10758))
% 157.76/157.54 [1076]~E(x10761,x10762)+E(f797(x10763,x10764,x10765,x10766,x10767,x10768,x10761),f797(x10763,x10764,x10765,x10766,x10767,x10768,x10762))
% 157.76/157.54 [1077]~E(x10771,x10772)+E(f720(x10771,x10773,x10774),f720(x10772,x10773,x10774))
% 157.76/157.54 [1078]~E(x10781,x10782)+E(f720(x10783,x10781,x10784),f720(x10783,x10782,x10784))
% 157.76/157.54 [1079]~E(x10791,x10792)+E(f720(x10793,x10794,x10791),f720(x10793,x10794,x10792))
% 157.76/157.54 [1080]~E(x10801,x10802)+E(f486(x10801,x10803,x10804),f486(x10802,x10803,x10804))
% 157.76/157.54 [1081]~E(x10811,x10812)+E(f486(x10813,x10811,x10814),f486(x10813,x10812,x10814))
% 157.76/157.54 [1082]~E(x10821,x10822)+E(f486(x10823,x10824,x10821),f486(x10823,x10824,x10822))
% 157.76/157.54 [1083]~E(x10831,x10832)+E(f276(x10831,x10833),f276(x10832,x10833))
% 157.76/157.54 [1084]~E(x10841,x10842)+E(f276(x10843,x10841),f276(x10843,x10842))
% 157.76/157.54 [1085]~E(x10851,x10852)+E(f681(x10851,x10853,x10854),f681(x10852,x10853,x10854))
% 157.76/157.54 [1086]~E(x10861,x10862)+E(f681(x10863,x10861,x10864),f681(x10863,x10862,x10864))
% 157.76/157.54 [1087]~E(x10871,x10872)+E(f681(x10873,x10874,x10871),f681(x10873,x10874,x10872))
% 157.76/157.54 [1088]~E(x10881,x10882)+E(f636(x10881,x10883,x10884,x10885),f636(x10882,x10883,x10884,x10885))
% 157.76/157.54 [1089]~E(x10891,x10892)+E(f636(x10893,x10891,x10894,x10895),f636(x10893,x10892,x10894,x10895))
% 157.76/157.54 [1090]~E(x10901,x10902)+E(f636(x10903,x10904,x10901,x10905),f636(x10903,x10904,x10902,x10905))
% 157.76/157.54 [1091]~E(x10911,x10912)+E(f636(x10913,x10914,x10915,x10911),f636(x10913,x10914,x10915,x10912))
% 157.76/157.54 [1092]~E(x10921,x10922)+E(f465(x10921,x10923,x10924,x10925),f465(x10922,x10923,x10924,x10925))
% 157.76/157.54 [1093]~E(x10931,x10932)+E(f465(x10933,x10931,x10934,x10935),f465(x10933,x10932,x10934,x10935))
% 157.76/157.54 [1094]~E(x10941,x10942)+E(f465(x10943,x10944,x10941,x10945),f465(x10943,x10944,x10942,x10945))
% 157.76/157.54 [1095]~E(x10951,x10952)+E(f465(x10953,x10954,x10955,x10951),f465(x10953,x10954,x10955,x10952))
% 157.76/157.54 [1096]~E(x10961,x10962)+E(f642(x10961,x10963,x10964),f642(x10962,x10963,x10964))
% 157.76/157.54 [1097]~E(x10971,x10972)+E(f642(x10973,x10971,x10974),f642(x10973,x10972,x10974))
% 157.76/157.54 [1098]~E(x10981,x10982)+E(f642(x10983,x10984,x10981),f642(x10983,x10984,x10982))
% 157.76/157.54 [1099]~E(x10991,x10992)+E(f733(x10991,x10993),f733(x10992,x10993))
% 157.76/157.54 [1100]~E(x11001,x11002)+E(f733(x11003,x11001),f733(x11003,x11002))
% 157.76/157.54 [1101]~E(x11011,x11012)+E(f416(x11011,x11013),f416(x11012,x11013))
% 157.76/157.54 [1102]~E(x11021,x11022)+E(f416(x11023,x11021),f416(x11023,x11022))
% 157.76/157.54 [1103]~E(x11031,x11032)+E(f706(x11031,x11033,x11034,x11035),f706(x11032,x11033,x11034,x11035))
% 157.76/157.54 [1104]~E(x11041,x11042)+E(f706(x11043,x11041,x11044,x11045),f706(x11043,x11042,x11044,x11045))
% 157.76/157.54 [1105]~E(x11051,x11052)+E(f706(x11053,x11054,x11051,x11055),f706(x11053,x11054,x11052,x11055))
% 157.76/157.54 [1106]~E(x11061,x11062)+E(f706(x11063,x11064,x11065,x11061),f706(x11063,x11064,x11065,x11062))
% 157.76/157.54 [1107]~E(x11071,x11072)+E(f792(x11071,x11073,x11074,x11075),f792(x11072,x11073,x11074,x11075))
% 157.76/157.54 [1108]~E(x11081,x11082)+E(f792(x11083,x11081,x11084,x11085),f792(x11083,x11082,x11084,x11085))
% 157.76/157.54 [1109]~E(x11091,x11092)+E(f792(x11093,x11094,x11091,x11095),f792(x11093,x11094,x11092,x11095))
% 157.76/157.54 [1110]~E(x11101,x11102)+E(f792(x11103,x11104,x11105,x11101),f792(x11103,x11104,x11105,x11102))
% 157.76/157.54 [1111]~E(x11111,x11112)+E(f842(x11111,x11113,x11114,x11115,x11116),f842(x11112,x11113,x11114,x11115,x11116))
% 157.76/157.54 [1112]~E(x11121,x11122)+E(f842(x11123,x11121,x11124,x11125,x11126),f842(x11123,x11122,x11124,x11125,x11126))
% 157.76/157.54 [1113]~E(x11131,x11132)+E(f842(x11133,x11134,x11131,x11135,x11136),f842(x11133,x11134,x11132,x11135,x11136))
% 157.76/157.54 [1114]~E(x11141,x11142)+E(f842(x11143,x11144,x11145,x11141,x11146),f842(x11143,x11144,x11145,x11142,x11146))
% 157.76/157.54 [1115]~E(x11151,x11152)+E(f842(x11153,x11154,x11155,x11156,x11151),f842(x11153,x11154,x11155,x11156,x11152))
% 157.76/157.54 [1116]~E(x11161,x11162)+E(f450(x11161,x11163,x11164,x11165),f450(x11162,x11163,x11164,x11165))
% 157.76/157.54 [1117]~E(x11171,x11172)+E(f450(x11173,x11171,x11174,x11175),f450(x11173,x11172,x11174,x11175))
% 157.76/157.54 [1118]~E(x11181,x11182)+E(f450(x11183,x11184,x11181,x11185),f450(x11183,x11184,x11182,x11185))
% 157.76/157.54 [1119]~E(x11191,x11192)+E(f450(x11193,x11194,x11195,x11191),f450(x11193,x11194,x11195,x11192))
% 157.76/157.54 [1120]~E(x11201,x11202)+E(f364(x11201,x11203,x11204),f364(x11202,x11203,x11204))
% 157.76/157.54 [1121]~E(x11211,x11212)+E(f364(x11213,x11211,x11214),f364(x11213,x11212,x11214))
% 157.76/157.54 [1122]~E(x11221,x11222)+E(f364(x11223,x11224,x11221),f364(x11223,x11224,x11222))
% 157.76/157.54 [1123]~E(x11231,x11232)+E(f463(x11231,x11233,x11234,x11235),f463(x11232,x11233,x11234,x11235))
% 157.76/157.54 [1124]~E(x11241,x11242)+E(f463(x11243,x11241,x11244,x11245),f463(x11243,x11242,x11244,x11245))
% 157.76/157.54 [1125]~E(x11251,x11252)+E(f463(x11253,x11254,x11251,x11255),f463(x11253,x11254,x11252,x11255))
% 157.76/157.54 [1126]~E(x11261,x11262)+E(f463(x11263,x11264,x11265,x11261),f463(x11263,x11264,x11265,x11262))
% 157.76/157.54 [1127]~E(x11271,x11272)+E(f796(x11271,x11273,x11274,x11275),f796(x11272,x11273,x11274,x11275))
% 157.76/157.54 [1128]~E(x11281,x11282)+E(f796(x11283,x11281,x11284,x11285),f796(x11283,x11282,x11284,x11285))
% 157.76/157.54 [1129]~E(x11291,x11292)+E(f796(x11293,x11294,x11291,x11295),f796(x11293,x11294,x11292,x11295))
% 157.76/157.54 [1130]~E(x11301,x11302)+E(f796(x11303,x11304,x11305,x11301),f796(x11303,x11304,x11305,x11302))
% 157.76/157.54 [1131]~E(x11311,x11312)+E(f311(x11311),f311(x11312))
% 157.76/157.54 [1132]~E(x11321,x11322)+E(f420(x11321,x11323,x11324),f420(x11322,x11323,x11324))
% 157.76/157.54 [1133]~E(x11331,x11332)+E(f420(x11333,x11331,x11334),f420(x11333,x11332,x11334))
% 157.76/157.54 [1134]~E(x11341,x11342)+E(f420(x11343,x11344,x11341),f420(x11343,x11344,x11342))
% 157.76/157.54 [1135]~E(x11351,x11352)+E(f418(x11351,x11353,x11354,x11355),f418(x11352,x11353,x11354,x11355))
% 157.76/157.54 [1136]~E(x11361,x11362)+E(f418(x11363,x11361,x11364,x11365),f418(x11363,x11362,x11364,x11365))
% 157.76/157.54 [1137]~E(x11371,x11372)+E(f418(x11373,x11374,x11371,x11375),f418(x11373,x11374,x11372,x11375))
% 157.76/157.54 [1138]~E(x11381,x11382)+E(f418(x11383,x11384,x11385,x11381),f418(x11383,x11384,x11385,x11382))
% 157.76/157.54 [1139]~E(x11391,x11392)+E(f487(x11391,x11393,x11394),f487(x11392,x11393,x11394))
% 157.76/157.54 [1140]~E(x11401,x11402)+E(f487(x11403,x11401,x11404),f487(x11403,x11402,x11404))
% 157.76/157.54 [1141]~E(x11411,x11412)+E(f487(x11413,x11414,x11411),f487(x11413,x11414,x11412))
% 157.76/157.54 [1142]~E(x11421,x11422)+E(f620(x11421,x11423,x11424,x11425,x11426,x11427,x11428),f620(x11422,x11423,x11424,x11425,x11426,x11427,x11428))
% 157.76/157.54 [1143]~E(x11431,x11432)+E(f620(x11433,x11431,x11434,x11435,x11436,x11437,x11438),f620(x11433,x11432,x11434,x11435,x11436,x11437,x11438))
% 157.76/157.54 [1144]~E(x11441,x11442)+E(f620(x11443,x11444,x11441,x11445,x11446,x11447,x11448),f620(x11443,x11444,x11442,x11445,x11446,x11447,x11448))
% 157.76/157.54 [1145]~E(x11451,x11452)+E(f620(x11453,x11454,x11455,x11451,x11456,x11457,x11458),f620(x11453,x11454,x11455,x11452,x11456,x11457,x11458))
% 157.76/157.54 [1146]~E(x11461,x11462)+E(f620(x11463,x11464,x11465,x11466,x11461,x11467,x11468),f620(x11463,x11464,x11465,x11466,x11462,x11467,x11468))
% 157.76/157.54 [1147]~E(x11471,x11472)+E(f620(x11473,x11474,x11475,x11476,x11477,x11471,x11478),f620(x11473,x11474,x11475,x11476,x11477,x11472,x11478))
% 157.76/157.54 [1148]~E(x11481,x11482)+E(f620(x11483,x11484,x11485,x11486,x11487,x11488,x11481),f620(x11483,x11484,x11485,x11486,x11487,x11488,x11482))
% 157.76/157.54 [1149]~E(x11491,x11492)+E(f794(x11491,x11493,x11494,x11495),f794(x11492,x11493,x11494,x11495))
% 157.76/157.54 [1150]~E(x11501,x11502)+E(f794(x11503,x11501,x11504,x11505),f794(x11503,x11502,x11504,x11505))
% 157.76/157.54 [1151]~E(x11511,x11512)+E(f794(x11513,x11514,x11511,x11515),f794(x11513,x11514,x11512,x11515))
% 157.76/157.54 [1152]~E(x11521,x11522)+E(f794(x11523,x11524,x11525,x11521),f794(x11523,x11524,x11525,x11522))
% 157.76/157.54 [1153]~E(x11531,x11532)+E(f375(x11531),f375(x11532))
% 157.76/157.54 [1154]~E(x11541,x11542)+E(f888(x11541,x11543,x11544,x11545),f888(x11542,x11543,x11544,x11545))
% 157.76/157.54 [1155]~E(x11551,x11552)+E(f888(x11553,x11551,x11554,x11555),f888(x11553,x11552,x11554,x11555))
% 157.76/157.54 [1156]~E(x11561,x11562)+E(f888(x11563,x11564,x11561,x11565),f888(x11563,x11564,x11562,x11565))
% 157.76/157.54 [1157]~E(x11571,x11572)+E(f888(x11573,x11574,x11575,x11571),f888(x11573,x11574,x11575,x11572))
% 157.76/157.54 [1158]~E(x11581,x11582)+E(f229(x11581,x11583,x11584,x11585),f229(x11582,x11583,x11584,x11585))
% 157.76/157.54 [1159]~E(x11591,x11592)+E(f229(x11593,x11591,x11594,x11595),f229(x11593,x11592,x11594,x11595))
% 157.76/157.54 [1160]~E(x11601,x11602)+E(f229(x11603,x11604,x11601,x11605),f229(x11603,x11604,x11602,x11605))
% 157.76/157.54 [1161]~E(x11611,x11612)+E(f229(x11613,x11614,x11615,x11611),f229(x11613,x11614,x11615,x11612))
% 157.76/157.54 [1162]~E(x11621,x11622)+E(f546(x11621,x11623,x11624,x11625,x11626,x11627,x11628,x11629),f546(x11622,x11623,x11624,x11625,x11626,x11627,x11628,x11629))
% 157.76/157.54 [1163]~E(x11631,x11632)+E(f546(x11633,x11631,x11634,x11635,x11636,x11637,x11638,x11639),f546(x11633,x11632,x11634,x11635,x11636,x11637,x11638,x11639))
% 157.76/157.54 [1164]~E(x11641,x11642)+E(f546(x11643,x11644,x11641,x11645,x11646,x11647,x11648,x11649),f546(x11643,x11644,x11642,x11645,x11646,x11647,x11648,x11649))
% 157.76/157.54 [1165]~E(x11651,x11652)+E(f546(x11653,x11654,x11655,x11651,x11656,x11657,x11658,x11659),f546(x11653,x11654,x11655,x11652,x11656,x11657,x11658,x11659))
% 157.76/157.54 [1166]~E(x11661,x11662)+E(f546(x11663,x11664,x11665,x11666,x11661,x11667,x11668,x11669),f546(x11663,x11664,x11665,x11666,x11662,x11667,x11668,x11669))
% 157.76/157.54 [1167]~E(x11671,x11672)+E(f546(x11673,x11674,x11675,x11676,x11677,x11671,x11678,x11679),f546(x11673,x11674,x11675,x11676,x11677,x11672,x11678,x11679))
% 157.76/157.54 [1168]~E(x11681,x11682)+E(f546(x11683,x11684,x11685,x11686,x11687,x11688,x11681,x11689),f546(x11683,x11684,x11685,x11686,x11687,x11688,x11682,x11689))
% 157.76/157.54 [1169]~E(x11691,x11692)+E(f546(x11693,x11694,x11695,x11696,x11697,x11698,x11699,x11691),f546(x11693,x11694,x11695,x11696,x11697,x11698,x11699,x11692))
% 157.76/157.54 [1170]~E(x11701,x11702)+E(f232(x11701,x11703,x11704,x11705,x11706),f232(x11702,x11703,x11704,x11705,x11706))
% 157.76/157.54 [1171]~E(x11711,x11712)+E(f232(x11713,x11711,x11714,x11715,x11716),f232(x11713,x11712,x11714,x11715,x11716))
% 157.76/157.54 [1172]~E(x11721,x11722)+E(f232(x11723,x11724,x11721,x11725,x11726),f232(x11723,x11724,x11722,x11725,x11726))
% 157.76/157.54 [1173]~E(x11731,x11732)+E(f232(x11733,x11734,x11735,x11731,x11736),f232(x11733,x11734,x11735,x11732,x11736))
% 157.76/157.54 [1174]~E(x11741,x11742)+E(f232(x11743,x11744,x11745,x11746,x11741),f232(x11743,x11744,x11745,x11746,x11742))
% 157.76/157.54 [1175]~E(x11751,x11752)+E(f304(x11751,x11753,x11754,x11755,x11756),f304(x11752,x11753,x11754,x11755,x11756))
% 157.76/157.54 [1176]~E(x11761,x11762)+E(f304(x11763,x11761,x11764,x11765,x11766),f304(x11763,x11762,x11764,x11765,x11766))
% 157.76/157.54 [1177]~E(x11771,x11772)+E(f304(x11773,x11774,x11771,x11775,x11776),f304(x11773,x11774,x11772,x11775,x11776))
% 157.76/157.54 [1178]~E(x11781,x11782)+E(f304(x11783,x11784,x11785,x11781,x11786),f304(x11783,x11784,x11785,x11782,x11786))
% 157.76/157.54 [1179]~E(x11791,x11792)+E(f304(x11793,x11794,x11795,x11796,x11791),f304(x11793,x11794,x11795,x11796,x11792))
% 157.76/157.54 [1180]~E(x11801,x11802)+E(f711(x11801,x11803,x11804),f711(x11802,x11803,x11804))
% 157.76/157.54 [1181]~E(x11811,x11812)+E(f711(x11813,x11811,x11814),f711(x11813,x11812,x11814))
% 157.76/157.54 [1182]~E(x11821,x11822)+E(f711(x11823,x11824,x11821),f711(x11823,x11824,x11822))
% 157.76/157.54 [1183]~E(x11831,x11832)+E(f236(x11831,x11833),f236(x11832,x11833))
% 157.76/157.54 [1184]~E(x11841,x11842)+E(f236(x11843,x11841),f236(x11843,x11842))
% 157.76/157.54 [1185]~E(x11851,x11852)+E(f494(x11851,x11853,x11854),f494(x11852,x11853,x11854))
% 157.76/157.54 [1186]~E(x11861,x11862)+E(f494(x11863,x11861,x11864),f494(x11863,x11862,x11864))
% 157.76/157.54 [1187]~E(x11871,x11872)+E(f494(x11873,x11874,x11871),f494(x11873,x11874,x11872))
% 157.76/157.54 [1188]~E(x11881,x11882)+E(f253(x11881,x11883,x11884),f253(x11882,x11883,x11884))
% 157.76/157.54 [1189]~E(x11891,x11892)+E(f253(x11893,x11891,x11894),f253(x11893,x11892,x11894))
% 157.76/157.54 [1190]~E(x11901,x11902)+E(f253(x11903,x11904,x11901),f253(x11903,x11904,x11902))
% 157.76/157.54 [1191]~E(x11911,x11912)+E(f780(x11911,x11913,x11914,x11915),f780(x11912,x11913,x11914,x11915))
% 157.76/157.54 [1192]~E(x11921,x11922)+E(f780(x11923,x11921,x11924,x11925),f780(x11923,x11922,x11924,x11925))
% 157.76/157.54 [1193]~E(x11931,x11932)+E(f780(x11933,x11934,x11931,x11935),f780(x11933,x11934,x11932,x11935))
% 157.76/157.54 [1194]~E(x11941,x11942)+E(f780(x11943,x11944,x11945,x11941),f780(x11943,x11944,x11945,x11942))
% 157.76/157.54 [1195]~E(x11951,x11952)+E(f417(x11951,x11953),f417(x11952,x11953))
% 157.76/157.54 [1196]~E(x11961,x11962)+E(f417(x11963,x11961),f417(x11963,x11962))
% 157.76/157.54 [1197]~E(x11971,x11972)+E(f772(x11971,x11973,x11974),f772(x11972,x11973,x11974))
% 157.76/157.54 [1198]~E(x11981,x11982)+E(f772(x11983,x11981,x11984),f772(x11983,x11982,x11984))
% 157.76/157.54 [1199]~E(x11991,x11992)+E(f772(x11993,x11994,x11991),f772(x11993,x11994,x11992))
% 157.76/157.54 [1200]~E(x12001,x12002)+E(f509(x12001,x12003,x12004,x12005,x12006,x12007,x12008),f509(x12002,x12003,x12004,x12005,x12006,x12007,x12008))
% 157.76/157.54 [1201]~E(x12011,x12012)+E(f509(x12013,x12011,x12014,x12015,x12016,x12017,x12018),f509(x12013,x12012,x12014,x12015,x12016,x12017,x12018))
% 157.76/157.54 [1202]~E(x12021,x12022)+E(f509(x12023,x12024,x12021,x12025,x12026,x12027,x12028),f509(x12023,x12024,x12022,x12025,x12026,x12027,x12028))
% 157.76/157.54 [1203]~E(x12031,x12032)+E(f509(x12033,x12034,x12035,x12031,x12036,x12037,x12038),f509(x12033,x12034,x12035,x12032,x12036,x12037,x12038))
% 157.76/157.54 [1204]~E(x12041,x12042)+E(f509(x12043,x12044,x12045,x12046,x12041,x12047,x12048),f509(x12043,x12044,x12045,x12046,x12042,x12047,x12048))
% 157.76/157.54 [1205]~E(x12051,x12052)+E(f509(x12053,x12054,x12055,x12056,x12057,x12051,x12058),f509(x12053,x12054,x12055,x12056,x12057,x12052,x12058))
% 157.76/157.54 [1206]~E(x12061,x12062)+E(f509(x12063,x12064,x12065,x12066,x12067,x12068,x12061),f509(x12063,x12064,x12065,x12066,x12067,x12068,x12062))
% 157.76/157.54 [1207]~E(x12071,x12072)+E(f833(x12071,x12073,x12074,x12075,x12076,x12077),f833(x12072,x12073,x12074,x12075,x12076,x12077))
% 157.76/157.54 [1208]~E(x12081,x12082)+E(f833(x12083,x12081,x12084,x12085,x12086,x12087),f833(x12083,x12082,x12084,x12085,x12086,x12087))
% 157.76/157.54 [1209]~E(x12091,x12092)+E(f833(x12093,x12094,x12091,x12095,x12096,x12097),f833(x12093,x12094,x12092,x12095,x12096,x12097))
% 157.76/157.54 [1210]~E(x12101,x12102)+E(f833(x12103,x12104,x12105,x12101,x12106,x12107),f833(x12103,x12104,x12105,x12102,x12106,x12107))
% 157.76/157.54 [1211]~E(x12111,x12112)+E(f833(x12113,x12114,x12115,x12116,x12111,x12117),f833(x12113,x12114,x12115,x12116,x12112,x12117))
% 157.76/157.54 [1212]~E(x12121,x12122)+E(f833(x12123,x12124,x12125,x12126,x12127,x12121),f833(x12123,x12124,x12125,x12126,x12127,x12122))
% 157.76/157.54 [1213]~E(x12131,x12132)+E(f58(x12131,x12133),f58(x12132,x12133))
% 157.76/157.54 [1214]~E(x12141,x12142)+E(f58(x12143,x12141),f58(x12143,x12142))
% 157.76/157.54 [1215]~E(x12151,x12152)+E(f131(x12151),f131(x12152))
% 157.76/157.54 [1216]~E(x12161,x12162)+E(f275(x12161),f275(x12162))
% 157.76/157.54 [1217]~E(x12171,x12172)+E(f278(x12171,x12173),f278(x12172,x12173))
% 157.76/157.54 [1218]~E(x12181,x12182)+E(f278(x12183,x12181),f278(x12183,x12182))
% 157.76/157.54 [1219]~E(x12191,x12192)+E(f920(x12191,x12193,x12194,x12195,x12196),f920(x12192,x12193,x12194,x12195,x12196))
% 157.76/157.54 [1220]~E(x12201,x12202)+E(f920(x12203,x12201,x12204,x12205,x12206),f920(x12203,x12202,x12204,x12205,x12206))
% 157.76/157.54 [1221]~E(x12211,x12212)+E(f920(x12213,x12214,x12211,x12215,x12216),f920(x12213,x12214,x12212,x12215,x12216))
% 157.76/157.54 [1222]~E(x12221,x12222)+E(f920(x12223,x12224,x12225,x12221,x12226),f920(x12223,x12224,x12225,x12222,x12226))
% 157.76/157.54 [1223]~E(x12231,x12232)+E(f920(x12233,x12234,x12235,x12236,x12231),f920(x12233,x12234,x12235,x12236,x12232))
% 157.76/157.54 [1224]~E(x12241,x12242)+E(f921(x12241,x12243,x12244,x12245,x12246),f921(x12242,x12243,x12244,x12245,x12246))
% 157.76/157.54 [1225]~E(x12251,x12252)+E(f921(x12253,x12251,x12254,x12255,x12256),f921(x12253,x12252,x12254,x12255,x12256))
% 157.76/157.54 [1226]~E(x12261,x12262)+E(f921(x12263,x12264,x12261,x12265,x12266),f921(x12263,x12264,x12262,x12265,x12266))
% 157.76/157.54 [1227]~E(x12271,x12272)+E(f921(x12273,x12274,x12275,x12271,x12276),f921(x12273,x12274,x12275,x12272,x12276))
% 157.76/157.54 [1228]~E(x12281,x12282)+E(f921(x12283,x12284,x12285,x12286,x12281),f921(x12283,x12284,x12285,x12286,x12282))
% 157.76/157.54 [1229]~E(x12291,x12292)+E(f454(x12291,x12293),f454(x12292,x12293))
% 157.76/157.54 [1230]~E(x12301,x12302)+E(f454(x12303,x12301),f454(x12303,x12302))
% 157.76/157.54 [1231]~E(x12311,x12312)+E(f699(x12311,x12313,x12314),f699(x12312,x12313,x12314))
% 157.76/157.54 [1232]~E(x12321,x12322)+E(f699(x12323,x12321,x12324),f699(x12323,x12322,x12324))
% 157.76/157.54 [1233]~E(x12331,x12332)+E(f699(x12333,x12334,x12331),f699(x12333,x12334,x12332))
% 157.76/157.54 [1234]~E(x12341,x12342)+E(f135(x12341,x12343),f135(x12342,x12343))
% 157.76/157.54 [1235]~E(x12351,x12352)+E(f135(x12353,x12351),f135(x12353,x12352))
% 157.76/157.54 [1236]~E(x12361,x12362)+E(f139(x12361,x12363),f139(x12362,x12363))
% 157.76/157.54 [1237]~E(x12371,x12372)+E(f139(x12373,x12371),f139(x12373,x12372))
% 157.76/157.54 [1238]~E(x12381,x12382)+E(f728(x12381,x12383),f728(x12382,x12383))
% 157.76/157.54 [1239]~E(x12391,x12392)+E(f728(x12393,x12391),f728(x12393,x12392))
% 157.76/157.54 [1240]~E(x12401,x12402)+E(f758(x12401,x12403),f758(x12402,x12403))
% 157.76/157.54 [1241]~E(x12411,x12412)+E(f758(x12413,x12411),f758(x12413,x12412))
% 157.76/157.54 [1242]~E(x12421,x12422)+E(f583(x12421,x12423,x12424,x12425,x12426),f583(x12422,x12423,x12424,x12425,x12426))
% 157.76/157.54 [1243]~E(x12431,x12432)+E(f583(x12433,x12431,x12434,x12435,x12436),f583(x12433,x12432,x12434,x12435,x12436))
% 157.76/157.54 [1244]~E(x12441,x12442)+E(f583(x12443,x12444,x12441,x12445,x12446),f583(x12443,x12444,x12442,x12445,x12446))
% 157.76/157.54 [1245]~E(x12451,x12452)+E(f583(x12453,x12454,x12455,x12451,x12456),f583(x12453,x12454,x12455,x12452,x12456))
% 157.76/157.54 [1246]~E(x12461,x12462)+E(f583(x12463,x12464,x12465,x12466,x12461),f583(x12463,x12464,x12465,x12466,x12462))
% 157.76/157.54 [1247]~E(x12471,x12472)+E(f737(x12471,x12473,x12474,x12475),f737(x12472,x12473,x12474,x12475))
% 157.76/157.54 [1248]~E(x12481,x12482)+E(f737(x12483,x12481,x12484,x12485),f737(x12483,x12482,x12484,x12485))
% 157.76/157.54 [1249]~E(x12491,x12492)+E(f737(x12493,x12494,x12491,x12495),f737(x12493,x12494,x12492,x12495))
% 157.76/157.54 [1250]~E(x12501,x12502)+E(f737(x12503,x12504,x12505,x12501),f737(x12503,x12504,x12505,x12502))
% 157.76/157.54 [1251]~E(x12511,x12512)+E(f173(x12511,x12513,x12514),f173(x12512,x12513,x12514))
% 157.76/157.54 [1252]~E(x12521,x12522)+E(f173(x12523,x12521,x12524),f173(x12523,x12522,x12524))
% 157.76/157.54 [1253]~E(x12531,x12532)+E(f173(x12533,x12534,x12531),f173(x12533,x12534,x12532))
% 157.76/157.54 [1254]~E(x12541,x12542)+E(f401(x12541,x12543,x12544,x12545,x12546),f401(x12542,x12543,x12544,x12545,x12546))
% 157.76/157.54 [1255]~E(x12551,x12552)+E(f401(x12553,x12551,x12554,x12555,x12556),f401(x12553,x12552,x12554,x12555,x12556))
% 157.76/157.54 [1256]~E(x12561,x12562)+E(f401(x12563,x12564,x12561,x12565,x12566),f401(x12563,x12564,x12562,x12565,x12566))
% 157.76/157.54 [1257]~E(x12571,x12572)+E(f401(x12573,x12574,x12575,x12571,x12576),f401(x12573,x12574,x12575,x12572,x12576))
% 157.76/157.54 [1258]~E(x12581,x12582)+E(f401(x12583,x12584,x12585,x12586,x12581),f401(x12583,x12584,x12585,x12586,x12582))
% 157.76/157.54 [1259]~E(x12591,x12592)+E(f627(x12591,x12593,x12594,x12595,x12596,x12597,x12598,x12599),f627(x12592,x12593,x12594,x12595,x12596,x12597,x12598,x12599))
% 157.76/157.54 [1260]~E(x12601,x12602)+E(f627(x12603,x12601,x12604,x12605,x12606,x12607,x12608,x12609),f627(x12603,x12602,x12604,x12605,x12606,x12607,x12608,x12609))
% 157.76/157.54 [1261]~E(x12611,x12612)+E(f627(x12613,x12614,x12611,x12615,x12616,x12617,x12618,x12619),f627(x12613,x12614,x12612,x12615,x12616,x12617,x12618,x12619))
% 157.76/157.54 [1262]~E(x12621,x12622)+E(f627(x12623,x12624,x12625,x12621,x12626,x12627,x12628,x12629),f627(x12623,x12624,x12625,x12622,x12626,x12627,x12628,x12629))
% 157.76/157.54 [1263]~E(x12631,x12632)+E(f627(x12633,x12634,x12635,x12636,x12631,x12637,x12638,x12639),f627(x12633,x12634,x12635,x12636,x12632,x12637,x12638,x12639))
% 157.76/157.54 [1264]~E(x12641,x12642)+E(f627(x12643,x12644,x12645,x12646,x12647,x12641,x12648,x12649),f627(x12643,x12644,x12645,x12646,x12647,x12642,x12648,x12649))
% 157.76/157.54 [1265]~E(x12651,x12652)+E(f627(x12653,x12654,x12655,x12656,x12657,x12658,x12651,x12659),f627(x12653,x12654,x12655,x12656,x12657,x12658,x12652,x12659))
% 157.76/157.54 [1266]~E(x12661,x12662)+E(f627(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12661),f627(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12662))
% 157.76/157.54 [1267]~E(x12671,x12672)+E(f499(x12671,x12673,x12674),f499(x12672,x12673,x12674))
% 157.76/157.54 [1268]~E(x12681,x12682)+E(f499(x12683,x12681,x12684),f499(x12683,x12682,x12684))
% 157.76/157.54 [1269]~E(x12691,x12692)+E(f499(x12693,x12694,x12691),f499(x12693,x12694,x12692))
% 157.76/157.54 [1270]~E(x12701,x12702)+E(f255(x12701,x12703,x12704),f255(x12702,x12703,x12704))
% 157.76/157.54 [1271]~E(x12711,x12712)+E(f255(x12713,x12711,x12714),f255(x12713,x12712,x12714))
% 157.76/157.54 [1272]~E(x12721,x12722)+E(f255(x12723,x12724,x12721),f255(x12723,x12724,x12722))
% 157.76/157.54 [1273]~E(x12731,x12732)+E(f595(x12731,x12733),f595(x12732,x12733))
% 157.76/157.54 [1274]~E(x12741,x12742)+E(f595(x12743,x12741),f595(x12743,x12742))
% 157.76/157.54 [1275]~E(x12751,x12752)+E(f844(x12751,x12753,x12754),f844(x12752,x12753,x12754))
% 157.76/157.54 [1276]~E(x12761,x12762)+E(f844(x12763,x12761,x12764),f844(x12763,x12762,x12764))
% 157.76/157.54 [1277]~E(x12771,x12772)+E(f844(x12773,x12774,x12771),f844(x12773,x12774,x12772))
% 157.76/157.54 [1278]~E(x12781,x12782)+E(f205(x12781,x12783,x12784,x12785),f205(x12782,x12783,x12784,x12785))
% 157.76/157.54 [1279]~E(x12791,x12792)+E(f205(x12793,x12791,x12794,x12795),f205(x12793,x12792,x12794,x12795))
% 157.76/157.54 [1280]~E(x12801,x12802)+E(f205(x12803,x12804,x12801,x12805),f205(x12803,x12804,x12802,x12805))
% 157.76/157.54 [1281]~E(x12811,x12812)+E(f205(x12813,x12814,x12815,x12811),f205(x12813,x12814,x12815,x12812))
% 157.76/157.54 [1282]~E(x12821,x12822)+E(f208(x12821,x12823),f208(x12822,x12823))
% 157.76/157.54 [1283]~E(x12831,x12832)+E(f208(x12833,x12831),f208(x12833,x12832))
% 157.76/157.54 [1284]~E(x12841,x12842)+E(f421(x12841,x12843,x12844),f421(x12842,x12843,x12844))
% 157.76/157.54 [1285]~E(x12851,x12852)+E(f421(x12853,x12851,x12854),f421(x12853,x12852,x12854))
% 157.76/157.54 [1286]~E(x12861,x12862)+E(f421(x12863,x12864,x12861),f421(x12863,x12864,x12862))
% 157.76/157.54 [1287]~E(x12871,x12872)+E(f136(x12871),f136(x12872))
% 157.76/157.54 [1288]~E(x12881,x12882)+E(f506(x12881,x12883,x12884,x12885,x12886,x12887,x12888),f506(x12882,x12883,x12884,x12885,x12886,x12887,x12888))
% 157.76/157.54 [1289]~E(x12891,x12892)+E(f506(x12893,x12891,x12894,x12895,x12896,x12897,x12898),f506(x12893,x12892,x12894,x12895,x12896,x12897,x12898))
% 157.76/157.54 [1290]~E(x12901,x12902)+E(f506(x12903,x12904,x12901,x12905,x12906,x12907,x12908),f506(x12903,x12904,x12902,x12905,x12906,x12907,x12908))
% 157.76/157.54 [1291]~E(x12911,x12912)+E(f506(x12913,x12914,x12915,x12911,x12916,x12917,x12918),f506(x12913,x12914,x12915,x12912,x12916,x12917,x12918))
% 157.76/157.54 [1292]~E(x12921,x12922)+E(f506(x12923,x12924,x12925,x12926,x12921,x12927,x12928),f506(x12923,x12924,x12925,x12926,x12922,x12927,x12928))
% 157.76/157.54 [1293]~E(x12931,x12932)+E(f506(x12933,x12934,x12935,x12936,x12937,x12931,x12938),f506(x12933,x12934,x12935,x12936,x12937,x12932,x12938))
% 157.76/157.54 [1294]~E(x12941,x12942)+E(f506(x12943,x12944,x12945,x12946,x12947,x12948,x12941),f506(x12943,x12944,x12945,x12946,x12947,x12948,x12942))
% 157.76/157.54 [1295]~E(x12951,x12952)+E(f835(x12951,x12953,x12954),f835(x12952,x12953,x12954))
% 157.76/157.54 [1296]~E(x12961,x12962)+E(f835(x12963,x12961,x12964),f835(x12963,x12962,x12964))
% 157.76/157.54 [1297]~E(x12971,x12972)+E(f835(x12973,x12974,x12971),f835(x12973,x12974,x12972))
% 157.76/157.54 [1298]~E(x12981,x12982)+E(f319(x12981,x12983),f319(x12982,x12983))
% 157.76/157.54 [1299]~E(x12991,x12992)+E(f319(x12993,x12991),f319(x12993,x12992))
% 157.76/157.54 [1300]~E(x13001,x13002)+E(f367(x13001,x13003,x13004),f367(x13002,x13003,x13004))
% 157.76/157.54 [1301]~E(x13011,x13012)+E(f367(x13013,x13011,x13014),f367(x13013,x13012,x13014))
% 157.76/157.54 [1302]~E(x13021,x13022)+E(f367(x13023,x13024,x13021),f367(x13023,x13024,x13022))
% 157.76/157.54 [1303]~E(x13031,x13032)+E(f147(x13031,x13033,x13034),f147(x13032,x13033,x13034))
% 157.76/157.54 [1304]~E(x13041,x13042)+E(f147(x13043,x13041,x13044),f147(x13043,x13042,x13044))
% 157.76/157.54 [1305]~E(x13051,x13052)+E(f147(x13053,x13054,x13051),f147(x13053,x13054,x13052))
% 157.76/157.54 [1306]~E(x13061,x13062)+E(f697(x13061,x13063,x13064,x13065,x13066),f697(x13062,x13063,x13064,x13065,x13066))
% 157.76/157.54 [1307]~E(x13071,x13072)+E(f697(x13073,x13071,x13074,x13075,x13076),f697(x13073,x13072,x13074,x13075,x13076))
% 157.76/157.54 [1308]~E(x13081,x13082)+E(f697(x13083,x13084,x13081,x13085,x13086),f697(x13083,x13084,x13082,x13085,x13086))
% 157.76/157.54 [1309]~E(x13091,x13092)+E(f697(x13093,x13094,x13095,x13091,x13096),f697(x13093,x13094,x13095,x13092,x13096))
% 157.76/157.54 [1310]~E(x13101,x13102)+E(f697(x13103,x13104,x13105,x13106,x13101),f697(x13103,x13104,x13105,x13106,x13102))
% 157.76/157.54 [1311]~E(x13111,x13112)+E(f472(x13111,x13113,x13114),f472(x13112,x13113,x13114))
% 157.76/157.54 [1312]~E(x13121,x13122)+E(f472(x13123,x13121,x13124),f472(x13123,x13122,x13124))
% 157.76/157.54 [1313]~E(x13131,x13132)+E(f472(x13133,x13134,x13131),f472(x13133,x13134,x13132))
% 157.76/157.54 [1314]~E(x13141,x13142)+E(f152(x13141,x13143),f152(x13142,x13143))
% 157.76/157.54 [1315]~E(x13151,x13152)+E(f152(x13153,x13151),f152(x13153,x13152))
% 157.76/157.54 [1316]~E(x13161,x13162)+E(f676(x13161,x13163,x13164,x13165),f676(x13162,x13163,x13164,x13165))
% 157.76/157.54 [1317]~E(x13171,x13172)+E(f676(x13173,x13171,x13174,x13175),f676(x13173,x13172,x13174,x13175))
% 157.76/157.54 [1318]~E(x13181,x13182)+E(f676(x13183,x13184,x13181,x13185),f676(x13183,x13184,x13182,x13185))
% 157.76/157.54 [1319]~E(x13191,x13192)+E(f676(x13193,x13194,x13195,x13191),f676(x13193,x13194,x13195,x13192))
% 157.76/157.54 [1320]~E(x13201,x13202)+E(f643(x13201,x13203,x13204),f643(x13202,x13203,x13204))
% 157.76/157.54 [1321]~E(x13211,x13212)+E(f643(x13213,x13211,x13214),f643(x13213,x13212,x13214))
% 157.76/157.54 [1322]~E(x13221,x13222)+E(f643(x13223,x13224,x13221),f643(x13223,x13224,x13222))
% 157.76/157.54 [1323]~E(x13231,x13232)+E(f668(x13231,x13233,x13234,x13235),f668(x13232,x13233,x13234,x13235))
% 157.76/157.54 [1324]~E(x13241,x13242)+E(f668(x13243,x13241,x13244,x13245),f668(x13243,x13242,x13244,x13245))
% 157.76/157.54 [1325]~E(x13251,x13252)+E(f668(x13253,x13254,x13251,x13255),f668(x13253,x13254,x13252,x13255))
% 157.76/157.54 [1326]~E(x13261,x13262)+E(f668(x13263,x13264,x13265,x13261),f668(x13263,x13264,x13265,x13262))
% 157.76/157.54 [1327]~E(x13271,x13272)+E(f791(x13271,x13273),f791(x13272,x13273))
% 157.76/157.54 [1328]~E(x13281,x13282)+E(f791(x13283,x13281),f791(x13283,x13282))
% 157.76/157.54 [1329]~E(x13291,x13292)+E(f731(x13291,x13293,x13294,x13295),f731(x13292,x13293,x13294,x13295))
% 157.76/157.54 [1330]~E(x13301,x13302)+E(f731(x13303,x13301,x13304,x13305),f731(x13303,x13302,x13304,x13305))
% 157.76/157.54 [1331]~E(x13311,x13312)+E(f731(x13313,x13314,x13311,x13315),f731(x13313,x13314,x13312,x13315))
% 157.76/157.54 [1332]~E(x13321,x13322)+E(f731(x13323,x13324,x13325,x13321),f731(x13323,x13324,x13325,x13322))
% 157.76/157.54 [1333]~E(x13331,x13332)+E(f263(x13331,x13333,x13334,x13335),f263(x13332,x13333,x13334,x13335))
% 157.76/157.54 [1334]~E(x13341,x13342)+E(f263(x13343,x13341,x13344,x13345),f263(x13343,x13342,x13344,x13345))
% 157.76/157.54 [1335]~E(x13351,x13352)+E(f263(x13353,x13354,x13351,x13355),f263(x13353,x13354,x13352,x13355))
% 157.76/157.54 [1336]~E(x13361,x13362)+E(f263(x13363,x13364,x13365,x13361),f263(x13363,x13364,x13365,x13362))
% 157.76/157.54 [1337]~E(x13371,x13372)+E(f492(x13371,x13373,x13374),f492(x13372,x13373,x13374))
% 157.76/157.54 [1338]~E(x13381,x13382)+E(f492(x13383,x13381,x13384),f492(x13383,x13382,x13384))
% 157.76/157.54 [1339]~E(x13391,x13392)+E(f492(x13393,x13394,x13391),f492(x13393,x13394,x13392))
% 157.76/157.54 [1340]~E(x13401,x13402)+E(f691(x13401,x13403,x13404,x13405,x13406),f691(x13402,x13403,x13404,x13405,x13406))
% 157.76/157.54 [1341]~E(x13411,x13412)+E(f691(x13413,x13411,x13414,x13415,x13416),f691(x13413,x13412,x13414,x13415,x13416))
% 157.76/157.54 [1342]~E(x13421,x13422)+E(f691(x13423,x13424,x13421,x13425,x13426),f691(x13423,x13424,x13422,x13425,x13426))
% 157.76/157.54 [1343]~E(x13431,x13432)+E(f691(x13433,x13434,x13435,x13431,x13436),f691(x13433,x13434,x13435,x13432,x13436))
% 157.76/157.54 [1344]~E(x13441,x13442)+E(f691(x13443,x13444,x13445,x13446,x13441),f691(x13443,x13444,x13445,x13446,x13442))
% 157.76/157.54 [1345]~E(x13451,x13452)+E(f564(x13451,x13453,x13454,x13455,x13456,x13457),f564(x13452,x13453,x13454,x13455,x13456,x13457))
% 157.76/157.54 [1346]~E(x13461,x13462)+E(f564(x13463,x13461,x13464,x13465,x13466,x13467),f564(x13463,x13462,x13464,x13465,x13466,x13467))
% 157.76/157.54 [1347]~E(x13471,x13472)+E(f564(x13473,x13474,x13471,x13475,x13476,x13477),f564(x13473,x13474,x13472,x13475,x13476,x13477))
% 157.76/157.54 [1348]~E(x13481,x13482)+E(f564(x13483,x13484,x13485,x13481,x13486,x13487),f564(x13483,x13484,x13485,x13482,x13486,x13487))
% 157.76/157.54 [1349]~E(x13491,x13492)+E(f564(x13493,x13494,x13495,x13496,x13491,x13497),f564(x13493,x13494,x13495,x13496,x13492,x13497))
% 157.76/157.54 [1350]~E(x13501,x13502)+E(f564(x13503,x13504,x13505,x13506,x13507,x13501),f564(x13503,x13504,x13505,x13506,x13507,x13502))
% 157.76/157.54 [1351]~E(x13511,x13512)+E(f415(x13511,x13513),f415(x13512,x13513))
% 157.76/157.54 [1352]~E(x13521,x13522)+E(f415(x13523,x13521),f415(x13523,x13522))
% 157.76/157.54 [1353]~E(x13531,x13532)+E(f752(x13531,x13533,x13534,x13535,x13536),f752(x13532,x13533,x13534,x13535,x13536))
% 157.76/157.54 [1354]~E(x13541,x13542)+E(f752(x13543,x13541,x13544,x13545,x13546),f752(x13543,x13542,x13544,x13545,x13546))
% 157.76/157.54 [1355]~E(x13551,x13552)+E(f752(x13553,x13554,x13551,x13555,x13556),f752(x13553,x13554,x13552,x13555,x13556))
% 157.76/157.54 [1356]~E(x13561,x13562)+E(f752(x13563,x13564,x13565,x13561,x13566),f752(x13563,x13564,x13565,x13562,x13566))
% 157.76/157.54 [1357]~E(x13571,x13572)+E(f752(x13573,x13574,x13575,x13576,x13571),f752(x13573,x13574,x13575,x13576,x13572))
% 157.76/157.54 [1358]~E(x13581,x13582)+E(f605(x13581,x13583,x13584,x13585,x13586),f605(x13582,x13583,x13584,x13585,x13586))
% 157.76/157.54 [1359]~E(x13591,x13592)+E(f605(x13593,x13591,x13594,x13595,x13596),f605(x13593,x13592,x13594,x13595,x13596))
% 157.76/157.54 [1360]~E(x13601,x13602)+E(f605(x13603,x13604,x13601,x13605,x13606),f605(x13603,x13604,x13602,x13605,x13606))
% 157.76/157.54 [1361]~E(x13611,x13612)+E(f605(x13613,x13614,x13615,x13611,x13616),f605(x13613,x13614,x13615,x13612,x13616))
% 157.76/157.54 [1362]~E(x13621,x13622)+E(f605(x13623,x13624,x13625,x13626,x13621),f605(x13623,x13624,x13625,x13626,x13622))
% 157.76/157.54 [1363]~E(x13631,x13632)+E(f303(x13631,x13633,x13634,x13635),f303(x13632,x13633,x13634,x13635))
% 157.76/157.54 [1364]~E(x13641,x13642)+E(f303(x13643,x13641,x13644,x13645),f303(x13643,x13642,x13644,x13645))
% 157.76/157.54 [1365]~E(x13651,x13652)+E(f303(x13653,x13654,x13651,x13655),f303(x13653,x13654,x13652,x13655))
% 157.76/157.54 [1366]~E(x13661,x13662)+E(f303(x13663,x13664,x13665,x13661),f303(x13663,x13664,x13665,x13662))
% 157.76/157.54 [1367]~E(x13671,x13672)+E(f806(x13671,x13673,x13674),f806(x13672,x13673,x13674))
% 157.76/157.54 [1368]~E(x13681,x13682)+E(f806(x13683,x13681,x13684),f806(x13683,x13682,x13684))
% 157.76/157.54 [1369]~E(x13691,x13692)+E(f806(x13693,x13694,x13691),f806(x13693,x13694,x13692))
% 157.76/157.54 [1370]~E(x13701,x13702)+E(f64(x13701,x13703,x13704,x13705),f64(x13702,x13703,x13704,x13705))
% 157.76/157.54 [1371]~E(x13711,x13712)+E(f64(x13713,x13711,x13714,x13715),f64(x13713,x13712,x13714,x13715))
% 157.76/157.54 [1372]~E(x13721,x13722)+E(f64(x13723,x13724,x13721,x13725),f64(x13723,x13724,x13722,x13725))
% 157.76/157.54 [1373]~E(x13731,x13732)+E(f64(x13733,x13734,x13735,x13731),f64(x13733,x13734,x13735,x13732))
% 157.76/157.54 [1374]~E(x13741,x13742)+E(f553(x13741),f553(x13742))
% 157.76/157.54 [1375]~E(x13751,x13752)+E(f614(x13751,x13753,x13754,x13755),f614(x13752,x13753,x13754,x13755))
% 157.76/157.54 [1376]~E(x13761,x13762)+E(f614(x13763,x13761,x13764,x13765),f614(x13763,x13762,x13764,x13765))
% 157.76/157.54 [1377]~E(x13771,x13772)+E(f614(x13773,x13774,x13771,x13775),f614(x13773,x13774,x13772,x13775))
% 157.76/157.54 [1378]~E(x13781,x13782)+E(f614(x13783,x13784,x13785,x13781),f614(x13783,x13784,x13785,x13782))
% 157.76/157.54 [1379]~E(x13791,x13792)+E(f422(x13791,x13793,x13794,x13795),f422(x13792,x13793,x13794,x13795))
% 157.76/157.54 [1380]~E(x13801,x13802)+E(f422(x13803,x13801,x13804,x13805),f422(x13803,x13802,x13804,x13805))
% 157.76/157.54 [1381]~E(x13811,x13812)+E(f422(x13813,x13814,x13811,x13815),f422(x13813,x13814,x13812,x13815))
% 157.76/157.54 [1382]~E(x13821,x13822)+E(f422(x13823,x13824,x13825,x13821),f422(x13823,x13824,x13825,x13822))
% 157.76/157.54 [1383]~E(x13831,x13832)+E(f670(x13831,x13833,x13834),f670(x13832,x13833,x13834))
% 157.76/157.54 [1384]~E(x13841,x13842)+E(f670(x13843,x13841,x13844),f670(x13843,x13842,x13844))
% 157.76/157.54 [1385]~E(x13851,x13852)+E(f670(x13853,x13854,x13851),f670(x13853,x13854,x13852))
% 157.76/157.54 [1386]~E(x13861,x13862)+E(f598(x13861,x13863,x13864,x13865,x13866),f598(x13862,x13863,x13864,x13865,x13866))
% 157.76/157.54 [1387]~E(x13871,x13872)+E(f598(x13873,x13871,x13874,x13875,x13876),f598(x13873,x13872,x13874,x13875,x13876))
% 157.76/157.54 [1388]~E(x13881,x13882)+E(f598(x13883,x13884,x13881,x13885,x13886),f598(x13883,x13884,x13882,x13885,x13886))
% 157.76/157.54 [1389]~E(x13891,x13892)+E(f598(x13893,x13894,x13895,x13891,x13896),f598(x13893,x13894,x13895,x13892,x13896))
% 157.76/157.54 [1390]~E(x13901,x13902)+E(f598(x13903,x13904,x13905,x13906,x13901),f598(x13903,x13904,x13905,x13906,x13902))
% 157.76/157.54 [1391]~E(x13911,x13912)+E(f137(x13911,x13913,x13914,x13915),f137(x13912,x13913,x13914,x13915))
% 157.76/157.54 [1392]~E(x13921,x13922)+E(f137(x13923,x13921,x13924,x13925),f137(x13923,x13922,x13924,x13925))
% 157.76/157.54 [1393]~E(x13931,x13932)+E(f137(x13933,x13934,x13931,x13935),f137(x13933,x13934,x13932,x13935))
% 157.76/157.54 [1394]~E(x13941,x13942)+E(f137(x13943,x13944,x13945,x13941),f137(x13943,x13944,x13945,x13942))
% 157.76/157.54 [1395]~E(x13951,x13952)+E(f882(x13951,x13953,x13954,x13955,x13956),f882(x13952,x13953,x13954,x13955,x13956))
% 157.76/157.54 [1396]~E(x13961,x13962)+E(f882(x13963,x13961,x13964,x13965,x13966),f882(x13963,x13962,x13964,x13965,x13966))
% 157.76/157.54 [1397]~E(x13971,x13972)+E(f882(x13973,x13974,x13971,x13975,x13976),f882(x13973,x13974,x13972,x13975,x13976))
% 157.76/157.54 [1398]~E(x13981,x13982)+E(f882(x13983,x13984,x13985,x13981,x13986),f882(x13983,x13984,x13985,x13982,x13986))
% 157.76/157.54 [1399]~E(x13991,x13992)+E(f882(x13993,x13994,x13995,x13996,x13991),f882(x13993,x13994,x13995,x13996,x13992))
% 157.76/157.54 [1400]~E(x14001,x14002)+E(f801(x14001,x14003,x14004,x14005,x14006,x14007,x14008),f801(x14002,x14003,x14004,x14005,x14006,x14007,x14008))
% 157.76/157.54 [1401]~E(x14011,x14012)+E(f801(x14013,x14011,x14014,x14015,x14016,x14017,x14018),f801(x14013,x14012,x14014,x14015,x14016,x14017,x14018))
% 157.76/157.54 [1402]~E(x14021,x14022)+E(f801(x14023,x14024,x14021,x14025,x14026,x14027,x14028),f801(x14023,x14024,x14022,x14025,x14026,x14027,x14028))
% 157.76/157.54 [1403]~E(x14031,x14032)+E(f801(x14033,x14034,x14035,x14031,x14036,x14037,x14038),f801(x14033,x14034,x14035,x14032,x14036,x14037,x14038))
% 157.76/157.54 [1404]~E(x14041,x14042)+E(f801(x14043,x14044,x14045,x14046,x14041,x14047,x14048),f801(x14043,x14044,x14045,x14046,x14042,x14047,x14048))
% 157.76/157.54 [1405]~E(x14051,x14052)+E(f801(x14053,x14054,x14055,x14056,x14057,x14051,x14058),f801(x14053,x14054,x14055,x14056,x14057,x14052,x14058))
% 157.76/157.54 [1406]~E(x14061,x14062)+E(f801(x14063,x14064,x14065,x14066,x14067,x14068,x14061),f801(x14063,x14064,x14065,x14066,x14067,x14068,x14062))
% 157.76/157.54 [1407]~E(x14071,x14072)+E(f813(x14071,x14073),f813(x14072,x14073))
% 157.76/157.54 [1408]~E(x14081,x14082)+E(f813(x14083,x14081),f813(x14083,x14082))
% 157.76/157.54 [1409]~E(x14091,x14092)+E(f588(x14091,x14093,x14094),f588(x14092,x14093,x14094))
% 157.76/157.54 [1410]~E(x14101,x14102)+E(f588(x14103,x14101,x14104),f588(x14103,x14102,x14104))
% 157.76/157.54 [1411]~E(x14111,x14112)+E(f588(x14113,x14114,x14111),f588(x14113,x14114,x14112))
% 157.76/157.54 [1412]~E(x14121,x14122)+E(f912(x14121,x14123,x14124),f912(x14122,x14123,x14124))
% 157.76/157.54 [1413]~E(x14131,x14132)+E(f912(x14133,x14131,x14134),f912(x14133,x14132,x14134))
% 157.76/157.54 [1414]~E(x14141,x14142)+E(f912(x14143,x14144,x14141),f912(x14143,x14144,x14142))
% 157.76/157.54 [1415]~E(x14151,x14152)+E(f573(x14151,x14153,x14154,x14155),f573(x14152,x14153,x14154,x14155))
% 157.76/157.54 [1416]~E(x14161,x14162)+E(f573(x14163,x14161,x14164,x14165),f573(x14163,x14162,x14164,x14165))
% 157.76/157.54 [1417]~E(x14171,x14172)+E(f573(x14173,x14174,x14171,x14175),f573(x14173,x14174,x14172,x14175))
% 157.76/157.54 [1418]~E(x14181,x14182)+E(f573(x14183,x14184,x14185,x14181),f573(x14183,x14184,x14185,x14182))
% 157.76/157.54 [1419]~E(x14191,x14192)+E(f862(x14191,x14193,x14194,x14195,x14196,x14197,x14198),f862(x14192,x14193,x14194,x14195,x14196,x14197,x14198))
% 157.76/157.54 [1420]~E(x14201,x14202)+E(f862(x14203,x14201,x14204,x14205,x14206,x14207,x14208),f862(x14203,x14202,x14204,x14205,x14206,x14207,x14208))
% 157.76/157.54 [1421]~E(x14211,x14212)+E(f862(x14213,x14214,x14211,x14215,x14216,x14217,x14218),f862(x14213,x14214,x14212,x14215,x14216,x14217,x14218))
% 157.76/157.54 [1422]~E(x14221,x14222)+E(f862(x14223,x14224,x14225,x14221,x14226,x14227,x14228),f862(x14223,x14224,x14225,x14222,x14226,x14227,x14228))
% 157.76/157.54 [1423]~E(x14231,x14232)+E(f862(x14233,x14234,x14235,x14236,x14231,x14237,x14238),f862(x14233,x14234,x14235,x14236,x14232,x14237,x14238))
% 157.76/157.54 [1424]~E(x14241,x14242)+E(f862(x14243,x14244,x14245,x14246,x14247,x14241,x14248),f862(x14243,x14244,x14245,x14246,x14247,x14242,x14248))
% 157.76/157.54 [1425]~E(x14251,x14252)+E(f862(x14253,x14254,x14255,x14256,x14257,x14258,x14251),f862(x14253,x14254,x14255,x14256,x14257,x14258,x14252))
% 157.76/157.54 [1426]~E(x14261,x14262)+E(f467(x14261,x14263,x14264,x14265),f467(x14262,x14263,x14264,x14265))
% 157.76/157.54 [1427]~E(x14271,x14272)+E(f467(x14273,x14271,x14274,x14275),f467(x14273,x14272,x14274,x14275))
% 157.76/157.54 [1428]~E(x14281,x14282)+E(f467(x14283,x14284,x14281,x14285),f467(x14283,x14284,x14282,x14285))
% 157.76/157.54 [1429]~E(x14291,x14292)+E(f467(x14293,x14294,x14295,x14291),f467(x14293,x14294,x14295,x14292))
% 157.76/157.54 [1430]~E(x14301,x14302)+E(f289(x14301),f289(x14302))
% 157.76/157.54 [1431]~E(x14311,x14312)+E(f750(x14311,x14313,x14314,x14315,x14316),f750(x14312,x14313,x14314,x14315,x14316))
% 157.76/157.54 [1432]~E(x14321,x14322)+E(f750(x14323,x14321,x14324,x14325,x14326),f750(x14323,x14322,x14324,x14325,x14326))
% 157.76/157.54 [1433]~E(x14331,x14332)+E(f750(x14333,x14334,x14331,x14335,x14336),f750(x14333,x14334,x14332,x14335,x14336))
% 157.76/157.54 [1434]~E(x14341,x14342)+E(f750(x14343,x14344,x14345,x14341,x14346),f750(x14343,x14344,x14345,x14342,x14346))
% 157.76/157.54 [1435]~E(x14351,x14352)+E(f750(x14353,x14354,x14355,x14356,x14351),f750(x14353,x14354,x14355,x14356,x14352))
% 157.76/157.54 [1436]~E(x14361,x14362)+E(f280(x14361,x14363),f280(x14362,x14363))
% 157.76/157.54 [1437]~E(x14371,x14372)+E(f280(x14373,x14371),f280(x14373,x14372))
% 157.76/157.54 [1438]~E(x14381,x14382)+E(f695(x14381,x14383,x14384,x14385),f695(x14382,x14383,x14384,x14385))
% 157.76/157.54 [1439]~E(x14391,x14392)+E(f695(x14393,x14391,x14394,x14395),f695(x14393,x14392,x14394,x14395))
% 157.76/157.54 [1440]~E(x14401,x14402)+E(f695(x14403,x14404,x14401,x14405),f695(x14403,x14404,x14402,x14405))
% 157.76/157.54 [1441]~E(x14411,x14412)+E(f695(x14413,x14414,x14415,x14411),f695(x14413,x14414,x14415,x14412))
% 157.76/157.54 [1442]~E(x14421,x14422)+E(f592(x14421,x14423,x14424),f592(x14422,x14423,x14424))
% 157.76/157.54 [1443]~E(x14431,x14432)+E(f592(x14433,x14431,x14434),f592(x14433,x14432,x14434))
% 157.76/157.54 [1444]~E(x14441,x14442)+E(f592(x14443,x14444,x14441),f592(x14443,x14444,x14442))
% 157.76/157.54 [1445]~E(x14451,x14452)+E(f452(x14451),f452(x14452))
% 157.76/157.54 [1446]~E(x14461,x14462)+E(f815(x14461,x14463),f815(x14462,x14463))
% 157.76/157.54 [1447]~E(x14471,x14472)+E(f815(x14473,x14471),f815(x14473,x14472))
% 157.76/157.54 [1448]~E(x14481,x14482)+E(f404(x14481,x14483,x14484,x14485,x14486,x14487),f404(x14482,x14483,x14484,x14485,x14486,x14487))
% 157.76/157.54 [1449]~E(x14491,x14492)+E(f404(x14493,x14491,x14494,x14495,x14496,x14497),f404(x14493,x14492,x14494,x14495,x14496,x14497))
% 157.76/157.54 [1450]~E(x14501,x14502)+E(f404(x14503,x14504,x14501,x14505,x14506,x14507),f404(x14503,x14504,x14502,x14505,x14506,x14507))
% 157.76/157.54 [1451]~E(x14511,x14512)+E(f404(x14513,x14514,x14515,x14511,x14516,x14517),f404(x14513,x14514,x14515,x14512,x14516,x14517))
% 157.76/157.54 [1452]~E(x14521,x14522)+E(f404(x14523,x14524,x14525,x14526,x14521,x14527),f404(x14523,x14524,x14525,x14526,x14522,x14527))
% 157.76/157.54 [1453]~E(x14531,x14532)+E(f404(x14533,x14534,x14535,x14536,x14537,x14531),f404(x14533,x14534,x14535,x14536,x14537,x14532))
% 157.76/157.54 [1454]~E(x14541,x14542)+E(f755(x14541,x14543,x14544,x14545,x14546,x14547,x14548),f755(x14542,x14543,x14544,x14545,x14546,x14547,x14548))
% 157.76/157.54 [1455]~E(x14551,x14552)+E(f755(x14553,x14551,x14554,x14555,x14556,x14557,x14558),f755(x14553,x14552,x14554,x14555,x14556,x14557,x14558))
% 157.76/157.54 [1456]~E(x14561,x14562)+E(f755(x14563,x14564,x14561,x14565,x14566,x14567,x14568),f755(x14563,x14564,x14562,x14565,x14566,x14567,x14568))
% 157.76/157.54 [1457]~E(x14571,x14572)+E(f755(x14573,x14574,x14575,x14571,x14576,x14577,x14578),f755(x14573,x14574,x14575,x14572,x14576,x14577,x14578))
% 157.76/157.54 [1458]~E(x14581,x14582)+E(f755(x14583,x14584,x14585,x14586,x14581,x14587,x14588),f755(x14583,x14584,x14585,x14586,x14582,x14587,x14588))
% 157.76/157.54 [1459]~E(x14591,x14592)+E(f755(x14593,x14594,x14595,x14596,x14597,x14591,x14598),f755(x14593,x14594,x14595,x14596,x14597,x14592,x14598))
% 157.76/157.54 [1460]~E(x14601,x14602)+E(f755(x14603,x14604,x14605,x14606,x14607,x14608,x14601),f755(x14603,x14604,x14605,x14606,x14607,x14608,x14602))
% 157.76/157.54 [1461]~E(x14611,x14612)+E(f892(x14611,x14613,x14614),f892(x14612,x14613,x14614))
% 157.76/157.54 [1462]~E(x14621,x14622)+E(f892(x14623,x14621,x14624),f892(x14623,x14622,x14624))
% 157.76/157.54 [1463]~E(x14631,x14632)+E(f892(x14633,x14634,x14631),f892(x14633,x14634,x14632))
% 157.76/157.54 [1464]~E(x14641,x14642)+E(f357(x14641,x14643,x14644),f357(x14642,x14643,x14644))
% 157.76/157.54 [1465]~E(x14651,x14652)+E(f357(x14653,x14651,x14654),f357(x14653,x14652,x14654))
% 157.76/157.54 [1466]~E(x14661,x14662)+E(f357(x14663,x14664,x14661),f357(x14663,x14664,x14662))
% 157.76/157.54 [1467]~E(x14671,x14672)+E(f918(x14671,x14673),f918(x14672,x14673))
% 157.76/157.54 [1468]~E(x14681,x14682)+E(f918(x14683,x14681),f918(x14683,x14682))
% 157.76/157.54 [1469]~E(x14691,x14692)+E(f557(x14691,x14693,x14694),f557(x14692,x14693,x14694))
% 157.76/157.54 [1470]~E(x14701,x14702)+E(f557(x14703,x14701,x14704),f557(x14703,x14702,x14704))
% 157.76/157.54 [1471]~E(x14711,x14712)+E(f557(x14713,x14714,x14711),f557(x14713,x14714,x14712))
% 157.76/157.54 [1472]~E(x14721,x14722)+E(f342(x14721,x14723),f342(x14722,x14723))
% 157.76/157.54 [1473]~E(x14731,x14732)+E(f342(x14733,x14731),f342(x14733,x14732))
% 157.76/157.54 [1474]~E(x14741,x14742)+E(f354(x14741,x14743,x14744,x14745,x14746),f354(x14742,x14743,x14744,x14745,x14746))
% 157.76/157.54 [1475]~E(x14751,x14752)+E(f354(x14753,x14751,x14754,x14755,x14756),f354(x14753,x14752,x14754,x14755,x14756))
% 157.76/157.54 [1476]~E(x14761,x14762)+E(f354(x14763,x14764,x14761,x14765,x14766),f354(x14763,x14764,x14762,x14765,x14766))
% 157.76/157.54 [1477]~E(x14771,x14772)+E(f354(x14773,x14774,x14775,x14771,x14776),f354(x14773,x14774,x14775,x14772,x14776))
% 157.76/157.54 [1478]~E(x14781,x14782)+E(f354(x14783,x14784,x14785,x14786,x14781),f354(x14783,x14784,x14785,x14786,x14782))
% 157.76/157.54 [1479]~E(x14791,x14792)+E(f726(x14791,x14793,x14794),f726(x14792,x14793,x14794))
% 157.76/157.54 [1480]~E(x14801,x14802)+E(f726(x14803,x14801,x14804),f726(x14803,x14802,x14804))
% 157.76/157.54 [1481]~E(x14811,x14812)+E(f726(x14813,x14814,x14811),f726(x14813,x14814,x14812))
% 157.76/157.54 [1482]~E(x14821,x14822)+E(f163(x14821,x14823,x14824,x14825),f163(x14822,x14823,x14824,x14825))
% 157.76/157.54 [1483]~E(x14831,x14832)+E(f163(x14833,x14831,x14834,x14835),f163(x14833,x14832,x14834,x14835))
% 157.76/157.54 [1484]~E(x14841,x14842)+E(f163(x14843,x14844,x14841,x14845),f163(x14843,x14844,x14842,x14845))
% 157.76/157.54 [1485]~E(x14851,x14852)+E(f163(x14853,x14854,x14855,x14851),f163(x14853,x14854,x14855,x14852))
% 157.76/157.54 [1486]~E(x14861,x14862)+E(f99(x14861,x14863,x14864),f99(x14862,x14863,x14864))
% 157.76/157.54 [1487]~E(x14871,x14872)+E(f99(x14873,x14871,x14874),f99(x14873,x14872,x14874))
% 157.76/157.54 [1488]~E(x14881,x14882)+E(f99(x14883,x14884,x14881),f99(x14883,x14884,x14882))
% 157.76/157.54 [1489]~E(x14891,x14892)+E(f544(x14891,x14893),f544(x14892,x14893))
% 157.76/157.54 [1490]~E(x14901,x14902)+E(f544(x14903,x14901),f544(x14903,x14902))
% 157.76/157.54 [1491]~E(x14911,x14912)+E(f615(x14911,x14913,x14914,x14915,x14916),f615(x14912,x14913,x14914,x14915,x14916))
% 157.76/157.54 [1492]~E(x14921,x14922)+E(f615(x14923,x14921,x14924,x14925,x14926),f615(x14923,x14922,x14924,x14925,x14926))
% 157.76/157.54 [1493]~E(x14931,x14932)+E(f615(x14933,x14934,x14931,x14935,x14936),f615(x14933,x14934,x14932,x14935,x14936))
% 157.76/157.54 [1494]~E(x14941,x14942)+E(f615(x14943,x14944,x14945,x14941,x14946),f615(x14943,x14944,x14945,x14942,x14946))
% 157.76/157.54 [1495]~E(x14951,x14952)+E(f615(x14953,x14954,x14955,x14956,x14951),f615(x14953,x14954,x14955,x14956,x14952))
% 157.76/157.54 [1496]~E(x14961,x14962)+E(f599(x14961,x14963,x14964,x14965,x14966),f599(x14962,x14963,x14964,x14965,x14966))
% 157.76/157.54 [1497]~E(x14971,x14972)+E(f599(x14973,x14971,x14974,x14975,x14976),f599(x14973,x14972,x14974,x14975,x14976))
% 157.76/157.54 [1498]~E(x14981,x14982)+E(f599(x14983,x14984,x14981,x14985,x14986),f599(x14983,x14984,x14982,x14985,x14986))
% 157.76/157.54 [1499]~E(x14991,x14992)+E(f599(x14993,x14994,x14995,x14991,x14996),f599(x14993,x14994,x14995,x14992,x14996))
% 157.76/157.54 [1500]~E(x15001,x15002)+E(f599(x15003,x15004,x15005,x15006,x15001),f599(x15003,x15004,x15005,x15006,x15002))
% 157.76/157.54 [1501]~E(x15011,x15012)+E(f365(x15011,x15013,x15014),f365(x15012,x15013,x15014))
% 157.76/157.54 [1502]~E(x15021,x15022)+E(f365(x15023,x15021,x15024),f365(x15023,x15022,x15024))
% 157.76/157.54 [1503]~E(x15031,x15032)+E(f365(x15033,x15034,x15031),f365(x15033,x15034,x15032))
% 157.76/157.54 [1504]~E(x15041,x15042)+E(f707(x15041,x15043,x15044,x15045,x15046),f707(x15042,x15043,x15044,x15045,x15046))
% 157.76/157.54 [1505]~E(x15051,x15052)+E(f707(x15053,x15051,x15054,x15055,x15056),f707(x15053,x15052,x15054,x15055,x15056))
% 157.76/157.54 [1506]~E(x15061,x15062)+E(f707(x15063,x15064,x15061,x15065,x15066),f707(x15063,x15064,x15062,x15065,x15066))
% 157.76/157.54 [1507]~E(x15071,x15072)+E(f707(x15073,x15074,x15075,x15071,x15076),f707(x15073,x15074,x15075,x15072,x15076))
% 157.76/157.54 [1508]~E(x15081,x15082)+E(f707(x15083,x15084,x15085,x15086,x15081),f707(x15083,x15084,x15085,x15086,x15082))
% 157.76/157.54 [1509]~E(x15091,x15092)+E(f480(x15091,x15093,x15094),f480(x15092,x15093,x15094))
% 157.76/157.54 [1510]~E(x15101,x15102)+E(f480(x15103,x15101,x15104),f480(x15103,x15102,x15104))
% 157.76/157.54 [1511]~E(x15111,x15112)+E(f480(x15113,x15114,x15111),f480(x15113,x15114,x15112))
% 157.76/157.54 [1512]~E(x15121,x15122)+E(f793(x15121,x15123,x15124,x15125),f793(x15122,x15123,x15124,x15125))
% 157.76/157.54 [1513]~E(x15131,x15132)+E(f793(x15133,x15131,x15134,x15135),f793(x15133,x15132,x15134,x15135))
% 157.76/157.54 [1514]~E(x15141,x15142)+E(f793(x15143,x15144,x15141,x15145),f793(x15143,x15144,x15142,x15145))
% 157.76/157.54 [1515]~E(x15151,x15152)+E(f793(x15153,x15154,x15155,x15151),f793(x15153,x15154,x15155,x15152))
% 157.76/157.54 [1516]~E(x15161,x15162)+E(f847(x15161,x15163,x15164,x15165,x15166,x15167,x15168),f847(x15162,x15163,x15164,x15165,x15166,x15167,x15168))
% 157.76/157.54 [1517]~E(x15171,x15172)+E(f847(x15173,x15171,x15174,x15175,x15176,x15177,x15178),f847(x15173,x15172,x15174,x15175,x15176,x15177,x15178))
% 157.76/157.54 [1518]~E(x15181,x15182)+E(f847(x15183,x15184,x15181,x15185,x15186,x15187,x15188),f847(x15183,x15184,x15182,x15185,x15186,x15187,x15188))
% 157.76/157.54 [1519]~E(x15191,x15192)+E(f847(x15193,x15194,x15195,x15191,x15196,x15197,x15198),f847(x15193,x15194,x15195,x15192,x15196,x15197,x15198))
% 157.76/157.54 [1520]~E(x15201,x15202)+E(f847(x15203,x15204,x15205,x15206,x15201,x15207,x15208),f847(x15203,x15204,x15205,x15206,x15202,x15207,x15208))
% 157.76/157.54 [1521]~E(x15211,x15212)+E(f847(x15213,x15214,x15215,x15216,x15217,x15211,x15218),f847(x15213,x15214,x15215,x15216,x15217,x15212,x15218))
% 157.76/157.54 [1522]~E(x15221,x15222)+E(f847(x15223,x15224,x15225,x15226,x15227,x15228,x15221),f847(x15223,x15224,x15225,x15226,x15227,x15228,x15222))
% 157.76/157.54 [1523]~E(x15231,x15232)+E(f150(x15231,x15233),f150(x15232,x15233))
% 157.76/157.54 [1524]~E(x15241,x15242)+E(f150(x15243,x15241),f150(x15243,x15242))
% 157.76/157.54 [1525]~E(x15251,x15252)+E(f374(x15251),f374(x15252))
% 157.76/157.54 [1526]~E(x15261,x15262)+E(f568(x15261,x15263,x15264,x15265,x15266,x15267),f568(x15262,x15263,x15264,x15265,x15266,x15267))
% 157.76/157.54 [1527]~E(x15271,x15272)+E(f568(x15273,x15271,x15274,x15275,x15276,x15277),f568(x15273,x15272,x15274,x15275,x15276,x15277))
% 157.76/157.54 [1528]~E(x15281,x15282)+E(f568(x15283,x15284,x15281,x15285,x15286,x15287),f568(x15283,x15284,x15282,x15285,x15286,x15287))
% 157.76/157.54 [1529]~E(x15291,x15292)+E(f568(x15293,x15294,x15295,x15291,x15296,x15297),f568(x15293,x15294,x15295,x15292,x15296,x15297))
% 157.76/157.54 [1530]~E(x15301,x15302)+E(f568(x15303,x15304,x15305,x15306,x15301,x15307),f568(x15303,x15304,x15305,x15306,x15302,x15307))
% 157.76/157.54 [1531]~E(x15311,x15312)+E(f568(x15313,x15314,x15315,x15316,x15317,x15311),f568(x15313,x15314,x15315,x15316,x15317,x15312))
% 157.76/157.54 [1532]~E(x15321,x15322)+E(f756(x15321,x15323,x15324,x15325,x15326,x15327,x15328),f756(x15322,x15323,x15324,x15325,x15326,x15327,x15328))
% 157.76/157.54 [1533]~E(x15331,x15332)+E(f756(x15333,x15331,x15334,x15335,x15336,x15337,x15338),f756(x15333,x15332,x15334,x15335,x15336,x15337,x15338))
% 157.76/157.54 [1534]~E(x15341,x15342)+E(f756(x15343,x15344,x15341,x15345,x15346,x15347,x15348),f756(x15343,x15344,x15342,x15345,x15346,x15347,x15348))
% 157.76/157.54 [1535]~E(x15351,x15352)+E(f756(x15353,x15354,x15355,x15351,x15356,x15357,x15358),f756(x15353,x15354,x15355,x15352,x15356,x15357,x15358))
% 157.76/157.54 [1536]~E(x15361,x15362)+E(f756(x15363,x15364,x15365,x15366,x15361,x15367,x15368),f756(x15363,x15364,x15365,x15366,x15362,x15367,x15368))
% 157.76/157.54 [1537]~E(x15371,x15372)+E(f756(x15373,x15374,x15375,x15376,x15377,x15371,x15378),f756(x15373,x15374,x15375,x15376,x15377,x15372,x15378))
% 157.76/157.54 [1538]~E(x15381,x15382)+E(f756(x15383,x15384,x15385,x15386,x15387,x15388,x15381),f756(x15383,x15384,x15385,x15386,x15387,x15388,x15382))
% 157.76/157.54 [1539]~E(x15391,x15392)+E(f621(x15391,x15393,x15394),f621(x15392,x15393,x15394))
% 157.76/157.54 [1540]~E(x15401,x15402)+E(f621(x15403,x15401,x15404),f621(x15403,x15402,x15404))
% 157.76/157.54 [1541]~E(x15411,x15412)+E(f621(x15413,x15414,x15411),f621(x15413,x15414,x15412))
% 157.76/157.54 [1542]~E(x15421,x15422)+E(f669(x15421,x15423,x15424),f669(x15422,x15423,x15424))
% 157.76/157.54 [1543]~E(x15431,x15432)+E(f669(x15433,x15431,x15434),f669(x15433,x15432,x15434))
% 157.76/157.54 [1544]~E(x15441,x15442)+E(f669(x15443,x15444,x15441),f669(x15443,x15444,x15442))
% 157.76/157.54 [1545]~E(x15451,x15452)+E(f485(x15451,x15453,x15454,x15455),f485(x15452,x15453,x15454,x15455))
% 157.76/157.54 [1546]~E(x15461,x15462)+E(f485(x15463,x15461,x15464,x15465),f485(x15463,x15462,x15464,x15465))
% 157.76/157.54 [1547]~E(x15471,x15472)+E(f485(x15473,x15474,x15471,x15475),f485(x15473,x15474,x15472,x15475))
% 157.76/157.54 [1548]~E(x15481,x15482)+E(f485(x15483,x15484,x15485,x15481),f485(x15483,x15484,x15485,x15482))
% 157.76/157.54 [1549]~E(x15491,x15492)+E(f562(x15491,x15493,x15494,x15495,x15496,x15497),f562(x15492,x15493,x15494,x15495,x15496,x15497))
% 157.76/157.54 [1550]~E(x15501,x15502)+E(f562(x15503,x15501,x15504,x15505,x15506,x15507),f562(x15503,x15502,x15504,x15505,x15506,x15507))
% 157.76/157.54 [1551]~E(x15511,x15512)+E(f562(x15513,x15514,x15511,x15515,x15516,x15517),f562(x15513,x15514,x15512,x15515,x15516,x15517))
% 157.76/157.54 [1552]~E(x15521,x15522)+E(f562(x15523,x15524,x15525,x15521,x15526,x15527),f562(x15523,x15524,x15525,x15522,x15526,x15527))
% 157.76/157.54 [1553]~E(x15531,x15532)+E(f562(x15533,x15534,x15535,x15536,x15531,x15537),f562(x15533,x15534,x15535,x15536,x15532,x15537))
% 157.76/157.54 [1554]~E(x15541,x15542)+E(f562(x15543,x15544,x15545,x15546,x15547,x15541),f562(x15543,x15544,x15545,x15546,x15547,x15542))
% 157.76/157.54 [1555]~E(x15551,x15552)+E(f652(x15551,x15553,x15554,x15555),f652(x15552,x15553,x15554,x15555))
% 157.76/157.54 [1556]~E(x15561,x15562)+E(f652(x15563,x15561,x15564,x15565),f652(x15563,x15562,x15564,x15565))
% 157.76/157.54 [1557]~E(x15571,x15572)+E(f652(x15573,x15574,x15571,x15575),f652(x15573,x15574,x15572,x15575))
% 157.76/157.54 [1558]~E(x15581,x15582)+E(f652(x15583,x15584,x15585,x15581),f652(x15583,x15584,x15585,x15582))
% 157.76/157.54 [1559]~E(x15591,x15592)+E(f207(x15591,x15593,x15594,x15595),f207(x15592,x15593,x15594,x15595))
% 157.76/157.54 [1560]~E(x15601,x15602)+E(f207(x15603,x15601,x15604,x15605),f207(x15603,x15602,x15604,x15605))
% 157.76/157.54 [1561]~E(x15611,x15612)+E(f207(x15613,x15614,x15611,x15615),f207(x15613,x15614,x15612,x15615))
% 157.76/157.54 [1562]~E(x15621,x15622)+E(f207(x15623,x15624,x15625,x15621),f207(x15623,x15624,x15625,x15622))
% 157.76/157.54 [1563]~E(x15631,x15632)+E(f390(x15631,x15633,x15634),f390(x15632,x15633,x15634))
% 157.76/157.54 [1564]~E(x15641,x15642)+E(f390(x15643,x15641,x15644),f390(x15643,x15642,x15644))
% 157.76/157.54 [1565]~E(x15651,x15652)+E(f390(x15653,x15654,x15651),f390(x15653,x15654,x15652))
% 157.76/157.54 [1566]~E(x15661,x15662)+E(f502(x15661,x15663,x15664),f502(x15662,x15663,x15664))
% 157.76/157.54 [1567]~E(x15671,x15672)+E(f502(x15673,x15671,x15674),f502(x15673,x15672,x15674))
% 157.76/157.54 [1568]~E(x15681,x15682)+E(f502(x15683,x15684,x15681),f502(x15683,x15684,x15682))
% 157.76/157.54 [1569]~E(x15691,x15692)+E(f257(x15691,x15693,x15694),f257(x15692,x15693,x15694))
% 157.76/157.54 [1570]~E(x15701,x15702)+E(f257(x15703,x15701,x15704),f257(x15703,x15702,x15704))
% 157.76/157.54 [1571]~E(x15711,x15712)+E(f257(x15713,x15714,x15711),f257(x15713,x15714,x15712))
% 157.76/157.54 [1572]~E(x15721,x15722)+E(f307(x15721,x15723,x15724,x15725,x15726),f307(x15722,x15723,x15724,x15725,x15726))
% 157.76/157.54 [1573]~E(x15731,x15732)+E(f307(x15733,x15731,x15734,x15735,x15736),f307(x15733,x15732,x15734,x15735,x15736))
% 157.76/157.54 [1574]~E(x15741,x15742)+E(f307(x15743,x15744,x15741,x15745,x15746),f307(x15743,x15744,x15742,x15745,x15746))
% 157.76/157.54 [1575]~E(x15751,x15752)+E(f307(x15753,x15754,x15755,x15751,x15756),f307(x15753,x15754,x15755,x15752,x15756))
% 157.76/157.54 [1576]~E(x15761,x15762)+E(f307(x15763,x15764,x15765,x15766,x15761),f307(x15763,x15764,x15765,x15766,x15762))
% 157.76/157.54 [1577]~E(x15771,x15772)+E(f202(x15771,x15773,x15774,x15775),f202(x15772,x15773,x15774,x15775))
% 157.76/157.54 [1578]~E(x15781,x15782)+E(f202(x15783,x15781,x15784,x15785),f202(x15783,x15782,x15784,x15785))
% 157.76/157.54 [1579]~E(x15791,x15792)+E(f202(x15793,x15794,x15791,x15795),f202(x15793,x15794,x15792,x15795))
% 157.76/157.54 [1580]~E(x15801,x15802)+E(f202(x15803,x15804,x15805,x15801),f202(x15803,x15804,x15805,x15802))
% 157.76/157.54 [1581]~E(x15811,x15812)+E(f715(x15811,x15813),f715(x15812,x15813))
% 157.76/157.54 [1582]~E(x15821,x15822)+E(f715(x15823,x15821),f715(x15823,x15822))
% 157.76/157.54 [1583]~E(x15831,x15832)+E(f493(x15831,x15833),f493(x15832,x15833))
% 157.76/157.54 [1584]~E(x15841,x15842)+E(f493(x15843,x15841),f493(x15843,x15842))
% 157.76/157.54 [1585]~E(x15851,x15852)+E(f469(x15851),f469(x15852))
% 157.76/157.54 [1586]~E(x15861,x15862)+E(f218(x15861,x15863,x15864,x15865),f218(x15862,x15863,x15864,x15865))
% 157.76/157.54 [1587]~E(x15871,x15872)+E(f218(x15873,x15871,x15874,x15875),f218(x15873,x15872,x15874,x15875))
% 157.76/157.54 [1588]~E(x15881,x15882)+E(f218(x15883,x15884,x15881,x15885),f218(x15883,x15884,x15882,x15885))
% 157.76/157.54 [1589]~E(x15891,x15892)+E(f218(x15893,x15894,x15895,x15891),f218(x15893,x15894,x15895,x15892))
% 157.76/157.54 [1590]~E(x15901,x15902)+E(f398(x15901,x15903,x15904,x15905,x15906),f398(x15902,x15903,x15904,x15905,x15906))
% 157.76/157.54 [1591]~E(x15911,x15912)+E(f398(x15913,x15911,x15914,x15915,x15916),f398(x15913,x15912,x15914,x15915,x15916))
% 157.76/157.54 [1592]~E(x15921,x15922)+E(f398(x15923,x15924,x15921,x15925,x15926),f398(x15923,x15924,x15922,x15925,x15926))
% 157.76/157.54 [1593]~E(x15931,x15932)+E(f398(x15933,x15934,x15935,x15931,x15936),f398(x15933,x15934,x15935,x15932,x15936))
% 157.76/157.54 [1594]~E(x15941,x15942)+E(f398(x15943,x15944,x15945,x15946,x15941),f398(x15943,x15944,x15945,x15946,x15942))
% 157.76/157.54 [1595]~E(x15951,x15952)+E(f216(x15951,x15953,x15954,x15955),f216(x15952,x15953,x15954,x15955))
% 157.76/157.54 [1596]~E(x15961,x15962)+E(f216(x15963,x15961,x15964,x15965),f216(x15963,x15962,x15964,x15965))
% 157.76/157.54 [1597]~E(x15971,x15972)+E(f216(x15973,x15974,x15971,x15975),f216(x15973,x15974,x15972,x15975))
% 157.76/157.54 [1598]~E(x15981,x15982)+E(f216(x15983,x15984,x15985,x15981),f216(x15983,x15984,x15985,x15982))
% 157.76/157.54 [1599]~E(x15991,x15992)+E(f477(x15991,x15993,x15994,x15995,x15996),f477(x15992,x15993,x15994,x15995,x15996))
% 157.76/157.54 [1600]~E(x16001,x16002)+E(f477(x16003,x16001,x16004,x16005,x16006),f477(x16003,x16002,x16004,x16005,x16006))
% 157.76/157.54 [1601]~E(x16011,x16012)+E(f477(x16013,x16014,x16011,x16015,x16016),f477(x16013,x16014,x16012,x16015,x16016))
% 157.76/157.54 [1602]~E(x16021,x16022)+E(f477(x16023,x16024,x16025,x16021,x16026),f477(x16023,x16024,x16025,x16022,x16026))
% 157.76/157.54 [1603]~E(x16031,x16032)+E(f477(x16033,x16034,x16035,x16036,x16031),f477(x16033,x16034,x16035,x16036,x16032))
% 157.76/157.54 [1604]~E(x16041,x16042)+E(f665(x16041,x16043,x16044,x16045),f665(x16042,x16043,x16044,x16045))
% 157.76/157.54 [1605]~E(x16051,x16052)+E(f665(x16053,x16051,x16054,x16055),f665(x16053,x16052,x16054,x16055))
% 157.76/157.54 [1606]~E(x16061,x16062)+E(f665(x16063,x16064,x16061,x16065),f665(x16063,x16064,x16062,x16065))
% 157.76/157.54 [1607]~E(x16071,x16072)+E(f665(x16073,x16074,x16075,x16071),f665(x16073,x16074,x16075,x16072))
% 157.76/157.54 [1608]~E(x16081,x16082)+E(f239(x16081,x16083,x16084),f239(x16082,x16083,x16084))
% 157.76/157.54 [1609]~E(x16091,x16092)+E(f239(x16093,x16091,x16094),f239(x16093,x16092,x16094))
% 157.76/157.54 [1610]~E(x16101,x16102)+E(f239(x16103,x16104,x16101),f239(x16103,x16104,x16102))
% 157.76/157.54 [1611]~E(x16111,x16112)+E(f841(x16111,x16113,x16114,x16115,x16116),f841(x16112,x16113,x16114,x16115,x16116))
% 157.76/157.54 [1612]~E(x16121,x16122)+E(f841(x16123,x16121,x16124,x16125,x16126),f841(x16123,x16122,x16124,x16125,x16126))
% 157.76/157.54 [1613]~E(x16131,x16132)+E(f841(x16133,x16134,x16131,x16135,x16136),f841(x16133,x16134,x16132,x16135,x16136))
% 157.76/157.54 [1614]~E(x16141,x16142)+E(f841(x16143,x16144,x16145,x16141,x16146),f841(x16143,x16144,x16145,x16142,x16146))
% 157.76/157.54 [1615]~E(x16151,x16152)+E(f841(x16153,x16154,x16155,x16156,x16151),f841(x16153,x16154,x16155,x16156,x16152))
% 157.76/157.54 [1616]~E(x16161,x16162)+E(f917(x16161,x16163,x16164),f917(x16162,x16163,x16164))
% 157.76/157.54 [1617]~E(x16171,x16172)+E(f917(x16173,x16171,x16174),f917(x16173,x16172,x16174))
% 157.76/157.54 [1618]~E(x16181,x16182)+E(f917(x16183,x16184,x16181),f917(x16183,x16184,x16182))
% 157.76/157.54 [1619]~E(x16191,x16192)+E(f524(x16191,x16193,x16194,x16195),f524(x16192,x16193,x16194,x16195))
% 157.76/157.54 [1620]~E(x16201,x16202)+E(f524(x16203,x16201,x16204,x16205),f524(x16203,x16202,x16204,x16205))
% 157.76/157.54 [1621]~E(x16211,x16212)+E(f524(x16213,x16214,x16211,x16215),f524(x16213,x16214,x16212,x16215))
% 157.76/157.54 [1622]~E(x16221,x16222)+E(f524(x16223,x16224,x16225,x16221),f524(x16223,x16224,x16225,x16222))
% 157.76/157.54 [1623]~E(x16231,x16232)+E(f410(x16231,x16233,x16234,x16235),f410(x16232,x16233,x16234,x16235))
% 157.76/157.54 [1624]~E(x16241,x16242)+E(f410(x16243,x16241,x16244,x16245),f410(x16243,x16242,x16244,x16245))
% 157.76/157.54 [1625]~E(x16251,x16252)+E(f410(x16253,x16254,x16251,x16255),f410(x16253,x16254,x16252,x16255))
% 157.76/157.54 [1626]~E(x16261,x16262)+E(f410(x16263,x16264,x16265,x16261),f410(x16263,x16264,x16265,x16262))
% 157.76/157.54 [1627]~E(x16271,x16272)+E(f754(x16271,x16273,x16274,x16275,x16276),f754(x16272,x16273,x16274,x16275,x16276))
% 157.76/157.54 [1628]~E(x16281,x16282)+E(f754(x16283,x16281,x16284,x16285,x16286),f754(x16283,x16282,x16284,x16285,x16286))
% 157.76/157.54 [1629]~E(x16291,x16292)+E(f754(x16293,x16294,x16291,x16295,x16296),f754(x16293,x16294,x16292,x16295,x16296))
% 157.76/157.54 [1630]~E(x16301,x16302)+E(f754(x16303,x16304,x16305,x16301,x16306),f754(x16303,x16304,x16305,x16302,x16306))
% 157.76/157.54 [1631]~E(x16311,x16312)+E(f754(x16313,x16314,x16315,x16316,x16311),f754(x16313,x16314,x16315,x16316,x16312))
% 157.76/157.54 [1632]~E(x16321,x16322)+E(f886(x16321,x16323),f886(x16322,x16323))
% 157.76/157.54 [1633]~E(x16331,x16332)+E(f886(x16333,x16331),f886(x16333,x16332))
% 157.76/157.54 [1634]~E(x16341,x16342)+E(f687(x16341,x16343,x16344,x16345,x16346),f687(x16342,x16343,x16344,x16345,x16346))
% 157.76/157.54 [1635]~E(x16351,x16352)+E(f687(x16353,x16351,x16354,x16355,x16356),f687(x16353,x16352,x16354,x16355,x16356))
% 157.76/157.54 [1636]~E(x16361,x16362)+E(f687(x16363,x16364,x16361,x16365,x16366),f687(x16363,x16364,x16362,x16365,x16366))
% 157.76/157.54 [1637]~E(x16371,x16372)+E(f687(x16373,x16374,x16375,x16371,x16376),f687(x16373,x16374,x16375,x16372,x16376))
% 157.76/157.54 [1638]~E(x16381,x16382)+E(f687(x16383,x16384,x16385,x16386,x16381),f687(x16383,x16384,x16385,x16386,x16382))
% 157.76/157.54 [1639]~E(x16391,x16392)+E(f370(x16391,x16393),f370(x16392,x16393))
% 157.76/157.54 [1640]~E(x16401,x16402)+E(f370(x16403,x16401),f370(x16403,x16402))
% 157.76/157.54 [1641]~E(x16411,x16412)+E(f539(x16411,x16413,x16414,x16415,x16416),f539(x16412,x16413,x16414,x16415,x16416))
% 157.76/157.54 [1642]~E(x16421,x16422)+E(f539(x16423,x16421,x16424,x16425,x16426),f539(x16423,x16422,x16424,x16425,x16426))
% 157.76/157.54 [1643]~E(x16431,x16432)+E(f539(x16433,x16434,x16431,x16435,x16436),f539(x16433,x16434,x16432,x16435,x16436))
% 157.76/157.54 [1644]~E(x16441,x16442)+E(f539(x16443,x16444,x16445,x16441,x16446),f539(x16443,x16444,x16445,x16442,x16446))
% 157.76/157.54 [1645]~E(x16451,x16452)+E(f539(x16453,x16454,x16455,x16456,x16451),f539(x16453,x16454,x16455,x16456,x16452))
% 157.76/157.54 [1646]~E(x16461,x16462)+E(f783(x16461,x16463,x16464),f783(x16462,x16463,x16464))
% 157.76/157.54 [1647]~E(x16471,x16472)+E(f783(x16473,x16471,x16474),f783(x16473,x16472,x16474))
% 157.76/157.54 [1648]~E(x16481,x16482)+E(f783(x16483,x16484,x16481),f783(x16483,x16484,x16482))
% 157.76/157.54 [1649]~E(x16491,x16492)+E(f138(x16491,x16493,x16494,x16495),f138(x16492,x16493,x16494,x16495))
% 157.76/157.54 [1650]~E(x16501,x16502)+E(f138(x16503,x16501,x16504,x16505),f138(x16503,x16502,x16504,x16505))
% 157.76/157.54 [1651]~E(x16511,x16512)+E(f138(x16513,x16514,x16511,x16515),f138(x16513,x16514,x16512,x16515))
% 157.76/157.54 [1652]~E(x16521,x16522)+E(f138(x16523,x16524,x16525,x16521),f138(x16523,x16524,x16525,x16522))
% 157.76/157.54 [1653]~E(x16531,x16532)+E(f379(x16531,x16533,x16534),f379(x16532,x16533,x16534))
% 157.76/157.54 [1654]~E(x16541,x16542)+E(f379(x16543,x16541,x16544),f379(x16543,x16542,x16544))
% 157.76/157.54 [1655]~E(x16551,x16552)+E(f379(x16553,x16554,x16551),f379(x16553,x16554,x16552))
% 157.76/157.54 [1656]~E(x16561,x16562)+E(f594(x16561,x16563,x16564,x16565),f594(x16562,x16563,x16564,x16565))
% 157.76/157.54 [1657]~E(x16571,x16572)+E(f594(x16573,x16571,x16574,x16575),f594(x16573,x16572,x16574,x16575))
% 157.76/157.54 [1658]~E(x16581,x16582)+E(f594(x16583,x16584,x16581,x16585),f594(x16583,x16584,x16582,x16585))
% 157.76/157.54 [1659]~E(x16591,x16592)+E(f594(x16593,x16594,x16595,x16591),f594(x16593,x16594,x16595,x16592))
% 157.76/157.54 [1660]~E(x16601,x16602)+E(f703(x16601,x16603,x16604,x16605,x16606),f703(x16602,x16603,x16604,x16605,x16606))
% 157.76/157.54 [1661]~E(x16611,x16612)+E(f703(x16613,x16611,x16614,x16615,x16616),f703(x16613,x16612,x16614,x16615,x16616))
% 157.76/157.54 [1662]~E(x16621,x16622)+E(f703(x16623,x16624,x16621,x16625,x16626),f703(x16623,x16624,x16622,x16625,x16626))
% 157.76/157.54 [1663]~E(x16631,x16632)+E(f703(x16633,x16634,x16635,x16631,x16636),f703(x16633,x16634,x16635,x16632,x16636))
% 157.76/157.54 [1664]~E(x16641,x16642)+E(f703(x16643,x16644,x16645,x16646,x16641),f703(x16643,x16644,x16645,x16646,x16642))
% 157.76/157.54 [1665]~E(x16651,x16652)+E(f430(x16651,x16653),f430(x16652,x16653))
% 157.76/157.54 [1666]~E(x16661,x16662)+E(f430(x16663,x16661),f430(x16663,x16662))
% 157.76/157.54 [1667]~E(x16671,x16672)+E(f648(x16671,x16673,x16674,x16675),f648(x16672,x16673,x16674,x16675))
% 157.76/157.54 [1668]~E(x16681,x16682)+E(f648(x16683,x16681,x16684,x16685),f648(x16683,x16682,x16684,x16685))
% 157.76/157.54 [1669]~E(x16691,x16692)+E(f648(x16693,x16694,x16691,x16695),f648(x16693,x16694,x16692,x16695))
% 157.76/157.54 [1670]~E(x16701,x16702)+E(f648(x16703,x16704,x16705,x16701),f648(x16703,x16704,x16705,x16702))
% 157.76/157.54 [1671]~E(x16711,x16712)+E(f604(x16711,x16713,x16714,x16715,x16716),f604(x16712,x16713,x16714,x16715,x16716))
% 157.76/157.54 [1672]~E(x16721,x16722)+E(f604(x16723,x16721,x16724,x16725,x16726),f604(x16723,x16722,x16724,x16725,x16726))
% 157.76/157.54 [1673]~E(x16731,x16732)+E(f604(x16733,x16734,x16731,x16735,x16736),f604(x16733,x16734,x16732,x16735,x16736))
% 157.76/157.54 [1674]~E(x16741,x16742)+E(f604(x16743,x16744,x16745,x16741,x16746),f604(x16743,x16744,x16745,x16742,x16746))
% 157.76/157.54 [1675]~E(x16751,x16752)+E(f604(x16753,x16754,x16755,x16756,x16751),f604(x16753,x16754,x16755,x16756,x16752))
% 157.76/157.54 [1676]~E(x16761,x16762)+E(f102(x16761,x16763,x16764,x16765),f102(x16762,x16763,x16764,x16765))
% 157.76/157.54 [1677]~E(x16771,x16772)+E(f102(x16773,x16771,x16774,x16775),f102(x16773,x16772,x16774,x16775))
% 157.76/157.54 [1678]~E(x16781,x16782)+E(f102(x16783,x16784,x16781,x16785),f102(x16783,x16784,x16782,x16785))
% 157.76/157.54 [1679]~E(x16791,x16792)+E(f102(x16793,x16794,x16795,x16791),f102(x16793,x16794,x16795,x16792))
% 157.76/157.54 [1680]~E(x16801,x16802)+E(f124(x16801,x16803,x16804),f124(x16802,x16803,x16804))
% 157.76/157.54 [1681]~E(x16811,x16812)+E(f124(x16813,x16811,x16814),f124(x16813,x16812,x16814))
% 157.76/157.54 [1682]~E(x16821,x16822)+E(f124(x16823,x16824,x16821),f124(x16823,x16824,x16822))
% 157.76/157.54 [1683]~E(x16831,x16832)+E(f489(x16831,x16833,x16834,x16835,x16836,x16837),f489(x16832,x16833,x16834,x16835,x16836,x16837))
% 157.76/157.54 [1684]~E(x16841,x16842)+E(f489(x16843,x16841,x16844,x16845,x16846,x16847),f489(x16843,x16842,x16844,x16845,x16846,x16847))
% 157.76/157.54 [1685]~E(x16851,x16852)+E(f489(x16853,x16854,x16851,x16855,x16856,x16857),f489(x16853,x16854,x16852,x16855,x16856,x16857))
% 157.76/157.54 [1686]~E(x16861,x16862)+E(f489(x16863,x16864,x16865,x16861,x16866,x16867),f489(x16863,x16864,x16865,x16862,x16866,x16867))
% 157.76/157.54 [1687]~E(x16871,x16872)+E(f489(x16873,x16874,x16875,x16876,x16871,x16877),f489(x16873,x16874,x16875,x16876,x16872,x16877))
% 157.76/157.54 [1688]~E(x16881,x16882)+E(f489(x16883,x16884,x16885,x16886,x16887,x16881),f489(x16883,x16884,x16885,x16886,x16887,x16882))
% 157.76/157.54 [1689]~E(x16891,x16892)+E(f491(x16891,x16893,x16894,x16895,x16896),f491(x16892,x16893,x16894,x16895,x16896))
% 157.76/157.54 [1690]~E(x16901,x16902)+E(f491(x16903,x16901,x16904,x16905,x16906),f491(x16903,x16902,x16904,x16905,x16906))
% 157.76/157.54 [1691]~E(x16911,x16912)+E(f491(x16913,x16914,x16911,x16915,x16916),f491(x16913,x16914,x16912,x16915,x16916))
% 157.76/157.54 [1692]~E(x16921,x16922)+E(f491(x16923,x16924,x16925,x16921,x16926),f491(x16923,x16924,x16925,x16922,x16926))
% 157.76/157.54 [1693]~E(x16931,x16932)+E(f491(x16933,x16934,x16935,x16936,x16931),f491(x16933,x16934,x16935,x16936,x16932))
% 157.76/157.54 [1694]~E(x16941,x16942)+E(f383(x16941,x16943),f383(x16942,x16943))
% 157.76/157.54 [1695]~E(x16951,x16952)+E(f383(x16953,x16951),f383(x16953,x16952))
% 157.76/157.54 [1696]~E(x16961,x16962)+E(f366(x16961,x16963,x16964),f366(x16962,x16963,x16964))
% 157.76/157.54 [1697]~E(x16971,x16972)+E(f366(x16973,x16971,x16974),f366(x16973,x16972,x16974))
% 157.76/157.54 [1698]~E(x16981,x16982)+E(f366(x16983,x16984,x16981),f366(x16983,x16984,x16982))
% 157.76/157.54 [1699]~E(x16991,x16992)+E(f624(x16991,x16993,x16994),f624(x16992,x16993,x16994))
% 157.76/157.54 [1700]~E(x17001,x17002)+E(f624(x17003,x17001,x17004),f624(x17003,x17002,x17004))
% 157.76/157.54 [1701]~E(x17011,x17012)+E(f624(x17013,x17014,x17011),f624(x17013,x17014,x17012))
% 157.76/157.54 [1702]~E(x17021,x17022)+E(f829(x17021,x17023),f829(x17022,x17023))
% 157.76/157.54 [1703]~E(x17031,x17032)+E(f829(x17033,x17031),f829(x17033,x17032))
% 157.76/157.54 [1704]~E(x17041,x17042)+E(f664(x17041,x17043,x17044,x17045),f664(x17042,x17043,x17044,x17045))
% 157.76/157.54 [1705]~E(x17051,x17052)+E(f664(x17053,x17051,x17054,x17055),f664(x17053,x17052,x17054,x17055))
% 157.76/157.54 [1706]~E(x17061,x17062)+E(f664(x17063,x17064,x17061,x17065),f664(x17063,x17064,x17062,x17065))
% 157.76/157.54 [1707]~E(x17071,x17072)+E(f664(x17073,x17074,x17075,x17071),f664(x17073,x17074,x17075,x17072))
% 157.76/157.54 [1708]~E(x17081,x17082)+E(f779(x17081,x17083,x17084,x17085),f779(x17082,x17083,x17084,x17085))
% 157.76/157.54 [1709]~E(x17091,x17092)+E(f779(x17093,x17091,x17094,x17095),f779(x17093,x17092,x17094,x17095))
% 157.76/157.54 [1710]~E(x17101,x17102)+E(f779(x17103,x17104,x17101,x17105),f779(x17103,x17104,x17102,x17105))
% 157.76/157.54 [1711]~E(x17111,x17112)+E(f779(x17113,x17114,x17115,x17111),f779(x17113,x17114,x17115,x17112))
% 157.76/157.54 [1712]~E(x17121,x17122)+E(f789(x17121),f789(x17122))
% 157.76/157.54 [1713]~E(x17131,x17132)+E(f914(x17131,x17133,x17134,x17135,x17136,x17137,x17138),f914(x17132,x17133,x17134,x17135,x17136,x17137,x17138))
% 157.76/157.54 [1714]~E(x17141,x17142)+E(f914(x17143,x17141,x17144,x17145,x17146,x17147,x17148),f914(x17143,x17142,x17144,x17145,x17146,x17147,x17148))
% 157.76/157.54 [1715]~E(x17151,x17152)+E(f914(x17153,x17154,x17151,x17155,x17156,x17157,x17158),f914(x17153,x17154,x17152,x17155,x17156,x17157,x17158))
% 157.76/157.54 [1716]~E(x17161,x17162)+E(f914(x17163,x17164,x17165,x17161,x17166,x17167,x17168),f914(x17163,x17164,x17165,x17162,x17166,x17167,x17168))
% 157.76/157.54 [1717]~E(x17171,x17172)+E(f914(x17173,x17174,x17175,x17176,x17171,x17177,x17178),f914(x17173,x17174,x17175,x17176,x17172,x17177,x17178))
% 157.76/157.54 [1718]~E(x17181,x17182)+E(f914(x17183,x17184,x17185,x17186,x17187,x17181,x17188),f914(x17183,x17184,x17185,x17186,x17187,x17182,x17188))
% 157.76/157.54 [1719]~E(x17191,x17192)+E(f914(x17193,x17194,x17195,x17196,x17197,x17198,x17191),f914(x17193,x17194,x17195,x17196,x17197,x17198,x17192))
% 157.76/157.54 [1720]~E(x17201,x17202)+E(f560(x17201,x17203,x17204),f560(x17202,x17203,x17204))
% 157.76/157.54 [1721]~E(x17211,x17212)+E(f560(x17213,x17211,x17214),f560(x17213,x17212,x17214))
% 157.76/157.54 [1722]~E(x17221,x17222)+E(f560(x17223,x17224,x17221),f560(x17223,x17224,x17222))
% 157.76/157.54 [1723]~E(x17231,x17232)+E(f661(x17231,x17233,x17234,x17235,x17236),f661(x17232,x17233,x17234,x17235,x17236))
% 157.76/157.54 [1724]~E(x17241,x17242)+E(f661(x17243,x17241,x17244,x17245,x17246),f661(x17243,x17242,x17244,x17245,x17246))
% 157.76/157.54 [1725]~E(x17251,x17252)+E(f661(x17253,x17254,x17251,x17255,x17256),f661(x17253,x17254,x17252,x17255,x17256))
% 157.76/157.54 [1726]~E(x17261,x17262)+E(f661(x17263,x17264,x17265,x17261,x17266),f661(x17263,x17264,x17265,x17262,x17266))
% 157.76/157.54 [1727]~E(x17271,x17272)+E(f661(x17273,x17274,x17275,x17276,x17271),f661(x17273,x17274,x17275,x17276,x17272))
% 157.76/157.54 [1728]~E(x17281,x17282)+E(f400(x17281,x17283,x17284,x17285,x17286),f400(x17282,x17283,x17284,x17285,x17286))
% 157.76/157.54 [1729]~E(x17291,x17292)+E(f400(x17293,x17291,x17294,x17295,x17296),f400(x17293,x17292,x17294,x17295,x17296))
% 157.76/157.54 [1730]~E(x17301,x17302)+E(f400(x17303,x17304,x17301,x17305,x17306),f400(x17303,x17304,x17302,x17305,x17306))
% 157.76/157.54 [1731]~E(x17311,x17312)+E(f400(x17313,x17314,x17315,x17311,x17316),f400(x17313,x17314,x17315,x17312,x17316))
% 157.76/157.54 [1732]~E(x17321,x17322)+E(f400(x17323,x17324,x17325,x17326,x17321),f400(x17323,x17324,x17325,x17326,x17322))
% 157.76/157.54 [1733]~E(x17331,x17332)+E(f498(x17331,x17333,x17334),f498(x17332,x17333,x17334))
% 157.76/157.54 [1734]~E(x17341,x17342)+E(f498(x17343,x17341,x17344),f498(x17343,x17342,x17344))
% 157.76/157.54 [1735]~E(x17351,x17352)+E(f498(x17353,x17354,x17351),f498(x17353,x17354,x17352))
% 157.76/157.54 [1736]~E(x17361,x17362)+E(f446(x17361,x17363,x17364,x17365),f446(x17362,x17363,x17364,x17365))
% 157.76/157.54 [1737]~E(x17371,x17372)+E(f446(x17373,x17371,x17374,x17375),f446(x17373,x17372,x17374,x17375))
% 157.76/157.54 [1738]~E(x17381,x17382)+E(f446(x17383,x17384,x17381,x17385),f446(x17383,x17384,x17382,x17385))
% 157.76/157.54 [1739]~E(x17391,x17392)+E(f446(x17393,x17394,x17395,x17391),f446(x17393,x17394,x17395,x17392))
% 157.76/157.54 [1740]~E(x17401,x17402)+E(f700(x17401,x17403,x17404),f700(x17402,x17403,x17404))
% 157.76/157.54 [1741]~E(x17411,x17412)+E(f700(x17413,x17411,x17414),f700(x17413,x17412,x17414))
% 157.76/157.54 [1742]~E(x17421,x17422)+E(f700(x17423,x17424,x17421),f700(x17423,x17424,x17422))
% 157.76/157.54 [1743]~E(x17431,x17432)+E(f565(x17431,x17433,x17434,x17435,x17436,x17437),f565(x17432,x17433,x17434,x17435,x17436,x17437))
% 157.76/157.54 [1744]~E(x17441,x17442)+E(f565(x17443,x17441,x17444,x17445,x17446,x17447),f565(x17443,x17442,x17444,x17445,x17446,x17447))
% 157.76/157.54 [1745]~E(x17451,x17452)+E(f565(x17453,x17454,x17451,x17455,x17456,x17457),f565(x17453,x17454,x17452,x17455,x17456,x17457))
% 157.76/157.54 [1746]~E(x17461,x17462)+E(f565(x17463,x17464,x17465,x17461,x17466,x17467),f565(x17463,x17464,x17465,x17462,x17466,x17467))
% 157.76/157.54 [1747]~E(x17471,x17472)+E(f565(x17473,x17474,x17475,x17476,x17471,x17477),f565(x17473,x17474,x17475,x17476,x17472,x17477))
% 157.76/157.54 [1748]~E(x17481,x17482)+E(f565(x17483,x17484,x17485,x17486,x17487,x17481),f565(x17483,x17484,x17485,x17486,x17487,x17482))
% 157.76/157.54 [1749]~E(x17491,x17492)+E(f563(x17491,x17493,x17494,x17495,x17496,x17497),f563(x17492,x17493,x17494,x17495,x17496,x17497))
% 157.76/157.54 [1750]~E(x17501,x17502)+E(f563(x17503,x17501,x17504,x17505,x17506,x17507),f563(x17503,x17502,x17504,x17505,x17506,x17507))
% 157.76/157.54 [1751]~E(x17511,x17512)+E(f563(x17513,x17514,x17511,x17515,x17516,x17517),f563(x17513,x17514,x17512,x17515,x17516,x17517))
% 157.76/157.54 [1752]~E(x17521,x17522)+E(f563(x17523,x17524,x17525,x17521,x17526,x17527),f563(x17523,x17524,x17525,x17522,x17526,x17527))
% 157.76/157.54 [1753]~E(x17531,x17532)+E(f563(x17533,x17534,x17535,x17536,x17531,x17537),f563(x17533,x17534,x17535,x17536,x17532,x17537))
% 157.76/157.54 [1754]~E(x17541,x17542)+E(f563(x17543,x17544,x17545,x17546,x17547,x17541),f563(x17543,x17544,x17545,x17546,x17547,x17542))
% 157.76/157.54 [1755]~E(x17551,x17552)+E(f273(x17551,x17553,x17554),f273(x17552,x17553,x17554))
% 157.76/157.54 [1756]~E(x17561,x17562)+E(f273(x17563,x17561,x17564),f273(x17563,x17562,x17564))
% 157.76/157.54 [1757]~E(x17571,x17572)+E(f273(x17573,x17574,x17571),f273(x17573,x17574,x17572))
% 157.76/157.54 [1758]~E(x17581,x17582)+E(f520(x17581,x17583,x17584,x17585),f520(x17582,x17583,x17584,x17585))
% 157.76/157.54 [1759]~E(x17591,x17592)+E(f520(x17593,x17591,x17594,x17595),f520(x17593,x17592,x17594,x17595))
% 157.76/157.54 [1760]~E(x17601,x17602)+E(f520(x17603,x17604,x17601,x17605),f520(x17603,x17604,x17602,x17605))
% 157.76/157.54 [1761]~E(x17611,x17612)+E(f520(x17613,x17614,x17615,x17611),f520(x17613,x17614,x17615,x17612))
% 157.76/157.54 [1762]~E(x17621,x17622)+E(f181(x17621,x17623,x17624),f181(x17622,x17623,x17624))
% 157.76/157.54 [1763]~E(x17631,x17632)+E(f181(x17633,x17631,x17634),f181(x17633,x17632,x17634))
% 157.76/157.54 [1764]~E(x17641,x17642)+E(f181(x17643,x17644,x17641),f181(x17643,x17644,x17642))
% 157.76/157.54 [1765]~E(x17651,x17652)+E(f522(x17651,x17653,x17654,x17655),f522(x17652,x17653,x17654,x17655))
% 157.76/157.54 [1766]~E(x17661,x17662)+E(f522(x17663,x17661,x17664,x17665),f522(x17663,x17662,x17664,x17665))
% 157.76/157.54 [1767]~E(x17671,x17672)+E(f522(x17673,x17674,x17671,x17675),f522(x17673,x17674,x17672,x17675))
% 157.76/157.54 [1768]~E(x17681,x17682)+E(f522(x17683,x17684,x17685,x17681),f522(x17683,x17684,x17685,x17682))
% 157.76/157.54 [1769]~E(x17691,x17692)+E(f579(x17691,x17693,x17694,x17695,x17696,x17697,x17698,x17699),f579(x17692,x17693,x17694,x17695,x17696,x17697,x17698,x17699))
% 157.76/157.54 [1770]~E(x17701,x17702)+E(f579(x17703,x17701,x17704,x17705,x17706,x17707,x17708,x17709),f579(x17703,x17702,x17704,x17705,x17706,x17707,x17708,x17709))
% 157.76/157.54 [1771]~E(x17711,x17712)+E(f579(x17713,x17714,x17711,x17715,x17716,x17717,x17718,x17719),f579(x17713,x17714,x17712,x17715,x17716,x17717,x17718,x17719))
% 157.76/157.54 [1772]~E(x17721,x17722)+E(f579(x17723,x17724,x17725,x17721,x17726,x17727,x17728,x17729),f579(x17723,x17724,x17725,x17722,x17726,x17727,x17728,x17729))
% 157.76/157.54 [1773]~E(x17731,x17732)+E(f579(x17733,x17734,x17735,x17736,x17731,x17737,x17738,x17739),f579(x17733,x17734,x17735,x17736,x17732,x17737,x17738,x17739))
% 157.76/157.54 [1774]~E(x17741,x17742)+E(f579(x17743,x17744,x17745,x17746,x17747,x17741,x17748,x17749),f579(x17743,x17744,x17745,x17746,x17747,x17742,x17748,x17749))
% 157.76/157.54 [1775]~E(x17751,x17752)+E(f579(x17753,x17754,x17755,x17756,x17757,x17758,x17751,x17759),f579(x17753,x17754,x17755,x17756,x17757,x17758,x17752,x17759))
% 157.76/157.54 [1776]~E(x17761,x17762)+E(f579(x17763,x17764,x17765,x17766,x17767,x17768,x17769,x17761),f579(x17763,x17764,x17765,x17766,x17767,x17768,x17769,x17762))
% 157.76/157.54 [1777]~E(x17771,x17772)+E(f674(x17771,x17773),f674(x17772,x17773))
% 157.76/157.54 [1778]~E(x17781,x17782)+E(f674(x17783,x17781),f674(x17783,x17782))
% 157.76/157.54 [1779]~E(x17791,x17792)+E(f923(x17791,x17793,x17794,x17795),f923(x17792,x17793,x17794,x17795))
% 157.76/157.54 [1780]~E(x17801,x17802)+E(f923(x17803,x17801,x17804,x17805),f923(x17803,x17802,x17804,x17805))
% 157.76/157.54 [1781]~E(x17811,x17812)+E(f923(x17813,x17814,x17811,x17815),f923(x17813,x17814,x17812,x17815))
% 157.76/157.54 [1782]~E(x17821,x17822)+E(f923(x17823,x17824,x17825,x17821),f923(x17823,x17824,x17825,x17822))
% 157.76/157.54 [1783]~E(x17831,x17832)+E(f551(x17831,x17833,x17834),f551(x17832,x17833,x17834))
% 157.76/157.54 [1784]~E(x17841,x17842)+E(f551(x17843,x17841,x17844),f551(x17843,x17842,x17844))
% 157.76/157.54 [1785]~E(x17851,x17852)+E(f551(x17853,x17854,x17851),f551(x17853,x17854,x17852))
% 157.76/157.54 [1786]~E(x17861,x17862)+E(f659(x17861,x17863,x17864,x17865,x17866),f659(x17862,x17863,x17864,x17865,x17866))
% 157.76/157.54 [1787]~E(x17871,x17872)+E(f659(x17873,x17871,x17874,x17875,x17876),f659(x17873,x17872,x17874,x17875,x17876))
% 157.76/157.54 [1788]~E(x17881,x17882)+E(f659(x17883,x17884,x17881,x17885,x17886),f659(x17883,x17884,x17882,x17885,x17886))
% 157.76/157.54 [1789]~E(x17891,x17892)+E(f659(x17893,x17894,x17895,x17891,x17896),f659(x17893,x17894,x17895,x17892,x17896))
% 157.76/157.54 [1790]~E(x17901,x17902)+E(f659(x17903,x17904,x17905,x17906,x17901),f659(x17903,x17904,x17905,x17906,x17902))
% 157.76/157.54 [1791]~E(x17911,x17912)+E(f125(x17911,x17913,x17914),f125(x17912,x17913,x17914))
% 157.76/157.54 [1792]~E(x17921,x17922)+E(f125(x17923,x17921,x17924),f125(x17923,x17922,x17924))
% 157.76/157.54 [1793]~E(x17931,x17932)+E(f125(x17933,x17934,x17931),f125(x17933,x17934,x17932))
% 157.76/157.54 [1794]~E(x17941,x17942)+E(f939(x17941),f939(x17942))
% 157.76/157.54 [1795]~E(x17951,x17952)+E(f433(x17951,x17953,x17954),f433(x17952,x17953,x17954))
% 157.76/157.54 [1796]~E(x17961,x17962)+E(f433(x17963,x17961,x17964),f433(x17963,x17962,x17964))
% 157.76/157.54 [1797]~E(x17971,x17972)+E(f433(x17973,x17974,x17971),f433(x17973,x17974,x17972))
% 157.76/157.54 [1798]~E(x17981,x17982)+E(f261(x17981,x17983,x17984,x17985,x17986),f261(x17982,x17983,x17984,x17985,x17986))
% 157.76/157.54 [1799]~E(x17991,x17992)+E(f261(x17993,x17991,x17994,x17995,x17996),f261(x17993,x17992,x17994,x17995,x17996))
% 157.76/157.54 [1800]~E(x18001,x18002)+E(f261(x18003,x18004,x18001,x18005,x18006),f261(x18003,x18004,x18002,x18005,x18006))
% 157.76/157.54 [1801]~E(x18011,x18012)+E(f261(x18013,x18014,x18015,x18011,x18016),f261(x18013,x18014,x18015,x18012,x18016))
% 157.76/157.54 [1802]~E(x18021,x18022)+E(f261(x18023,x18024,x18025,x18026,x18021),f261(x18023,x18024,x18025,x18026,x18022))
% 157.76/157.54 [1803]~E(x18031,x18032)+E(f889(x18031,x18033,x18034,x18035,x18036),f889(x18032,x18033,x18034,x18035,x18036))
% 157.76/157.54 [1804]~E(x18041,x18042)+E(f889(x18043,x18041,x18044,x18045,x18046),f889(x18043,x18042,x18044,x18045,x18046))
% 157.76/157.54 [1805]~E(x18051,x18052)+E(f889(x18053,x18054,x18051,x18055,x18056),f889(x18053,x18054,x18052,x18055,x18056))
% 157.76/157.54 [1806]~E(x18061,x18062)+E(f889(x18063,x18064,x18065,x18061,x18066),f889(x18063,x18064,x18065,x18062,x18066))
% 157.76/157.54 [1807]~E(x18071,x18072)+E(f889(x18073,x18074,x18075,x18076,x18071),f889(x18073,x18074,x18075,x18076,x18072))
% 157.76/157.54 [1808]~E(x18081,x18082)+E(f566(x18081,x18083,x18084,x18085,x18086,x18087),f566(x18082,x18083,x18084,x18085,x18086,x18087))
% 157.76/157.54 [1809]~E(x18091,x18092)+E(f566(x18093,x18091,x18094,x18095,x18096,x18097),f566(x18093,x18092,x18094,x18095,x18096,x18097))
% 157.76/157.54 [1810]~E(x18101,x18102)+E(f566(x18103,x18104,x18101,x18105,x18106,x18107),f566(x18103,x18104,x18102,x18105,x18106,x18107))
% 157.76/157.54 [1811]~E(x18111,x18112)+E(f566(x18113,x18114,x18115,x18111,x18116,x18117),f566(x18113,x18114,x18115,x18112,x18116,x18117))
% 157.76/157.54 [1812]~E(x18121,x18122)+E(f566(x18123,x18124,x18125,x18126,x18121,x18127),f566(x18123,x18124,x18125,x18126,x18122,x18127))
% 157.76/157.54 [1813]~E(x18131,x18132)+E(f566(x18133,x18134,x18135,x18136,x18137,x18131),f566(x18133,x18134,x18135,x18136,x18137,x18132))
% 157.76/157.54 [1814]~E(x18141,x18142)+E(f619(x18141,x18143,x18144,x18145,x18146),f619(x18142,x18143,x18144,x18145,x18146))
% 157.76/157.54 [1815]~E(x18151,x18152)+E(f619(x18153,x18151,x18154,x18155,x18156),f619(x18153,x18152,x18154,x18155,x18156))
% 157.76/157.54 [1816]~E(x18161,x18162)+E(f619(x18163,x18164,x18161,x18165,x18166),f619(x18163,x18164,x18162,x18165,x18166))
% 157.76/157.54 [1817]~E(x18171,x18172)+E(f619(x18173,x18174,x18175,x18171,x18176),f619(x18173,x18174,x18175,x18172,x18176))
% 157.76/157.54 [1818]~E(x18181,x18182)+E(f619(x18183,x18184,x18185,x18186,x18181),f619(x18183,x18184,x18185,x18186,x18182))
% 157.76/157.54 [1819]~E(x18191,x18192)+E(f870(x18191,x18193,x18194),f870(x18192,x18193,x18194))
% 157.76/157.54 [1820]~E(x18201,x18202)+E(f870(x18203,x18201,x18204),f870(x18203,x18202,x18204))
% 157.76/157.54 [1821]~E(x18211,x18212)+E(f870(x18213,x18214,x18211),f870(x18213,x18214,x18212))
% 157.76/157.54 [1822]~E(x18221,x18222)+E(f799(x18221,x18223),f799(x18222,x18223))
% 157.76/157.54 [1823]~E(x18231,x18232)+E(f799(x18233,x18231),f799(x18233,x18232))
% 157.76/157.54 [1824]~E(x18241,x18242)+E(f811(x18241),f811(x18242))
% 157.76/157.54 [1825]~E(x18251,x18252)+E(f460(x18251,x18253),f460(x18252,x18253))
% 157.76/157.54 [1826]~E(x18261,x18262)+E(f460(x18263,x18261),f460(x18263,x18262))
% 157.76/157.54 [1827]~E(x18271,x18272)+E(f581(x18271,x18273),f581(x18272,x18273))
% 157.76/157.54 [1828]~E(x18281,x18282)+E(f581(x18283,x18281),f581(x18283,x18282))
% 157.76/157.54 [1829]~E(x18291,x18292)+E(f834(x18291,x18293,x18294,x18295,x18296),f834(x18292,x18293,x18294,x18295,x18296))
% 157.76/157.54 [1830]~E(x18301,x18302)+E(f834(x18303,x18301,x18304,x18305,x18306),f834(x18303,x18302,x18304,x18305,x18306))
% 157.76/157.54 [1831]~E(x18311,x18312)+E(f834(x18313,x18314,x18311,x18315,x18316),f834(x18313,x18314,x18312,x18315,x18316))
% 157.76/157.54 [1832]~E(x18321,x18322)+E(f834(x18323,x18324,x18325,x18321,x18326),f834(x18323,x18324,x18325,x18322,x18326))
% 157.76/157.54 [1833]~E(x18331,x18332)+E(f834(x18333,x18334,x18335,x18336,x18331),f834(x18333,x18334,x18335,x18336,x18332))
% 157.76/157.54 [1834]~E(x18341,x18342)+E(f617(x18341,x18343,x18344,x18345,x18346),f617(x18342,x18343,x18344,x18345,x18346))
% 157.76/157.54 [1835]~E(x18351,x18352)+E(f617(x18353,x18351,x18354,x18355,x18356),f617(x18353,x18352,x18354,x18355,x18356))
% 157.76/157.54 [1836]~E(x18361,x18362)+E(f617(x18363,x18364,x18361,x18365,x18366),f617(x18363,x18364,x18362,x18365,x18366))
% 157.76/157.54 [1837]~E(x18371,x18372)+E(f617(x18373,x18374,x18375,x18371,x18376),f617(x18373,x18374,x18375,x18372,x18376))
% 157.76/157.54 [1838]~E(x18381,x18382)+E(f617(x18383,x18384,x18385,x18386,x18381),f617(x18383,x18384,x18385,x18386,x18382))
% 157.76/157.54 [1839]~E(x18391,x18392)+E(f550(x18391,x18393,x18394),f550(x18392,x18393,x18394))
% 157.76/157.54 [1840]~E(x18401,x18402)+E(f550(x18403,x18401,x18404),f550(x18403,x18402,x18404))
% 157.76/157.54 [1841]~E(x18411,x18412)+E(f550(x18413,x18414,x18411),f550(x18413,x18414,x18412))
% 157.76/157.54 [1842]~E(x18421,x18422)+E(f657(x18421,x18423,x18424),f657(x18422,x18423,x18424))
% 157.76/157.54 [1843]~E(x18431,x18432)+E(f657(x18433,x18431,x18434),f657(x18433,x18432,x18434))
% 157.76/157.54 [1844]~E(x18441,x18442)+E(f657(x18443,x18444,x18441),f657(x18443,x18444,x18442))
% 157.76/157.54 [1845]~E(x18451,x18452)+E(f607(x18451,x18453,x18454,x18455,x18456),f607(x18452,x18453,x18454,x18455,x18456))
% 157.76/157.54 [1846]~E(x18461,x18462)+E(f607(x18463,x18461,x18464,x18465,x18466),f607(x18463,x18462,x18464,x18465,x18466))
% 157.76/157.54 [1847]~E(x18471,x18472)+E(f607(x18473,x18474,x18471,x18475,x18476),f607(x18473,x18474,x18472,x18475,x18476))
% 157.76/157.54 [1848]~E(x18481,x18482)+E(f607(x18483,x18484,x18485,x18481,x18486),f607(x18483,x18484,x18485,x18482,x18486))
% 157.76/157.54 [1849]~E(x18491,x18492)+E(f607(x18493,x18494,x18495,x18496,x18491),f607(x18493,x18494,x18495,x18496,x18492))
% 157.76/157.54 [1850]~E(x18501,x18502)+E(f735(x18501,x18503),f735(x18502,x18503))
% 157.76/157.54 [1851]~E(x18511,x18512)+E(f735(x18513,x18511),f735(x18513,x18512))
% 157.76/157.54 [1852]~E(x18521,x18522)+E(f219(x18521,x18523,x18524,x18525),f219(x18522,x18523,x18524,x18525))
% 157.76/157.54 [1853]~E(x18531,x18532)+E(f219(x18533,x18531,x18534,x18535),f219(x18533,x18532,x18534,x18535))
% 157.76/157.54 [1854]~E(x18541,x18542)+E(f219(x18543,x18544,x18541,x18545),f219(x18543,x18544,x18542,x18545))
% 157.76/157.54 [1855]~E(x18551,x18552)+E(f219(x18553,x18554,x18555,x18551),f219(x18553,x18554,x18555,x18552))
% 157.76/157.54 [1856]~E(x18561,x18562)+E(f451(x18561),f451(x18562))
% 157.76/157.54 [1857]~E(x18571,x18572)+E(f827(x18571,x18573,x18574),f827(x18572,x18573,x18574))
% 157.76/157.54 [1858]~E(x18581,x18582)+E(f827(x18583,x18581,x18584),f827(x18583,x18582,x18584))
% 157.76/157.54 [1859]~E(x18591,x18592)+E(f827(x18593,x18594,x18591),f827(x18593,x18594,x18592))
% 157.76/157.54 [1860]~E(x18601,x18602)+E(f854(x18601,x18603,x18604,x18605,x18606,x18607,x18608,x18609),f854(x18602,x18603,x18604,x18605,x18606,x18607,x18608,x18609))
% 157.76/157.54 [1861]~E(x18611,x18612)+E(f854(x18613,x18611,x18614,x18615,x18616,x18617,x18618,x18619),f854(x18613,x18612,x18614,x18615,x18616,x18617,x18618,x18619))
% 157.76/157.54 [1862]~E(x18621,x18622)+E(f854(x18623,x18624,x18621,x18625,x18626,x18627,x18628,x18629),f854(x18623,x18624,x18622,x18625,x18626,x18627,x18628,x18629))
% 157.76/157.54 [1863]~E(x18631,x18632)+E(f854(x18633,x18634,x18635,x18631,x18636,x18637,x18638,x18639),f854(x18633,x18634,x18635,x18632,x18636,x18637,x18638,x18639))
% 157.76/157.54 [1864]~E(x18641,x18642)+E(f854(x18643,x18644,x18645,x18646,x18641,x18647,x18648,x18649),f854(x18643,x18644,x18645,x18646,x18642,x18647,x18648,x18649))
% 157.76/157.54 [1865]~E(x18651,x18652)+E(f854(x18653,x18654,x18655,x18656,x18657,x18651,x18658,x18659),f854(x18653,x18654,x18655,x18656,x18657,x18652,x18658,x18659))
% 157.76/157.54 [1866]~E(x18661,x18662)+E(f854(x18663,x18664,x18665,x18666,x18667,x18668,x18661,x18669),f854(x18663,x18664,x18665,x18666,x18667,x18668,x18662,x18669))
% 157.76/157.54 [1867]~E(x18671,x18672)+E(f854(x18673,x18674,x18675,x18676,x18677,x18678,x18679,x18671),f854(x18673,x18674,x18675,x18676,x18677,x18678,x18679,x18672))
% 157.76/157.54 [1868]~E(x18681,x18682)+E(f340(x18681),f340(x18682))
% 157.76/157.54 [1869]~E(x18691,x18692)+E(f283(x18691,x18693),f283(x18692,x18693))
% 157.76/157.54 [1870]~E(x18701,x18702)+E(f283(x18703,x18701),f283(x18703,x18702))
% 157.76/157.54 [1871]~E(x18711,x18712)+E(f826(x18711,x18713,x18714,x18715,x18716),f826(x18712,x18713,x18714,x18715,x18716))
% 157.76/157.54 [1872]~E(x18721,x18722)+E(f826(x18723,x18721,x18724,x18725,x18726),f826(x18723,x18722,x18724,x18725,x18726))
% 157.76/157.54 [1873]~E(x18731,x18732)+E(f826(x18733,x18734,x18731,x18735,x18736),f826(x18733,x18734,x18732,x18735,x18736))
% 157.76/157.54 [1874]~E(x18741,x18742)+E(f826(x18743,x18744,x18745,x18741,x18746),f826(x18743,x18744,x18745,x18742,x18746))
% 157.76/157.54 [1875]~E(x18751,x18752)+E(f826(x18753,x18754,x18755,x18756,x18751),f826(x18753,x18754,x18755,x18756,x18752))
% 157.76/157.54 [1876]~E(x18761,x18762)+E(f906(x18761,x18763),f906(x18762,x18763))
% 157.76/157.54 [1877]~E(x18771,x18772)+E(f906(x18773,x18771),f906(x18773,x18772))
% 157.76/157.54 [1878]~E(x18781,x18782)+E(f590(x18781,x18783),f590(x18782,x18783))
% 157.76/157.54 [1879]~E(x18791,x18792)+E(f590(x18793,x18791),f590(x18793,x18792))
% 157.76/157.54 [1880]~E(x18801,x18802)+E(f855(x18801,x18803,x18804,x18805,x18806,x18807,x18808,x18809),f855(x18802,x18803,x18804,x18805,x18806,x18807,x18808,x18809))
% 157.76/157.54 [1881]~E(x18811,x18812)+E(f855(x18813,x18811,x18814,x18815,x18816,x18817,x18818,x18819),f855(x18813,x18812,x18814,x18815,x18816,x18817,x18818,x18819))
% 157.76/157.54 [1882]~E(x18821,x18822)+E(f855(x18823,x18824,x18821,x18825,x18826,x18827,x18828,x18829),f855(x18823,x18824,x18822,x18825,x18826,x18827,x18828,x18829))
% 157.76/157.54 [1883]~E(x18831,x18832)+E(f855(x18833,x18834,x18835,x18831,x18836,x18837,x18838,x18839),f855(x18833,x18834,x18835,x18832,x18836,x18837,x18838,x18839))
% 157.76/157.54 [1884]~E(x18841,x18842)+E(f855(x18843,x18844,x18845,x18846,x18841,x18847,x18848,x18849),f855(x18843,x18844,x18845,x18846,x18842,x18847,x18848,x18849))
% 157.76/157.54 [1885]~E(x18851,x18852)+E(f855(x18853,x18854,x18855,x18856,x18857,x18851,x18858,x18859),f855(x18853,x18854,x18855,x18856,x18857,x18852,x18858,x18859))
% 157.76/157.54 [1886]~E(x18861,x18862)+E(f855(x18863,x18864,x18865,x18866,x18867,x18868,x18861,x18869),f855(x18863,x18864,x18865,x18866,x18867,x18868,x18862,x18869))
% 157.76/157.54 [1887]~E(x18871,x18872)+E(f855(x18873,x18874,x18875,x18876,x18877,x18878,x18879,x18871),f855(x18873,x18874,x18875,x18876,x18877,x18878,x18879,x18872))
% 157.76/157.54 [1888]~E(x18881,x18882)+E(f466(x18881,x18883,x18884,x18885),f466(x18882,x18883,x18884,x18885))
% 157.76/157.54 [1889]~E(x18891,x18892)+E(f466(x18893,x18891,x18894,x18895),f466(x18893,x18892,x18894,x18895))
% 157.76/157.54 [1890]~E(x18901,x18902)+E(f466(x18903,x18904,x18901,x18905),f466(x18903,x18904,x18902,x18905))
% 157.76/157.54 [1891]~E(x18911,x18912)+E(f466(x18913,x18914,x18915,x18911),f466(x18913,x18914,x18915,x18912))
% 157.76/157.54 [1892]~E(x18921,x18922)+E(f481(x18921,x18923,x18924,x18925),f481(x18922,x18923,x18924,x18925))
% 157.76/157.54 [1893]~E(x18931,x18932)+E(f481(x18933,x18931,x18934,x18935),f481(x18933,x18932,x18934,x18935))
% 157.76/157.54 [1894]~E(x18941,x18942)+E(f481(x18943,x18944,x18941,x18945),f481(x18943,x18944,x18942,x18945))
% 157.76/157.54 [1895]~E(x18951,x18952)+E(f481(x18953,x18954,x18955,x18951),f481(x18953,x18954,x18955,x18952))
% 157.76/157.54 [1896]~E(x18961,x18962)+E(f306(x18961,x18963,x18964,x18965),f306(x18962,x18963,x18964,x18965))
% 157.76/157.54 [1897]~E(x18971,x18972)+E(f306(x18973,x18971,x18974,x18975),f306(x18973,x18972,x18974,x18975))
% 157.76/157.54 [1898]~E(x18981,x18982)+E(f306(x18983,x18984,x18981,x18985),f306(x18983,x18984,x18982,x18985))
% 157.76/157.54 [1899]~E(x18991,x18992)+E(f306(x18993,x18994,x18995,x18991),f306(x18993,x18994,x18995,x18992))
% 157.76/157.54 [1900]~E(x19001,x19002)+E(f901(x19001,x19003),f901(x19002,x19003))
% 157.76/157.54 [1901]~E(x19011,x19012)+E(f901(x19013,x19011),f901(x19013,x19012))
% 157.76/157.54 [1902]~E(x19021,x19022)+E(f432(x19021,x19023,x19024),f432(x19022,x19023,x19024))
% 157.76/157.54 [1903]~E(x19031,x19032)+E(f432(x19033,x19031,x19034),f432(x19033,x19032,x19034))
% 157.76/157.54 [1904]~E(x19041,x19042)+E(f432(x19043,x19044,x19041),f432(x19043,x19044,x19042))
% 157.76/157.54 [1905]~E(x19051,x19052)+E(f394(x19051,x19053,x19054),f394(x19052,x19053,x19054))
% 157.76/157.54 [1906]~E(x19061,x19062)+E(f394(x19063,x19061,x19064),f394(x19063,x19062,x19064))
% 157.76/157.54 [1907]~E(x19071,x19072)+E(f394(x19073,x19074,x19071),f394(x19073,x19074,x19072))
% 157.76/157.54 [1908]~E(x19081,x19082)+E(f601(x19081,x19083,x19084,x19085),f601(x19082,x19083,x19084,x19085))
% 157.76/157.54 [1909]~E(x19091,x19092)+E(f601(x19093,x19091,x19094,x19095),f601(x19093,x19092,x19094,x19095))
% 157.76/157.54 [1910]~E(x19101,x19102)+E(f601(x19103,x19104,x19101,x19105),f601(x19103,x19104,x19102,x19105))
% 157.76/157.54 [1911]~E(x19111,x19112)+E(f601(x19113,x19114,x19115,x19111),f601(x19113,x19114,x19115,x19112))
% 157.76/157.54 [1912]~E(x19121,x19122)+E(f214(x19121),f214(x19122))
% 157.76/157.54 [1913]~E(x19131,x19132)+E(f427(x19131),f427(x19132))
% 157.76/157.54 [1914]~E(x19141,x19142)+E(f419(x19141,x19143,x19144,x19145),f419(x19142,x19143,x19144,x19145))
% 157.76/157.54 [1915]~E(x19151,x19152)+E(f419(x19153,x19151,x19154,x19155),f419(x19153,x19152,x19154,x19155))
% 157.76/157.54 [1916]~E(x19161,x19162)+E(f419(x19163,x19164,x19161,x19165),f419(x19163,x19164,x19162,x19165))
% 157.76/157.54 [1917]~E(x19171,x19172)+E(f419(x19173,x19174,x19175,x19171),f419(x19173,x19174,x19175,x19172))
% 157.76/157.54 [1918]~E(x19181,x19182)+E(f94(x19181),f94(x19182))
% 157.76/157.54 [1919]~E(x19191,x19192)+E(f373(x19191),f373(x19192))
% 157.76/157.54 [1920]~E(x19201,x19202)+E(f355(x19201,x19203,x19204),f355(x19202,x19203,x19204))
% 157.76/157.54 [1921]~E(x19211,x19212)+E(f355(x19213,x19211,x19214),f355(x19213,x19212,x19214))
% 157.76/157.54 [1922]~E(x19221,x19222)+E(f355(x19223,x19224,x19221),f355(x19223,x19224,x19222))
% 157.76/157.54 [1923]~E(x19231,x19232)+E(f396(x19231,x19233,x19234,x19235),f396(x19232,x19233,x19234,x19235))
% 157.76/157.54 [1924]~E(x19241,x19242)+E(f396(x19243,x19241,x19244,x19245),f396(x19243,x19242,x19244,x19245))
% 157.76/157.54 [1925]~E(x19251,x19252)+E(f396(x19253,x19254,x19251,x19255),f396(x19253,x19254,x19252,x19255))
% 157.76/157.54 [1926]~E(x19261,x19262)+E(f396(x19263,x19264,x19265,x19261),f396(x19263,x19264,x19265,x19262))
% 157.76/157.54 [1927]~E(x19271,x19272)+E(f513(x19271,x19273,x19274,x19275,x19276),f513(x19272,x19273,x19274,x19275,x19276))
% 157.76/157.54 [1928]~E(x19281,x19282)+E(f513(x19283,x19281,x19284,x19285,x19286),f513(x19283,x19282,x19284,x19285,x19286))
% 157.76/157.54 [1929]~E(x19291,x19292)+E(f513(x19293,x19294,x19291,x19295,x19296),f513(x19293,x19294,x19292,x19295,x19296))
% 157.76/157.54 [1930]~E(x19301,x19302)+E(f513(x19303,x19304,x19305,x19301,x19306),f513(x19303,x19304,x19305,x19302,x19306))
% 157.76/157.54 [1931]~E(x19311,x19312)+E(f513(x19313,x19314,x19315,x19316,x19311),f513(x19313,x19314,x19315,x19316,x19312))
% 157.76/157.54 [1932]~E(x19321,x19322)+E(f371(x19321,x19323),f371(x19322,x19323))
% 157.76/157.54 [1933]~E(x19331,x19332)+E(f371(x19333,x19331),f371(x19333,x19332))
% 157.76/157.54 [1934]~E(x19341,x19342)+E(f867(x19341,x19343,x19344),f867(x19342,x19343,x19344))
% 157.76/157.54 [1935]~E(x19351,x19352)+E(f867(x19353,x19351,x19354),f867(x19353,x19352,x19354))
% 157.76/157.54 [1936]~E(x19361,x19362)+E(f867(x19363,x19364,x19361),f867(x19363,x19364,x19362))
% 157.76/157.54 [1937]~E(x19371,x19372)+E(f47(x19371),f47(x19372))
% 157.76/157.54 [1938]~E(x19381,x19382)+E(f647(x19381,x19383,x19384,x19385,x19386),f647(x19382,x19383,x19384,x19385,x19386))
% 157.76/157.54 [1939]~E(x19391,x19392)+E(f647(x19393,x19391,x19394,x19395,x19396),f647(x19393,x19392,x19394,x19395,x19396))
% 157.76/157.54 [1940]~E(x19401,x19402)+E(f647(x19403,x19404,x19401,x19405,x19406),f647(x19403,x19404,x19402,x19405,x19406))
% 157.76/157.54 [1941]~E(x19411,x19412)+E(f647(x19413,x19414,x19415,x19411,x19416),f647(x19413,x19414,x19415,x19412,x19416))
% 157.76/157.54 [1942]~E(x19421,x19422)+E(f647(x19423,x19424,x19425,x19426,x19421),f647(x19423,x19424,x19425,x19426,x19422))
% 157.76/157.54 [1943]~E(x19431,x19432)+E(f206(x19431,x19433,x19434,x19435),f206(x19432,x19433,x19434,x19435))
% 157.76/157.54 [1944]~E(x19441,x19442)+E(f206(x19443,x19441,x19444,x19445),f206(x19443,x19442,x19444,x19445))
% 157.76/157.54 [1945]~E(x19451,x19452)+E(f206(x19453,x19454,x19451,x19455),f206(x19453,x19454,x19452,x19455))
% 157.76/157.54 [1946]~E(x19461,x19462)+E(f206(x19463,x19464,x19465,x19461),f206(x19463,x19464,x19465,x19462))
% 157.76/157.54 [1947]~E(x19471,x19472)+E(f61(x19471),f61(x19472))
% 157.76/157.54 [1948]~E(x19481,x19482)+E(f197(x19481,x19483,x19484,x19485),f197(x19482,x19483,x19484,x19485))
% 157.76/157.54 [1949]~E(x19491,x19492)+E(f197(x19493,x19491,x19494,x19495),f197(x19493,x19492,x19494,x19495))
% 157.76/157.54 [1950]~E(x19501,x19502)+E(f197(x19503,x19504,x19501,x19505),f197(x19503,x19504,x19502,x19505))
% 157.76/157.54 [1951]~E(x19511,x19512)+E(f197(x19513,x19514,x19515,x19511),f197(x19513,x19514,x19515,x19512))
% 157.76/157.54 [1952]~E(x19521,x19522)+E(f470(x19521,x19523,x19524),f470(x19522,x19523,x19524))
% 157.76/157.54 [1953]~E(x19531,x19532)+E(f470(x19533,x19531,x19534),f470(x19533,x19532,x19534))
% 157.76/157.54 [1954]~E(x19541,x19542)+E(f470(x19543,x19544,x19541),f470(x19543,x19544,x19542))
% 157.76/157.54 [1955]~E(x19551,x19552)+E(f428(x19551),f428(x19552))
% 157.76/157.54 [1956]~E(x19561,x19562)+E(f628(x19561,x19563,x19564),f628(x19562,x19563,x19564))
% 157.76/157.54 [1957]~E(x19571,x19572)+E(f628(x19573,x19571,x19574),f628(x19573,x19572,x19574))
% 157.76/157.54 [1958]~E(x19581,x19582)+E(f628(x19583,x19584,x19581),f628(x19583,x19584,x19582))
% 157.76/157.54 [1959]~E(x19591,x19592)+E(f612(x19591,x19593,x19594,x19595,x19596,x19597,x19598),f612(x19592,x19593,x19594,x19595,x19596,x19597,x19598))
% 157.76/157.54 [1960]~E(x19601,x19602)+E(f612(x19603,x19601,x19604,x19605,x19606,x19607,x19608),f612(x19603,x19602,x19604,x19605,x19606,x19607,x19608))
% 157.76/157.54 [1961]~E(x19611,x19612)+E(f612(x19613,x19614,x19611,x19615,x19616,x19617,x19618),f612(x19613,x19614,x19612,x19615,x19616,x19617,x19618))
% 157.76/157.54 [1962]~E(x19621,x19622)+E(f612(x19623,x19624,x19625,x19621,x19626,x19627,x19628),f612(x19623,x19624,x19625,x19622,x19626,x19627,x19628))
% 157.76/157.54 [1963]~E(x19631,x19632)+E(f612(x19633,x19634,x19635,x19636,x19631,x19637,x19638),f612(x19633,x19634,x19635,x19636,x19632,x19637,x19638))
% 157.76/157.54 [1964]~E(x19641,x19642)+E(f612(x19643,x19644,x19645,x19646,x19647,x19641,x19648),f612(x19643,x19644,x19645,x19646,x19647,x19642,x19648))
% 157.76/157.54 [1965]~E(x19651,x19652)+E(f612(x19653,x19654,x19655,x19656,x19657,x19658,x19651),f612(x19653,x19654,x19655,x19656,x19657,x19658,x19652))
% 157.76/157.54 [1966]~E(x19661,x19662)+E(f387(x19661,x19663,x19664),f387(x19662,x19663,x19664))
% 157.76/157.54 [1967]~E(x19671,x19672)+E(f387(x19673,x19671,x19674),f387(x19673,x19672,x19674))
% 157.76/157.54 [1968]~E(x19681,x19682)+E(f387(x19683,x19684,x19681),f387(x19683,x19684,x19682))
% 157.76/157.54 [1969]~E(x19691,x19692)+E(f602(x19691,x19693,x19694,x19695,x19696),f602(x19692,x19693,x19694,x19695,x19696))
% 157.76/157.54 [1970]~E(x19701,x19702)+E(f602(x19703,x19701,x19704,x19705,x19706),f602(x19703,x19702,x19704,x19705,x19706))
% 157.76/157.54 [1971]~E(x19711,x19712)+E(f602(x19713,x19714,x19711,x19715,x19716),f602(x19713,x19714,x19712,x19715,x19716))
% 157.76/157.54 [1972]~E(x19721,x19722)+E(f602(x19723,x19724,x19725,x19721,x19726),f602(x19723,x19724,x19725,x19722,x19726))
% 157.76/157.54 [1973]~E(x19731,x19732)+E(f602(x19733,x19734,x19735,x19736,x19731),f602(x19733,x19734,x19735,x19736,x19732))
% 157.76/157.54 [1974]~E(x19741,x19742)+E(f908(x19741,x19743),f908(x19742,x19743))
% 157.76/157.54 [1975]~E(x19751,x19752)+E(f908(x19753,x19751),f908(x19753,x19752))
% 157.76/157.54 [1976]~E(x19761,x19762)+E(f504(x19761,x19763,x19764),f504(x19762,x19763,x19764))
% 157.76/157.54 [1977]~E(x19771,x19772)+E(f504(x19773,x19771,x19774),f504(x19773,x19772,x19774))
% 157.76/157.54 [1978]~E(x19781,x19782)+E(f504(x19783,x19784,x19781),f504(x19783,x19784,x19782))
% 157.76/157.54 [1979]~E(x19791,x19792)+E(f734(x19791,x19793),f734(x19792,x19793))
% 157.76/157.54 [1980]~E(x19801,x19802)+E(f734(x19803,x19801),f734(x19803,x19802))
% 157.76/157.54 [1981]~E(x19811,x19812)+E(f233(x19811,x19813,x19814,x19815,x19816),f233(x19812,x19813,x19814,x19815,x19816))
% 157.76/157.54 [1982]~E(x19821,x19822)+E(f233(x19823,x19821,x19824,x19825,x19826),f233(x19823,x19822,x19824,x19825,x19826))
% 157.76/157.54 [1983]~E(x19831,x19832)+E(f233(x19833,x19834,x19831,x19835,x19836),f233(x19833,x19834,x19832,x19835,x19836))
% 157.76/157.54 [1984]~E(x19841,x19842)+E(f233(x19843,x19844,x19845,x19841,x19846),f233(x19843,x19844,x19845,x19842,x19846))
% 157.76/157.54 [1985]~E(x19851,x19852)+E(f233(x19853,x19854,x19855,x19856,x19851),f233(x19853,x19854,x19855,x19856,x19852))
% 157.76/157.54 [1986]~E(x19861,x19862)+E(f503(x19861,x19863,x19864),f503(x19862,x19863,x19864))
% 157.76/157.54 [1987]~E(x19871,x19872)+E(f503(x19873,x19871,x19874),f503(x19873,x19872,x19874))
% 157.76/157.54 [1988]~E(x19881,x19882)+E(f503(x19883,x19884,x19881),f503(x19883,x19884,x19882))
% 157.76/157.54 [1989]~E(x19891,x19892)+E(f613(x19891,x19893,x19894,x19895),f613(x19892,x19893,x19894,x19895))
% 157.76/157.54 [1990]~E(x19901,x19902)+E(f613(x19903,x19901,x19904,x19905),f613(x19903,x19902,x19904,x19905))
% 157.76/157.54 [1991]~E(x19911,x19912)+E(f613(x19913,x19914,x19911,x19915),f613(x19913,x19914,x19912,x19915))
% 157.76/157.54 [1992]~E(x19921,x19922)+E(f613(x19923,x19924,x19925,x19921),f613(x19923,x19924,x19925,x19922))
% 157.76/157.54 [1993]~E(x19931,x19932)+E(f254(x19931,x19933,x19934,x19935,x19936,x19937),f254(x19932,x19933,x19934,x19935,x19936,x19937))
% 157.76/157.54 [1994]~E(x19941,x19942)+E(f254(x19943,x19941,x19944,x19945,x19946,x19947),f254(x19943,x19942,x19944,x19945,x19946,x19947))
% 157.76/157.54 [1995]~E(x19951,x19952)+E(f254(x19953,x19954,x19951,x19955,x19956,x19957),f254(x19953,x19954,x19952,x19955,x19956,x19957))
% 157.76/157.54 [1996]~E(x19961,x19962)+E(f254(x19963,x19964,x19965,x19961,x19966,x19967),f254(x19963,x19964,x19965,x19962,x19966,x19967))
% 157.76/157.54 [1997]~E(x19971,x19972)+E(f254(x19973,x19974,x19975,x19976,x19971,x19977),f254(x19973,x19974,x19975,x19976,x19972,x19977))
% 157.76/157.54 [1998]~E(x19981,x19982)+E(f254(x19983,x19984,x19985,x19986,x19987,x19981),f254(x19983,x19984,x19985,x19986,x19987,x19982))
% 157.76/157.54 [1999]~E(x19991,x19992)+E(f343(x19991,x19993,x19994),f343(x19992,x19993,x19994))
% 157.76/157.54 [2000]~E(x20001,x20002)+E(f343(x20003,x20001,x20004),f343(x20003,x20002,x20004))
% 157.76/157.54 [2001]~E(x20011,x20012)+E(f343(x20013,x20014,x20011),f343(x20013,x20014,x20012))
% 157.76/157.54 [2002]~E(x20021,x20022)+E(f187(x20021),f187(x20022))
% 157.76/157.54 [2003]~E(x20031,x20032)+E(f542(x20031,x20033,x20034,x20035),f542(x20032,x20033,x20034,x20035))
% 157.76/157.54 [2004]~E(x20041,x20042)+E(f542(x20043,x20041,x20044,x20045),f542(x20043,x20042,x20044,x20045))
% 157.76/157.54 [2005]~E(x20051,x20052)+E(f542(x20053,x20054,x20051,x20055),f542(x20053,x20054,x20052,x20055))
% 157.76/157.54 [2006]~E(x20061,x20062)+E(f542(x20063,x20064,x20065,x20061),f542(x20063,x20064,x20065,x20062))
% 157.76/157.54 [2007]~E(x20071,x20072)+E(f631(x20071,x20073,x20074),f631(x20072,x20073,x20074))
% 157.76/157.54 [2008]~E(x20081,x20082)+E(f631(x20083,x20081,x20084),f631(x20083,x20082,x20084))
% 157.76/157.54 [2009]~E(x20091,x20092)+E(f631(x20093,x20094,x20091),f631(x20093,x20094,x20092))
% 157.76/157.54 [2010]~E(x20101,x20102)+E(f663(x20101,x20103,x20104,x20105,x20106),f663(x20102,x20103,x20104,x20105,x20106))
% 157.76/157.54 [2011]~E(x20111,x20112)+E(f663(x20113,x20111,x20114,x20115,x20116),f663(x20113,x20112,x20114,x20115,x20116))
% 157.76/157.54 [2012]~E(x20121,x20122)+E(f663(x20123,x20124,x20121,x20125,x20126),f663(x20123,x20124,x20122,x20125,x20126))
% 157.76/157.54 [2013]~E(x20131,x20132)+E(f663(x20133,x20134,x20135,x20131,x20136),f663(x20133,x20134,x20135,x20132,x20136))
% 157.76/157.54 [2014]~E(x20141,x20142)+E(f663(x20143,x20144,x20145,x20146,x20141),f663(x20143,x20144,x20145,x20146,x20142))
% 157.76/157.54 [2015]~E(x20151,x20152)+E(f447(x20151,x20153,x20154,x20155),f447(x20152,x20153,x20154,x20155))
% 157.76/157.54 [2016]~E(x20161,x20162)+E(f447(x20163,x20161,x20164,x20165),f447(x20163,x20162,x20164,x20165))
% 157.76/157.54 [2017]~E(x20171,x20172)+E(f447(x20173,x20174,x20171,x20175),f447(x20173,x20174,x20172,x20175))
% 157.76/157.54 [2018]~E(x20181,x20182)+E(f447(x20183,x20184,x20185,x20181),f447(x20183,x20184,x20185,x20182))
% 157.76/157.54 [2019]~E(x20191,x20192)+E(f210(x20191),f210(x20192))
% 157.76/157.54 [2020]~E(x20201,x20202)+E(f298(x20201,x20203),f298(x20202,x20203))
% 157.76/157.54 [2021]~E(x20211,x20212)+E(f298(x20213,x20211),f298(x20213,x20212))
% 157.76/157.54 [2022]~E(x20221,x20222)+E(f684(x20221,x20223,x20224),f684(x20222,x20223,x20224))
% 157.76/157.54 [2023]~E(x20231,x20232)+E(f684(x20233,x20231,x20234),f684(x20233,x20232,x20234))
% 157.76/157.54 [2024]~E(x20241,x20242)+E(f684(x20243,x20244,x20241),f684(x20243,x20244,x20242))
% 157.76/157.54 [2025]~E(x20251,x20252)+E(f770(x20251,x20253,x20254),f770(x20252,x20253,x20254))
% 157.76/157.54 [2026]~E(x20261,x20262)+E(f770(x20263,x20261,x20264),f770(x20263,x20262,x20264))
% 157.76/157.54 [2027]~E(x20271,x20272)+E(f770(x20273,x20274,x20271),f770(x20273,x20274,x20272))
% 157.76/157.54 [2028]~E(x20281,x20282)+E(f211(x20281,x20283),f211(x20282,x20283))
% 157.76/157.54 [2029]~E(x20291,x20292)+E(f211(x20293,x20291),f211(x20293,x20292))
% 157.76/157.54 [2030]~E(x20301,x20302)+E(f816(x20301,x20303),f816(x20302,x20303))
% 157.76/157.54 [2031]~E(x20311,x20312)+E(f816(x20313,x20311),f816(x20313,x20312))
% 157.76/157.54 [2032]~E(x20321,x20322)+E(f736(x20321,x20323,x20324),f736(x20322,x20323,x20324))
% 157.76/157.54 [2033]~E(x20331,x20332)+E(f736(x20333,x20331,x20334),f736(x20333,x20332,x20334))
% 157.76/157.54 [2034]~E(x20341,x20342)+E(f736(x20343,x20344,x20341),f736(x20343,x20344,x20342))
% 157.76/157.54 [2035]~E(x20351,x20352)+E(f413(x20351,x20353,x20354,x20355,x20356,x20357),f413(x20352,x20353,x20354,x20355,x20356,x20357))
% 157.76/157.54 [2036]~E(x20361,x20362)+E(f413(x20363,x20361,x20364,x20365,x20366,x20367),f413(x20363,x20362,x20364,x20365,x20366,x20367))
% 157.76/157.54 [2037]~E(x20371,x20372)+E(f413(x20373,x20374,x20371,x20375,x20376,x20377),f413(x20373,x20374,x20372,x20375,x20376,x20377))
% 157.76/157.54 [2038]~E(x20381,x20382)+E(f413(x20383,x20384,x20385,x20381,x20386,x20387),f413(x20383,x20384,x20385,x20382,x20386,x20387))
% 157.76/157.54 [2039]~E(x20391,x20392)+E(f413(x20393,x20394,x20395,x20396,x20391,x20397),f413(x20393,x20394,x20395,x20396,x20392,x20397))
% 157.76/157.54 [2040]~E(x20401,x20402)+E(f413(x20403,x20404,x20405,x20406,x20407,x20401),f413(x20403,x20404,x20405,x20406,x20407,x20402))
% 157.76/157.54 [2041]~E(x20411,x20412)+E(f438(x20411,x20413,x20414,x20415),f438(x20412,x20413,x20414,x20415))
% 157.76/157.54 [2042]~E(x20421,x20422)+E(f438(x20423,x20421,x20424,x20425),f438(x20423,x20422,x20424,x20425))
% 157.76/157.54 [2043]~E(x20431,x20432)+E(f438(x20433,x20434,x20431,x20435),f438(x20433,x20434,x20432,x20435))
% 157.76/157.54 [2044]~E(x20441,x20442)+E(f438(x20443,x20444,x20445,x20441),f438(x20443,x20444,x20445,x20442))
% 157.76/157.54 [2045]~E(x20451,x20452)+E(f441(x20451,x20453,x20454),f441(x20452,x20453,x20454))
% 157.76/157.54 [2046]~E(x20461,x20462)+E(f441(x20463,x20461,x20464),f441(x20463,x20462,x20464))
% 157.76/157.54 [2047]~E(x20471,x20472)+E(f441(x20473,x20474,x20471),f441(x20473,x20474,x20472))
% 157.76/157.54 [2048]~E(x20481,x20482)+E(f545(x20481,x20483,x20484),f545(x20482,x20483,x20484))
% 157.76/157.54 [2049]~E(x20491,x20492)+E(f545(x20493,x20491,x20494),f545(x20493,x20492,x20494))
% 157.76/157.54 [2050]~E(x20501,x20502)+E(f545(x20503,x20504,x20501),f545(x20503,x20504,x20502))
% 157.76/157.54 [2051]~E(x20511,x20512)+E(f719(x20511,x20513,x20514,x20515),f719(x20512,x20513,x20514,x20515))
% 157.76/157.54 [2052]~E(x20521,x20522)+E(f719(x20523,x20521,x20524,x20525),f719(x20523,x20522,x20524,x20525))
% 157.76/157.54 [2053]~E(x20531,x20532)+E(f719(x20533,x20534,x20531,x20535),f719(x20533,x20534,x20532,x20535))
% 157.76/157.54 [2054]~E(x20541,x20542)+E(f719(x20543,x20544,x20545,x20541),f719(x20543,x20544,x20545,x20542))
% 157.76/157.54 [2055]~E(x20551,x20552)+E(f749(x20551,x20553,x20554,x20555),f749(x20552,x20553,x20554,x20555))
% 157.76/157.54 [2056]~E(x20561,x20562)+E(f749(x20563,x20561,x20564,x20565),f749(x20563,x20562,x20564,x20565))
% 157.76/157.54 [2057]~E(x20571,x20572)+E(f749(x20573,x20574,x20571,x20575),f749(x20573,x20574,x20572,x20575))
% 157.76/157.54 [2058]~E(x20581,x20582)+E(f749(x20583,x20584,x20585,x20581),f749(x20583,x20584,x20585,x20582))
% 157.76/157.54 [2059]~E(x20591,x20592)+E(f572(x20591,x20593,x20594),f572(x20592,x20593,x20594))
% 157.76/157.54 [2060]~E(x20601,x20602)+E(f572(x20603,x20601,x20604),f572(x20603,x20602,x20604))
% 157.76/157.54 [2061]~E(x20611,x20612)+E(f572(x20613,x20614,x20611),f572(x20613,x20614,x20612))
% 157.76/157.54 [2062]~E(x20621,x20622)+E(f837(x20621,x20623,x20624,x20625),f837(x20622,x20623,x20624,x20625))
% 157.76/157.54 [2063]~E(x20631,x20632)+E(f837(x20633,x20631,x20634,x20635),f837(x20633,x20632,x20634,x20635))
% 157.76/157.54 [2064]~E(x20641,x20642)+E(f837(x20643,x20644,x20641,x20645),f837(x20643,x20644,x20642,x20645))
% 157.76/157.54 [2065]~E(x20651,x20652)+E(f837(x20653,x20654,x20655,x20651),f837(x20653,x20654,x20655,x20652))
% 157.76/157.54 [2066]~E(x20661,x20662)+E(f359(x20661,x20663),f359(x20662,x20663))
% 157.76/157.54 [2067]~E(x20671,x20672)+E(f359(x20673,x20671),f359(x20673,x20672))
% 157.76/157.54 [2068]~E(x20681,x20682)+E(f444(x20681,x20683),f444(x20682,x20683))
% 157.76/157.54 [2069]~E(x20691,x20692)+E(f444(x20693,x20691),f444(x20693,x20692))
% 157.76/157.54 [2070]~E(x20701,x20702)+E(f679(x20701,x20703),f679(x20702,x20703))
% 157.76/157.54 [2071]~E(x20711,x20712)+E(f679(x20713,x20711),f679(x20713,x20712))
% 157.76/157.54 [2072]~E(x20721,x20722)+E(f781(x20721,x20723,x20724,x20725),f781(x20722,x20723,x20724,x20725))
% 157.76/157.54 [2073]~E(x20731,x20732)+E(f781(x20733,x20731,x20734,x20735),f781(x20733,x20732,x20734,x20735))
% 157.76/157.54 [2074]~E(x20741,x20742)+E(f781(x20743,x20744,x20741,x20745),f781(x20743,x20744,x20742,x20745))
% 157.76/157.54 [2075]~E(x20751,x20752)+E(f781(x20753,x20754,x20755,x20751),f781(x20753,x20754,x20755,x20752))
% 157.76/157.54 [2076]~E(x20761,x20762)+E(f514(x20761),f514(x20762))
% 157.76/157.54 [2077]~E(x20771,x20772)+E(f724(x20771,x20773),f724(x20772,x20773))
% 157.76/157.54 [2078]~E(x20781,x20782)+E(f724(x20783,x20781),f724(x20783,x20782))
% 157.76/157.54 [2079]~E(x20791,x20792)+E(f549(x20791,x20793,x20794,x20795,x20796),f549(x20792,x20793,x20794,x20795,x20796))
% 157.76/157.54 [2080]~E(x20801,x20802)+E(f549(x20803,x20801,x20804,x20805,x20806),f549(x20803,x20802,x20804,x20805,x20806))
% 157.76/157.54 [2081]~E(x20811,x20812)+E(f549(x20813,x20814,x20811,x20815,x20816),f549(x20813,x20814,x20812,x20815,x20816))
% 157.76/157.54 [2082]~E(x20821,x20822)+E(f549(x20823,x20824,x20825,x20821,x20826),f549(x20823,x20824,x20825,x20822,x20826))
% 157.76/157.54 [2083]~E(x20831,x20832)+E(f549(x20833,x20834,x20835,x20836,x20831),f549(x20833,x20834,x20835,x20836,x20832))
% 157.76/157.54 [2084]~E(x20841,x20842)+E(f788(x20841,x20843,x20844,x20845),f788(x20842,x20843,x20844,x20845))
% 157.76/157.54 [2085]~E(x20851,x20852)+E(f788(x20853,x20851,x20854,x20855),f788(x20853,x20852,x20854,x20855))
% 157.76/157.54 [2086]~E(x20861,x20862)+E(f788(x20863,x20864,x20861,x20865),f788(x20863,x20864,x20862,x20865))
% 157.76/157.54 [2087]~E(x20871,x20872)+E(f788(x20873,x20874,x20875,x20871),f788(x20873,x20874,x20875,x20872))
% 157.76/157.54 [2088]~E(x20881,x20882)+E(f555(x20881,x20883),f555(x20882,x20883))
% 157.76/157.54 [2089]~E(x20891,x20892)+E(f555(x20893,x20891),f555(x20893,x20892))
% 157.76/157.54 [2090]~E(x20901,x20902)+E(f46(x20901),f46(x20902))
% 157.76/157.54 [2091]~E(x20911,x20912)+E(f531(x20911,x20913),f531(x20912,x20913))
% 157.76/157.54 [2092]~E(x20921,x20922)+E(f531(x20923,x20921),f531(x20923,x20922))
% 157.76/157.54 [2093]~E(x20931,x20932)+E(f435(x20931,x20933,x20934,x20935),f435(x20932,x20933,x20934,x20935))
% 157.76/157.54 [2094]~E(x20941,x20942)+E(f435(x20943,x20941,x20944,x20945),f435(x20943,x20942,x20944,x20945))
% 157.76/157.54 [2095]~E(x20951,x20952)+E(f435(x20953,x20954,x20951,x20955),f435(x20953,x20954,x20952,x20955))
% 157.76/157.54 [2096]~E(x20961,x20962)+E(f435(x20963,x20964,x20965,x20961),f435(x20963,x20964,x20965,x20962))
% 157.76/157.54 [2097]~E(x20971,x20972)+E(f836(x20971,x20973,x20974,x20975),f836(x20972,x20973,x20974,x20975))
% 157.76/157.54 [2098]~E(x20981,x20982)+E(f836(x20983,x20981,x20984,x20985),f836(x20983,x20982,x20984,x20985))
% 157.76/157.54 [2099]~E(x20991,x20992)+E(f836(x20993,x20994,x20991,x20995),f836(x20993,x20994,x20992,x20995))
% 157.76/157.54 [2100]~E(x21001,x21002)+E(f836(x21003,x21004,x21005,x21001),f836(x21003,x21004,x21005,x21002))
% 157.76/157.54 [2101]~E(x21011,x21012)+E(f718(x21011,x21013,x21014),f718(x21012,x21013,x21014))
% 157.76/157.54 [2102]~E(x21021,x21022)+E(f718(x21023,x21021,x21024),f718(x21023,x21022,x21024))
% 157.76/157.54 [2103]~E(x21031,x21032)+E(f718(x21033,x21034,x21031),f718(x21033,x21034,x21032))
% 157.76/157.54 [2104]~E(x21041,x21042)+E(f449(x21041,x21043,x21044,x21045),f449(x21042,x21043,x21044,x21045))
% 157.76/157.54 [2105]~E(x21051,x21052)+E(f449(x21053,x21051,x21054,x21055),f449(x21053,x21052,x21054,x21055))
% 157.76/157.54 [2106]~E(x21061,x21062)+E(f449(x21063,x21064,x21061,x21065),f449(x21063,x21064,x21062,x21065))
% 157.76/157.54 [2107]~E(x21071,x21072)+E(f449(x21073,x21074,x21075,x21071),f449(x21073,x21074,x21075,x21072))
% 157.76/157.54 [2108]~E(x21081,x21082)+E(f129(x21081,x21083,x21084,x21085),f129(x21082,x21083,x21084,x21085))
% 157.76/157.54 [2109]~E(x21091,x21092)+E(f129(x21093,x21091,x21094,x21095),f129(x21093,x21092,x21094,x21095))
% 157.76/157.54 [2110]~E(x21101,x21102)+E(f129(x21103,x21104,x21101,x21105),f129(x21103,x21104,x21102,x21105))
% 157.76/157.54 [2111]~E(x21111,x21112)+E(f129(x21113,x21114,x21115,x21111),f129(x21113,x21114,x21115,x21112))
% 157.76/157.54 [2112]~E(x21121,x21122)+E(f850(x21121,x21123,x21124,x21125,x21126,x21127,x21128,x21129),f850(x21122,x21123,x21124,x21125,x21126,x21127,x21128,x21129))
% 157.76/157.54 [2113]~E(x21131,x21132)+E(f850(x21133,x21131,x21134,x21135,x21136,x21137,x21138,x21139),f850(x21133,x21132,x21134,x21135,x21136,x21137,x21138,x21139))
% 157.76/157.54 [2114]~E(x21141,x21142)+E(f850(x21143,x21144,x21141,x21145,x21146,x21147,x21148,x21149),f850(x21143,x21144,x21142,x21145,x21146,x21147,x21148,x21149))
% 157.76/157.54 [2115]~E(x21151,x21152)+E(f850(x21153,x21154,x21155,x21151,x21156,x21157,x21158,x21159),f850(x21153,x21154,x21155,x21152,x21156,x21157,x21158,x21159))
% 157.76/157.54 [2116]~E(x21161,x21162)+E(f850(x21163,x21164,x21165,x21166,x21161,x21167,x21168,x21169),f850(x21163,x21164,x21165,x21166,x21162,x21167,x21168,x21169))
% 157.76/157.54 [2117]~E(x21171,x21172)+E(f850(x21173,x21174,x21175,x21176,x21177,x21171,x21178,x21179),f850(x21173,x21174,x21175,x21176,x21177,x21172,x21178,x21179))
% 157.76/157.54 [2118]~E(x21181,x21182)+E(f850(x21183,x21184,x21185,x21186,x21187,x21188,x21181,x21189),f850(x21183,x21184,x21185,x21186,x21187,x21188,x21182,x21189))
% 157.76/157.54 [2119]~E(x21191,x21192)+E(f850(x21193,x21194,x21195,x21196,x21197,x21198,x21199,x21191),f850(x21193,x21194,x21195,x21196,x21197,x21198,x21199,x21192))
% 157.76/157.54 [2120]~E(x21201,x21202)+E(f59(x21201,x21203),f59(x21202,x21203))
% 157.76/157.54 [2121]~E(x21211,x21212)+E(f59(x21213,x21211),f59(x21213,x21212))
% 157.76/157.54 [2122]~E(x21221,x21222)+E(f606(x21221,x21223,x21224,x21225,x21226),f606(x21222,x21223,x21224,x21225,x21226))
% 157.76/157.54 [2123]~E(x21231,x21232)+E(f606(x21233,x21231,x21234,x21235,x21236),f606(x21233,x21232,x21234,x21235,x21236))
% 157.76/157.54 [2124]~E(x21241,x21242)+E(f606(x21243,x21244,x21241,x21245,x21246),f606(x21243,x21244,x21242,x21245,x21246))
% 157.76/157.54 [2125]~E(x21251,x21252)+E(f606(x21253,x21254,x21255,x21251,x21256),f606(x21253,x21254,x21255,x21252,x21256))
% 157.76/157.54 [2126]~E(x21261,x21262)+E(f606(x21263,x21264,x21265,x21266,x21261),f606(x21263,x21264,x21265,x21266,x21262))
% 157.76/157.54 [2127]~E(x21271,x21272)+E(f608(x21271,x21273,x21274,x21275,x21276),f608(x21272,x21273,x21274,x21275,x21276))
% 157.76/157.54 [2128]~E(x21281,x21282)+E(f608(x21283,x21281,x21284,x21285,x21286),f608(x21283,x21282,x21284,x21285,x21286))
% 157.76/157.54 [2129]~E(x21291,x21292)+E(f608(x21293,x21294,x21291,x21295,x21296),f608(x21293,x21294,x21292,x21295,x21296))
% 157.76/157.54 [2130]~E(x21301,x21302)+E(f608(x21303,x21304,x21305,x21301,x21306),f608(x21303,x21304,x21305,x21302,x21306))
% 157.76/157.54 [2131]~E(x21311,x21312)+E(f608(x21313,x21314,x21315,x21316,x21311),f608(x21313,x21314,x21315,x21316,x21312))
% 157.76/157.54 [2132]~E(x21321,x21322)+E(f907(x21321,x21323,x21324),f907(x21322,x21323,x21324))
% 157.76/157.54 [2133]~E(x21331,x21332)+E(f907(x21333,x21331,x21334),f907(x21333,x21332,x21334))
% 157.76/157.54 [2134]~E(x21341,x21342)+E(f907(x21343,x21344,x21341),f907(x21343,x21344,x21342))
% 157.76/157.54 [2135]~E(x21351,x21352)+E(f223(x21351,x21353),f223(x21352,x21353))
% 157.76/157.54 [2136]~E(x21361,x21362)+E(f223(x21363,x21361),f223(x21363,x21362))
% 157.76/157.54 [2137]~E(x21371,x21372)+E(f169(x21371,x21373),f169(x21372,x21373))
% 157.76/157.54 [2138]~E(x21381,x21382)+E(f169(x21383,x21381),f169(x21383,x21382))
% 157.76/157.54 [2139]~E(x21391,x21392)+E(f640(x21391,x21393,x21394,x21395),f640(x21392,x21393,x21394,x21395))
% 157.76/157.54 [2140]~E(x21401,x21402)+E(f640(x21403,x21401,x21404,x21405),f640(x21403,x21402,x21404,x21405))
% 157.76/157.54 [2141]~E(x21411,x21412)+E(f640(x21413,x21414,x21411,x21415),f640(x21413,x21414,x21412,x21415))
% 157.76/157.54 [2142]~E(x21421,x21422)+E(f640(x21423,x21424,x21425,x21421),f640(x21423,x21424,x21425,x21422))
% 157.76/157.54 [2143]~E(x21431,x21432)+E(f739(x21431,x21433),f739(x21432,x21433))
% 157.76/157.54 [2144]~E(x21441,x21442)+E(f739(x21443,x21441),f739(x21443,x21442))
% 157.76/157.54 [2145]~E(x21451,x21452)+E(f682(x21451,x21453,x21454),f682(x21452,x21453,x21454))
% 157.76/157.54 [2146]~E(x21461,x21462)+E(f682(x21463,x21461,x21464),f682(x21463,x21462,x21464))
% 157.76/157.54 [2147]~E(x21471,x21472)+E(f682(x21473,x21474,x21471),f682(x21473,x21474,x21472))
% 157.76/157.54 [2148]~E(x21481,x21482)+E(f559(x21481,x21483,x21484,x21485),f559(x21482,x21483,x21484,x21485))
% 157.76/157.54 [2149]~E(x21491,x21492)+E(f559(x21493,x21491,x21494,x21495),f559(x21493,x21492,x21494,x21495))
% 157.76/157.54 [2150]~E(x21501,x21502)+E(f559(x21503,x21504,x21501,x21505),f559(x21503,x21504,x21502,x21505))
% 157.76/157.54 [2151]~E(x21511,x21512)+E(f559(x21513,x21514,x21515,x21511),f559(x21513,x21514,x21515,x21512))
% 157.76/157.54 [2152]~E(x21521,x21522)+E(f597(x21521,x21523,x21524),f597(x21522,x21523,x21524))
% 157.76/157.54 [2153]~E(x21531,x21532)+E(f597(x21533,x21531,x21534),f597(x21533,x21532,x21534))
% 157.76/157.54 [2154]~E(x21541,x21542)+E(f597(x21543,x21544,x21541),f597(x21543,x21544,x21542))
% 157.76/157.54 [2155]~E(x21551,x21552)+E(f134(x21551,x21553,x21554,x21555,x21556),f134(x21552,x21553,x21554,x21555,x21556))
% 157.76/157.54 [2156]~E(x21561,x21562)+E(f134(x21563,x21561,x21564,x21565,x21566),f134(x21563,x21562,x21564,x21565,x21566))
% 157.76/157.54 [2157]~E(x21571,x21572)+E(f134(x21573,x21574,x21571,x21575,x21576),f134(x21573,x21574,x21572,x21575,x21576))
% 157.76/157.54 [2158]~E(x21581,x21582)+E(f134(x21583,x21584,x21585,x21581,x21586),f134(x21583,x21584,x21585,x21582,x21586))
% 157.76/157.54 [2159]~E(x21591,x21592)+E(f134(x21593,x21594,x21595,x21596,x21591),f134(x21593,x21594,x21595,x21596,x21592))
% 157.76/157.54 [2160]~E(x21601,x21602)+E(f753(x21601,x21603,x21604,x21605,x21606),f753(x21602,x21603,x21604,x21605,x21606))
% 157.76/157.54 [2161]~E(x21611,x21612)+E(f753(x21613,x21611,x21614,x21615,x21616),f753(x21613,x21612,x21614,x21615,x21616))
% 157.76/157.54 [2162]~E(x21621,x21622)+E(f753(x21623,x21624,x21621,x21625,x21626),f753(x21623,x21624,x21622,x21625,x21626))
% 157.76/157.54 [2163]~E(x21631,x21632)+E(f753(x21633,x21634,x21635,x21631,x21636),f753(x21633,x21634,x21635,x21632,x21636))
% 157.76/157.54 [2164]~E(x21641,x21642)+E(f753(x21643,x21644,x21645,x21646,x21641),f753(x21643,x21644,x21645,x21646,x21642))
% 157.76/157.54 [2165]~E(x21651,x21652)+E(f849(x21651,x21653,x21654,x21655,x21656,x21657,x21658,x21659),f849(x21652,x21653,x21654,x21655,x21656,x21657,x21658,x21659))
% 157.76/157.54 [2166]~E(x21661,x21662)+E(f849(x21663,x21661,x21664,x21665,x21666,x21667,x21668,x21669),f849(x21663,x21662,x21664,x21665,x21666,x21667,x21668,x21669))
% 157.76/157.54 [2167]~E(x21671,x21672)+E(f849(x21673,x21674,x21671,x21675,x21676,x21677,x21678,x21679),f849(x21673,x21674,x21672,x21675,x21676,x21677,x21678,x21679))
% 157.76/157.54 [2168]~E(x21681,x21682)+E(f849(x21683,x21684,x21685,x21681,x21686,x21687,x21688,x21689),f849(x21683,x21684,x21685,x21682,x21686,x21687,x21688,x21689))
% 157.76/157.54 [2169]~E(x21691,x21692)+E(f849(x21693,x21694,x21695,x21696,x21691,x21697,x21698,x21699),f849(x21693,x21694,x21695,x21696,x21692,x21697,x21698,x21699))
% 157.76/157.54 [2170]~E(x21701,x21702)+E(f849(x21703,x21704,x21705,x21706,x21707,x21701,x21708,x21709),f849(x21703,x21704,x21705,x21706,x21707,x21702,x21708,x21709))
% 157.76/157.54 [2171]~E(x21711,x21712)+E(f849(x21713,x21714,x21715,x21716,x21717,x21718,x21711,x21719),f849(x21713,x21714,x21715,x21716,x21717,x21718,x21712,x21719))
% 157.76/157.54 [2172]~E(x21721,x21722)+E(f849(x21723,x21724,x21725,x21726,x21727,x21728,x21729,x21721),f849(x21723,x21724,x21725,x21726,x21727,x21728,x21729,x21722))
% 157.76/157.54 [2173]~E(x21731,x21732)+E(f845(x21731,x21733,x21734,x21735,x21736,x21737),f845(x21732,x21733,x21734,x21735,x21736,x21737))
% 157.76/157.54 [2174]~E(x21741,x21742)+E(f845(x21743,x21741,x21744,x21745,x21746,x21747),f845(x21743,x21742,x21744,x21745,x21746,x21747))
% 157.76/157.54 [2175]~E(x21751,x21752)+E(f845(x21753,x21754,x21751,x21755,x21756,x21757),f845(x21753,x21754,x21752,x21755,x21756,x21757))
% 157.76/157.54 [2176]~E(x21761,x21762)+E(f845(x21763,x21764,x21765,x21761,x21766,x21767),f845(x21763,x21764,x21765,x21762,x21766,x21767))
% 157.76/157.54 [2177]~E(x21771,x21772)+E(f845(x21773,x21774,x21775,x21776,x21771,x21777),f845(x21773,x21774,x21775,x21776,x21772,x21777))
% 157.76/157.54 [2178]~E(x21781,x21782)+E(f845(x21783,x21784,x21785,x21786,x21787,x21781),f845(x21783,x21784,x21785,x21786,x21787,x21782))
% 157.76/157.54 [2179]~E(x21791,x21792)+E(f858(x21791,x21793,x21794,x21795,x21796,x21797),f858(x21792,x21793,x21794,x21795,x21796,x21797))
% 157.76/157.54 [2180]~E(x21801,x21802)+E(f858(x21803,x21801,x21804,x21805,x21806,x21807),f858(x21803,x21802,x21804,x21805,x21806,x21807))
% 157.76/157.54 [2181]~E(x21811,x21812)+E(f858(x21813,x21814,x21811,x21815,x21816,x21817),f858(x21813,x21814,x21812,x21815,x21816,x21817))
% 157.76/157.54 [2182]~E(x21821,x21822)+E(f858(x21823,x21824,x21825,x21821,x21826,x21827),f858(x21823,x21824,x21825,x21822,x21826,x21827))
% 157.76/157.54 [2183]~E(x21831,x21832)+E(f858(x21833,x21834,x21835,x21836,x21831,x21837),f858(x21833,x21834,x21835,x21836,x21832,x21837))
% 157.76/157.54 [2184]~E(x21841,x21842)+E(f858(x21843,x21844,x21845,x21846,x21847,x21841),f858(x21843,x21844,x21845,x21846,x21847,x21842))
% 157.76/157.54 [2185]~E(x21851,x21852)+E(f824(x21851,x21853,x21854,x21855,x21856,x21857),f824(x21852,x21853,x21854,x21855,x21856,x21857))
% 157.76/157.54 [2186]~E(x21861,x21862)+E(f824(x21863,x21861,x21864,x21865,x21866,x21867),f824(x21863,x21862,x21864,x21865,x21866,x21867))
% 157.76/157.54 [2187]~E(x21871,x21872)+E(f824(x21873,x21874,x21871,x21875,x21876,x21877),f824(x21873,x21874,x21872,x21875,x21876,x21877))
% 157.76/157.54 [2188]~E(x21881,x21882)+E(f824(x21883,x21884,x21885,x21881,x21886,x21887),f824(x21883,x21884,x21885,x21882,x21886,x21887))
% 157.76/157.54 [2189]~E(x21891,x21892)+E(f824(x21893,x21894,x21895,x21896,x21891,x21897),f824(x21893,x21894,x21895,x21896,x21892,x21897))
% 157.76/157.54 [2190]~E(x21901,x21902)+E(f824(x21903,x21904,x21905,x21906,x21907,x21901),f824(x21903,x21904,x21905,x21906,x21907,x21902))
% 157.76/157.54 [2191]~E(x21911,x21912)+E(f916(x21911,x21913,x21914),f916(x21912,x21913,x21914))
% 157.76/157.54 [2192]~E(x21921,x21922)+E(f916(x21923,x21921,x21924),f916(x21923,x21922,x21924))
% 157.76/157.54 [2193]~E(x21931,x21932)+E(f916(x21933,x21934,x21931),f916(x21933,x21934,x21932))
% 157.76/157.54 [2194]~E(x21941,x21942)+E(f476(x21941,x21943,x21944,x21945,x21946),f476(x21942,x21943,x21944,x21945,x21946))
% 157.76/157.54 [2195]~E(x21951,x21952)+E(f476(x21953,x21951,x21954,x21955,x21956),f476(x21953,x21952,x21954,x21955,x21956))
% 157.76/157.54 [2196]~E(x21961,x21962)+E(f476(x21963,x21964,x21961,x21965,x21966),f476(x21963,x21964,x21962,x21965,x21966))
% 157.76/157.54 [2197]~E(x21971,x21972)+E(f476(x21973,x21974,x21975,x21971,x21976),f476(x21973,x21974,x21975,x21972,x21976))
% 157.76/157.54 [2198]~E(x21981,x21982)+E(f476(x21983,x21984,x21985,x21986,x21981),f476(x21983,x21984,x21985,x21986,x21982))
% 157.76/157.54 [2199]~E(x21991,x21992)+E(f360(x21991,x21993,x21994),f360(x21992,x21993,x21994))
% 157.76/157.54 [2200]~E(x22001,x22002)+E(f360(x22003,x22001,x22004),f360(x22003,x22002,x22004))
% 157.76/157.54 [2201]~E(x22011,x22012)+E(f360(x22013,x22014,x22011),f360(x22013,x22014,x22012))
% 157.76/157.54 [2202]~E(x22021,x22022)+E(f745(x22021,x22023),f745(x22022,x22023))
% 157.76/157.54 [2203]~E(x22031,x22032)+E(f745(x22033,x22031),f745(x22033,x22032))
% 157.76/157.54 [2204]~E(x22041,x22042)+E(f713(x22041,x22043),f713(x22042,x22043))
% 157.76/157.54 [2205]~E(x22051,x22052)+E(f713(x22053,x22051),f713(x22053,x22052))
% 157.76/157.54 [2206]~E(x22061,x22062)+E(f773(x22061,x22063,x22064),f773(x22062,x22063,x22064))
% 157.76/157.54 [2207]~E(x22071,x22072)+E(f773(x22073,x22071,x22074),f773(x22073,x22072,x22074))
% 157.76/157.54 [2208]~E(x22081,x22082)+E(f773(x22083,x22084,x22081),f773(x22083,x22084,x22082))
% 157.76/157.54 [2209]~E(x22091,x22092)+E(f634(x22091,x22093,x22094,x22095),f634(x22092,x22093,x22094,x22095))
% 157.76/157.54 [2210]~E(x22101,x22102)+E(f634(x22103,x22101,x22104,x22105),f634(x22103,x22102,x22104,x22105))
% 157.76/157.54 [2211]~E(x22111,x22112)+E(f634(x22113,x22114,x22111,x22115),f634(x22113,x22114,x22112,x22115))
% 157.76/157.54 [2212]~E(x22121,x22122)+E(f634(x22123,x22124,x22125,x22121),f634(x22123,x22124,x22125,x22122))
% 157.76/157.54 [2213]~E(x22131,x22132)+E(f683(x22131,x22133),f683(x22132,x22133))
% 157.76/157.54 [2214]~E(x22141,x22142)+E(f683(x22143,x22141),f683(x22143,x22142))
% 157.76/157.54 [2215]~E(x22151,x22152)+E(f809(x22151,x22153,x22154,x22155),f809(x22152,x22153,x22154,x22155))
% 157.76/157.54 [2216]~E(x22161,x22162)+E(f809(x22163,x22161,x22164,x22165),f809(x22163,x22162,x22164,x22165))
% 157.76/157.54 [2217]~E(x22171,x22172)+E(f809(x22173,x22174,x22171,x22175),f809(x22173,x22174,x22172,x22175))
% 157.76/157.54 [2218]~E(x22181,x22182)+E(f809(x22183,x22184,x22185,x22181),f809(x22183,x22184,x22185,x22182))
% 157.76/157.54 [2219]~E(x22191,x22192)+E(f673(x22191,x22193,x22194,x22195,x22196,x22197),f673(x22192,x22193,x22194,x22195,x22196,x22197))
% 157.76/157.54 [2220]~E(x22201,x22202)+E(f673(x22203,x22201,x22204,x22205,x22206,x22207),f673(x22203,x22202,x22204,x22205,x22206,x22207))
% 157.76/157.54 [2221]~E(x22211,x22212)+E(f673(x22213,x22214,x22211,x22215,x22216,x22217),f673(x22213,x22214,x22212,x22215,x22216,x22217))
% 157.76/157.54 [2222]~E(x22221,x22222)+E(f673(x22223,x22224,x22225,x22221,x22226,x22227),f673(x22223,x22224,x22225,x22222,x22226,x22227))
% 157.76/157.54 [2223]~E(x22231,x22232)+E(f673(x22233,x22234,x22235,x22236,x22231,x22237),f673(x22233,x22234,x22235,x22236,x22232,x22237))
% 157.76/157.54 [2224]~E(x22241,x22242)+E(f673(x22243,x22244,x22245,x22246,x22247,x22241),f673(x22243,x22244,x22245,x22246,x22247,x22242))
% 157.76/157.54 [2225]~E(x22251,x22252)+E(f351(x22251,x22253,x22254,x22255,x22256),f351(x22252,x22253,x22254,x22255,x22256))
% 157.76/157.54 [2226]~E(x22261,x22262)+E(f351(x22263,x22261,x22264,x22265,x22266),f351(x22263,x22262,x22264,x22265,x22266))
% 157.76/157.54 [2227]~E(x22271,x22272)+E(f351(x22273,x22274,x22271,x22275,x22276),f351(x22273,x22274,x22272,x22275,x22276))
% 157.76/157.54 [2228]~E(x22281,x22282)+E(f351(x22283,x22284,x22285,x22281,x22286),f351(x22283,x22284,x22285,x22282,x22286))
% 157.76/157.54 [2229]~E(x22291,x22292)+E(f351(x22293,x22294,x22295,x22296,x22291),f351(x22293,x22294,x22295,x22296,x22292))
% 157.76/157.54 [2230]~E(x22301,x22302)+E(f622(x22301,x22303,x22304),f622(x22302,x22303,x22304))
% 157.76/157.54 [2231]~E(x22311,x22312)+E(f622(x22313,x22311,x22314),f622(x22313,x22312,x22314))
% 157.76/157.54 [2232]~E(x22321,x22322)+E(f622(x22323,x22324,x22321),f622(x22323,x22324,x22322))
% 157.76/157.54 [2233]~E(x22331,x22332)+E(f501(x22331,x22333),f501(x22332,x22333))
% 157.76/157.54 [2234]~E(x22341,x22342)+E(f501(x22343,x22341),f501(x22343,x22342))
% 157.76/157.54 [2235]~E(x22351,x22352)+E(f609(x22351,x22353,x22354,x22355,x22356),f609(x22352,x22353,x22354,x22355,x22356))
% 157.76/157.54 [2236]~E(x22361,x22362)+E(f609(x22363,x22361,x22364,x22365,x22366),f609(x22363,x22362,x22364,x22365,x22366))
% 157.76/157.54 [2237]~E(x22371,x22372)+E(f609(x22373,x22374,x22371,x22375,x22376),f609(x22373,x22374,x22372,x22375,x22376))
% 157.76/157.54 [2238]~E(x22381,x22382)+E(f609(x22383,x22384,x22385,x22381,x22386),f609(x22383,x22384,x22385,x22382,x22386))
% 157.76/157.54 [2239]~E(x22391,x22392)+E(f609(x22393,x22394,x22395,x22396,x22391),f609(x22393,x22394,x22395,x22396,x22392))
% 157.76/157.54 [2240]~E(x22401,x22402)+E(f305(x22401,x22403,x22404),f305(x22402,x22403,x22404))
% 157.76/157.54 [2241]~E(x22411,x22412)+E(f305(x22413,x22411,x22414),f305(x22413,x22412,x22414))
% 157.76/157.54 [2242]~E(x22421,x22422)+E(f305(x22423,x22424,x22421),f305(x22423,x22424,x22422))
% 157.76/157.54 [2243]~E(x22431,x22432)+E(f448(x22431,x22433,x22434,x22435),f448(x22432,x22433,x22434,x22435))
% 157.76/157.54 [2244]~E(x22441,x22442)+E(f448(x22443,x22441,x22444,x22445),f448(x22443,x22442,x22444,x22445))
% 157.76/157.54 [2245]~E(x22451,x22452)+E(f448(x22453,x22454,x22451,x22455),f448(x22453,x22454,x22452,x22455))
% 157.76/157.54 [2246]~E(x22461,x22462)+E(f448(x22463,x22464,x22465,x22461),f448(x22463,x22464,x22465,x22462))
% 157.76/157.54 [2247]~E(x22471,x22472)+E(f100(x22471,x22473,x22474),f100(x22472,x22473,x22474))
% 157.76/157.54 [2248]~E(x22481,x22482)+E(f100(x22483,x22481,x22484),f100(x22483,x22482,x22484))
% 157.76/157.54 [2249]~E(x22491,x22492)+E(f100(x22493,x22494,x22491),f100(x22493,x22494,x22492))
% 157.76/157.54 [2250]~E(x22501,x22502)+E(f742(x22501,x22503),f742(x22502,x22503))
% 157.76/157.54 [2251]~E(x22511,x22512)+E(f742(x22513,x22511),f742(x22513,x22512))
% 157.76/157.54 [2252]~E(x22521,x22522)+E(f771(x22521,x22523,x22524),f771(x22522,x22523,x22524))
% 157.76/157.54 [2253]~E(x22531,x22532)+E(f771(x22533,x22531,x22534),f771(x22533,x22532,x22534))
% 157.76/157.54 [2254]~E(x22541,x22542)+E(f771(x22543,x22544,x22541),f771(x22543,x22544,x22542))
% 157.76/157.54 [2255]~E(x22551,x22552)+E(f409(x22551),f409(x22552))
% 157.76/157.54 [2256]~E(x22561,x22562)+E(f723(x22561,x22563,x22564),f723(x22562,x22563,x22564))
% 157.76/157.54 [2257]~E(x22571,x22572)+E(f723(x22573,x22571,x22574),f723(x22573,x22572,x22574))
% 157.76/157.54 [2258]~E(x22581,x22582)+E(f723(x22583,x22584,x22581),f723(x22583,x22584,x22582))
% 157.76/157.54 [2259]~E(x22591,x22592)+E(f425(x22591,x22593),f425(x22592,x22593))
% 157.76/157.54 [2260]~E(x22601,x22602)+E(f425(x22603,x22601),f425(x22603,x22602))
% 157.76/157.54 [2261]~E(x22611,x22612)+E(f828(x22611,x22613,x22614),f828(x22612,x22613,x22614))
% 157.76/157.54 [2262]~E(x22621,x22622)+E(f828(x22623,x22621,x22624),f828(x22623,x22622,x22624))
% 157.76/157.54 [2263]~E(x22631,x22632)+E(f828(x22633,x22634,x22631),f828(x22633,x22634,x22632))
% 157.76/157.54 [2264]~E(x22641,x22642)+E(f384(x22641,x22643),f384(x22642,x22643))
% 157.76/157.54 [2265]~E(x22651,x22652)+E(f384(x22653,x22651),f384(x22653,x22652))
% 157.76/157.54 [2266]~E(x22661,x22662)+E(f698(x22661,x22663,x22664),f698(x22662,x22663,x22664))
% 157.76/157.54 [2267]~E(x22671,x22672)+E(f698(x22673,x22671,x22674),f698(x22673,x22672,x22674))
% 157.76/157.54 [2268]~E(x22681,x22682)+E(f698(x22683,x22684,x22681),f698(x22683,x22684,x22682))
% 157.76/157.54 [2269]~E(x22691,x22692)+E(f896(x22691,x22693,x22694),f896(x22692,x22693,x22694))
% 157.76/157.54 [2270]~E(x22701,x22702)+E(f896(x22703,x22701,x22704),f896(x22703,x22702,x22704))
% 157.76/157.54 [2271]~E(x22711,x22712)+E(f896(x22713,x22714,x22711),f896(x22713,x22714,x22712))
% 157.76/157.54 [2272]~E(x22721,x22722)+E(f17(x22721,x22723,x22724,x22725),f17(x22722,x22723,x22724,x22725))
% 157.76/157.54 [2273]~E(x22731,x22732)+E(f17(x22733,x22731,x22734,x22735),f17(x22733,x22732,x22734,x22735))
% 157.76/157.54 [2274]~E(x22741,x22742)+E(f17(x22743,x22744,x22741,x22745),f17(x22743,x22744,x22742,x22745))
% 157.76/157.54 [2275]~E(x22751,x22752)+E(f17(x22753,x22754,x22755,x22751),f17(x22753,x22754,x22755,x22752))
% 157.76/157.54 [2276]~E(x22761,x22762)+E(f286(x22761),f286(x22762))
% 157.76/157.54 [2277]~E(x22771,x22772)+E(f885(x22771,x22773),f885(x22772,x22773))
% 157.76/157.54 [2278]~E(x22781,x22782)+E(f885(x22783,x22781),f885(x22783,x22782))
% 157.76/157.54 [2279]~E(x22791,x22792)+E(f395(x22791,x22793,x22794,x22795),f395(x22792,x22793,x22794,x22795))
% 157.76/157.54 [2280]~E(x22801,x22802)+E(f395(x22803,x22801,x22804,x22805),f395(x22803,x22802,x22804,x22805))
% 157.76/157.54 [2281]~E(x22811,x22812)+E(f395(x22813,x22814,x22811,x22815),f395(x22813,x22814,x22812,x22815))
% 157.76/157.54 [2282]~E(x22821,x22822)+E(f395(x22823,x22824,x22825,x22821),f395(x22823,x22824,x22825,x22822))
% 157.76/157.54 [2283]~E(x22831,x22832)+E(f671(x22831,x22833,x22834,x22835),f671(x22832,x22833,x22834,x22835))
% 157.76/157.54 [2284]~E(x22841,x22842)+E(f671(x22843,x22841,x22844,x22845),f671(x22843,x22842,x22844,x22845))
% 157.76/157.54 [2285]~E(x22851,x22852)+E(f671(x22853,x22854,x22851,x22855),f671(x22853,x22854,x22852,x22855))
% 157.76/157.54 [2286]~E(x22861,x22862)+E(f671(x22863,x22864,x22865,x22861),f671(x22863,x22864,x22865,x22862))
% 157.76/157.54 [2287]~E(x22871,x22872)+E(f215(x22871,x22873,x22874,x22875),f215(x22872,x22873,x22874,x22875))
% 157.76/157.54 [2288]~E(x22881,x22882)+E(f215(x22883,x22881,x22884,x22885),f215(x22883,x22882,x22884,x22885))
% 157.76/157.54 [2289]~E(x22891,x22892)+E(f215(x22893,x22894,x22891,x22895),f215(x22893,x22894,x22892,x22895))
% 157.76/157.54 [2290]~E(x22901,x22902)+E(f215(x22903,x22904,x22905,x22901),f215(x22903,x22904,x22905,x22902))
% 157.76/157.54 [2291]~E(x22911,x22912)+E(f281(x22911,x22913,x22914,x22915),f281(x22912,x22913,x22914,x22915))
% 157.76/157.54 [2292]~E(x22921,x22922)+E(f281(x22923,x22921,x22924,x22925),f281(x22923,x22922,x22924,x22925))
% 157.76/157.54 [2293]~E(x22931,x22932)+E(f281(x22933,x22934,x22931,x22935),f281(x22933,x22934,x22932,x22935))
% 157.76/157.54 [2294]~E(x22941,x22942)+E(f281(x22943,x22944,x22945,x22941),f281(x22943,x22944,x22945,x22942))
% 157.76/157.54 [2295]~E(x22951,x22952)+E(f746(x22951,x22953,x22954),f746(x22952,x22953,x22954))
% 157.76/157.54 [2296]~E(x22961,x22962)+E(f746(x22963,x22961,x22964),f746(x22963,x22962,x22964))
% 157.76/157.54 [2297]~E(x22971,x22972)+E(f746(x22973,x22974,x22971),f746(x22973,x22974,x22972))
% 157.76/157.54 [2298]~E(x22981,x22982)+E(f464(x22981,x22983,x22984),f464(x22982,x22983,x22984))
% 157.76/157.54 [2299]~E(x22991,x22992)+E(f464(x22993,x22991,x22994),f464(x22993,x22992,x22994))
% 157.76/157.54 [2300]~E(x23001,x23002)+E(f464(x23003,x23004,x23001),f464(x23003,x23004,x23002))
% 157.76/157.54 [2301]~E(x23011,x23012)+E(f212(x23011,x23013,x23014),f212(x23012,x23013,x23014))
% 157.76/157.54 [2302]~E(x23021,x23022)+E(f212(x23023,x23021,x23024),f212(x23023,x23022,x23024))
% 157.76/157.54 [2303]~E(x23031,x23032)+E(f212(x23033,x23034,x23031),f212(x23033,x23034,x23032))
% 157.76/157.54 [2304]~E(x23041,x23042)+E(f533(x23041,x23043,x23044,x23045),f533(x23042,x23043,x23044,x23045))
% 157.76/157.54 [2305]~E(x23051,x23052)+E(f533(x23053,x23051,x23054,x23055),f533(x23053,x23052,x23054,x23055))
% 157.76/157.54 [2306]~E(x23061,x23062)+E(f533(x23063,x23064,x23061,x23065),f533(x23063,x23064,x23062,x23065))
% 157.76/157.54 [2307]~E(x23071,x23072)+E(f533(x23073,x23074,x23075,x23071),f533(x23073,x23074,x23075,x23072))
% 157.76/157.54 [2308]~E(x23081,x23082)+E(f585(x23081,x23083,x23084),f585(x23082,x23083,x23084))
% 157.76/157.54 [2309]~E(x23091,x23092)+E(f585(x23093,x23091,x23094),f585(x23093,x23092,x23094))
% 157.76/157.54 [2310]~E(x23101,x23102)+E(f585(x23103,x23104,x23101),f585(x23103,x23104,x23102))
% 157.76/157.54 [2311]~E(x23111,x23112)+E(f339(x23111),f339(x23112))
% 157.76/157.54 [2312]~E(x23121,x23122)+E(f857(x23121,x23123,x23124,x23125,x23126,x23127),f857(x23122,x23123,x23124,x23125,x23126,x23127))
% 157.76/157.54 [2313]~E(x23131,x23132)+E(f857(x23133,x23131,x23134,x23135,x23136,x23137),f857(x23133,x23132,x23134,x23135,x23136,x23137))
% 157.76/157.54 [2314]~E(x23141,x23142)+E(f857(x23143,x23144,x23141,x23145,x23146,x23147),f857(x23143,x23144,x23142,x23145,x23146,x23147))
% 157.76/157.54 [2315]~E(x23151,x23152)+E(f857(x23153,x23154,x23155,x23151,x23156,x23157),f857(x23153,x23154,x23155,x23152,x23156,x23157))
% 157.76/157.54 [2316]~E(x23161,x23162)+E(f857(x23163,x23164,x23165,x23166,x23161,x23167),f857(x23163,x23164,x23165,x23166,x23162,x23167))
% 157.76/157.54 [2317]~E(x23171,x23172)+E(f857(x23173,x23174,x23175,x23176,x23177,x23171),f857(x23173,x23174,x23175,x23176,x23177,x23172))
% 157.76/157.54 [2318]~E(x23181,x23182)+E(f805(x23181,x23183,x23184,x23185),f805(x23182,x23183,x23184,x23185))
% 157.76/157.54 [2319]~E(x23191,x23192)+E(f805(x23193,x23191,x23194,x23195),f805(x23193,x23192,x23194,x23195))
% 157.76/157.54 [2320]~E(x23201,x23202)+E(f805(x23203,x23204,x23201,x23205),f805(x23203,x23204,x23202,x23205))
% 157.76/157.54 [2321]~E(x23211,x23212)+E(f805(x23213,x23214,x23215,x23211),f805(x23213,x23214,x23215,x23212))
% 157.76/157.54 [2322]~E(x23221,x23222)+E(f368(x23221,x23223,x23224),f368(x23222,x23223,x23224))
% 157.76/157.54 [2323]~E(x23231,x23232)+E(f368(x23233,x23231,x23234),f368(x23233,x23232,x23234))
% 157.76/157.54 [2324]~E(x23241,x23242)+E(f368(x23243,x23244,x23241),f368(x23243,x23244,x23242))
% 157.76/157.54 [2325]~E(x23251,x23252)+E(f338(x23251,x23253,x23254,x23255),f338(x23252,x23253,x23254,x23255))
% 157.76/157.54 [2326]~E(x23261,x23262)+E(f338(x23263,x23261,x23264,x23265),f338(x23263,x23262,x23264,x23265))
% 157.76/157.54 [2327]~E(x23271,x23272)+E(f338(x23273,x23274,x23271,x23275),f338(x23273,x23274,x23272,x23275))
% 157.76/157.54 [2328]~E(x23281,x23282)+E(f338(x23283,x23284,x23285,x23281),f338(x23283,x23284,x23285,x23282))
% 157.76/157.54 [2329]~E(x23291,x23292)+E(f431(x23291,x23293,x23294),f431(x23292,x23293,x23294))
% 157.76/157.54 [2330]~E(x23301,x23302)+E(f431(x23303,x23301,x23304),f431(x23303,x23302,x23304))
% 157.76/157.54 [2331]~E(x23311,x23312)+E(f431(x23313,x23314,x23311),f431(x23313,x23314,x23312))
% 157.76/157.54 [2332]~E(x23321,x23322)+E(f807(x23321,x23323,x23324),f807(x23322,x23323,x23324))
% 157.76/157.54 [2333]~E(x23331,x23332)+E(f807(x23333,x23331,x23334),f807(x23333,x23332,x23334))
% 157.76/157.54 [2334]~E(x23341,x23342)+E(f807(x23343,x23344,x23341),f807(x23343,x23344,x23342))
% 157.76/157.54 [2335]~E(x23351,x23352)+E(f526(x23351,x23353,x23354),f526(x23352,x23353,x23354))
% 157.76/157.54 [2336]~E(x23361,x23362)+E(f526(x23363,x23361,x23364),f526(x23363,x23362,x23364))
% 157.76/157.54 [2337]~E(x23371,x23372)+E(f526(x23373,x23374,x23371),f526(x23373,x23374,x23372))
% 157.76/157.54 [2338]~E(x23381,x23382)+E(f786(x23381,x23383,x23384,x23385,x23386,x23387),f786(x23382,x23383,x23384,x23385,x23386,x23387))
% 157.76/157.54 [2339]~E(x23391,x23392)+E(f786(x23393,x23391,x23394,x23395,x23396,x23397),f786(x23393,x23392,x23394,x23395,x23396,x23397))
% 157.76/157.54 [2340]~E(x23401,x23402)+E(f786(x23403,x23404,x23401,x23405,x23406,x23407),f786(x23403,x23404,x23402,x23405,x23406,x23407))
% 157.76/157.54 [2341]~E(x23411,x23412)+E(f786(x23413,x23414,x23415,x23411,x23416,x23417),f786(x23413,x23414,x23415,x23412,x23416,x23417))
% 157.76/157.54 [2342]~E(x23421,x23422)+E(f786(x23423,x23424,x23425,x23426,x23421,x23427),f786(x23423,x23424,x23425,x23426,x23422,x23427))
% 157.76/157.54 [2343]~E(x23431,x23432)+E(f786(x23433,x23434,x23435,x23436,x23437,x23431),f786(x23433,x23434,x23435,x23436,x23437,x23432))
% 157.76/157.54 [2344]~E(x23441,x23442)+E(f458(x23441,x23443,x23444),f458(x23442,x23443,x23444))
% 157.76/157.54 [2345]~E(x23451,x23452)+E(f458(x23453,x23451,x23454),f458(x23453,x23452,x23454))
% 157.76/157.54 [2346]~E(x23461,x23462)+E(f458(x23463,x23464,x23461),f458(x23463,x23464,x23462))
% 157.76/157.54 [2347]~E(x23471,x23472)+E(f632(x23471,x23473,x23474),f632(x23472,x23473,x23474))
% 157.76/157.54 [2348]~E(x23481,x23482)+E(f632(x23483,x23481,x23484),f632(x23483,x23482,x23484))
% 157.76/157.54 [2349]~E(x23491,x23492)+E(f632(x23493,x23494,x23491),f632(x23493,x23494,x23492))
% 157.76/157.54 [2350]~E(x23501,x23502)+E(f678(x23501,x23503,x23504,x23505),f678(x23502,x23503,x23504,x23505))
% 157.76/157.54 [2351]~E(x23511,x23512)+E(f678(x23513,x23511,x23514,x23515),f678(x23513,x23512,x23514,x23515))
% 157.76/157.54 [2352]~E(x23521,x23522)+E(f678(x23523,x23524,x23521,x23525),f678(x23523,x23524,x23522,x23525))
% 157.76/157.54 [2353]~E(x23531,x23532)+E(f678(x23533,x23534,x23535,x23531),f678(x23533,x23534,x23535,x23532))
% 157.76/157.54 [2354]~E(x23541,x23542)+E(f246(x23541,x23543),f246(x23542,x23543))
% 157.76/157.54 [2355]~E(x23551,x23552)+E(f246(x23553,x23551),f246(x23553,x23552))
% 157.76/157.54 [2356]~E(x23561,x23562)+E(f593(x23561,x23563,x23564),f593(x23562,x23563,x23564))
% 157.76/157.54 [2357]~E(x23571,x23572)+E(f593(x23573,x23571,x23574),f593(x23573,x23572,x23574))
% 157.76/157.54 [2358]~E(x23581,x23582)+E(f593(x23583,x23584,x23581),f593(x23583,x23584,x23582))
% 157.76/157.54 [2359]~E(x23591,x23592)+E(f528(x23591,x23593,x23594,x23595),f528(x23592,x23593,x23594,x23595))
% 157.76/157.54 [2360]~E(x23601,x23602)+E(f528(x23603,x23601,x23604,x23605),f528(x23603,x23602,x23604,x23605))
% 157.76/157.54 [2361]~E(x23611,x23612)+E(f528(x23613,x23614,x23611,x23615),f528(x23613,x23614,x23612,x23615))
% 157.76/157.54 [2362]~E(x23621,x23622)+E(f528(x23623,x23624,x23625,x23621),f528(x23623,x23624,x23625,x23622))
% 157.76/157.54 [2363]~E(x23631,x23632)+E(f429(x23631,x23633,x23634,x23635,x23636),f429(x23632,x23633,x23634,x23635,x23636))
% 157.76/157.54 [2364]~E(x23641,x23642)+E(f429(x23643,x23641,x23644,x23645,x23646),f429(x23643,x23642,x23644,x23645,x23646))
% 157.76/157.54 [2365]~E(x23651,x23652)+E(f429(x23653,x23654,x23651,x23655,x23656),f429(x23653,x23654,x23652,x23655,x23656))
% 157.76/157.54 [2366]~E(x23661,x23662)+E(f429(x23663,x23664,x23665,x23661,x23666),f429(x23663,x23664,x23665,x23662,x23666))
% 157.76/157.54 [2367]~E(x23671,x23672)+E(f429(x23673,x23674,x23675,x23676,x23671),f429(x23673,x23674,x23675,x23676,x23672))
% 157.76/157.54 [2368]~E(x23681,x23682)+E(f268(x23681,x23683,x23684,x23685,x23686),f268(x23682,x23683,x23684,x23685,x23686))
% 157.76/157.54 [2369]~E(x23691,x23692)+E(f268(x23693,x23691,x23694,x23695,x23696),f268(x23693,x23692,x23694,x23695,x23696))
% 157.76/157.54 [2370]~E(x23701,x23702)+E(f268(x23703,x23704,x23701,x23705,x23706),f268(x23703,x23704,x23702,x23705,x23706))
% 157.76/157.54 [2371]~E(x23711,x23712)+E(f268(x23713,x23714,x23715,x23711,x23716),f268(x23713,x23714,x23715,x23712,x23716))
% 157.76/157.54 [2372]~E(x23721,x23722)+E(f268(x23723,x23724,x23725,x23726,x23721),f268(x23723,x23724,x23725,x23726,x23722))
% 157.76/157.54 [2373]~E(x23731,x23732)+E(f79(x23731,x23733),f79(x23732,x23733))
% 157.76/157.54 [2374]~E(x23741,x23742)+E(f79(x23743,x23741),f79(x23743,x23742))
% 157.76/157.54 [2375]~E(x23751,x23752)+E(f543(x23751),f543(x23752))
% 157.76/157.54 [2376]~E(x23761,x23762)+E(f170(x23761,x23763,x23764,x23765),f170(x23762,x23763,x23764,x23765))
% 157.76/157.54 [2377]~E(x23771,x23772)+E(f170(x23773,x23771,x23774,x23775),f170(x23773,x23772,x23774,x23775))
% 157.76/157.54 [2378]~E(x23781,x23782)+E(f170(x23783,x23784,x23781,x23785),f170(x23783,x23784,x23782,x23785))
% 157.76/157.54 [2379]~E(x23791,x23792)+E(f170(x23793,x23794,x23795,x23791),f170(x23793,x23794,x23795,x23792))
% 157.76/157.54 [2380]~E(x23801,x23802)+E(f913(x23801,x23803,x23804,x23805),f913(x23802,x23803,x23804,x23805))
% 157.76/157.54 [2381]~E(x23811,x23812)+E(f913(x23813,x23811,x23814,x23815),f913(x23813,x23812,x23814,x23815))
% 157.76/157.54 [2382]~E(x23821,x23822)+E(f913(x23823,x23824,x23821,x23825),f913(x23823,x23824,x23822,x23825))
% 157.76/157.54 [2383]~E(x23831,x23832)+E(f913(x23833,x23834,x23835,x23831),f913(x23833,x23834,x23835,x23832))
% 157.76/157.54 [2384]~E(x23841,x23842)+E(f705(x23841,x23843),f705(x23842,x23843))
% 157.76/157.54 [2385]~E(x23851,x23852)+E(f705(x23853,x23851),f705(x23853,x23852))
% 157.76/157.54 [2386]~E(x23861,x23862)+E(f743(x23861,x23863,x23864,x23865),f743(x23862,x23863,x23864,x23865))
% 157.76/157.54 [2387]~E(x23871,x23872)+E(f743(x23873,x23871,x23874,x23875),f743(x23873,x23872,x23874,x23875))
% 157.76/157.54 [2388]~E(x23881,x23882)+E(f743(x23883,x23884,x23881,x23885),f743(x23883,x23884,x23882,x23885))
% 157.76/157.54 [2389]~E(x23891,x23892)+E(f743(x23893,x23894,x23895,x23891),f743(x23893,x23894,x23895,x23892))
% 157.76/157.54 [2390]~E(x23901,x23902)+E(f662(x23901,x23903,x23904,x23905),f662(x23902,x23903,x23904,x23905))
% 157.76/157.54 [2391]~E(x23911,x23912)+E(f662(x23913,x23911,x23914,x23915),f662(x23913,x23912,x23914,x23915))
% 157.76/157.54 [2392]~E(x23921,x23922)+E(f662(x23923,x23924,x23921,x23925),f662(x23923,x23924,x23922,x23925))
% 157.76/157.54 [2393]~E(x23931,x23932)+E(f662(x23933,x23934,x23935,x23931),f662(x23933,x23934,x23935,x23932))
% 157.76/157.54 [2394]~E(x23941,x23942)+E(f710(x23941,x23943,x23944,x23945),f710(x23942,x23943,x23944,x23945))
% 157.76/157.54 [2395]~E(x23951,x23952)+E(f710(x23953,x23951,x23954,x23955),f710(x23953,x23952,x23954,x23955))
% 157.76/157.54 [2396]~E(x23961,x23962)+E(f710(x23963,x23964,x23961,x23965),f710(x23963,x23964,x23962,x23965))
% 157.76/157.54 [2397]~E(x23971,x23972)+E(f710(x23973,x23974,x23975,x23971),f710(x23973,x23974,x23975,x23972))
% 157.76/157.54 [2398]~E(x23981,x23982)+E(f153(x23981,x23983),f153(x23982,x23983))
% 157.76/157.54 [2399]~E(x23991,x23992)+E(f153(x23993,x23991),f153(x23993,x23992))
% 157.76/157.54 [2400]~E(x24001,x24002)+E(f204(x24001,x24003),f204(x24002,x24003))
% 157.76/157.54 [2401]~E(x24011,x24012)+E(f204(x24013,x24011),f204(x24013,x24012))
% 157.76/157.54 [2402]~E(x24021,x24022)+E(f277(x24021,x24023),f277(x24022,x24023))
% 157.76/157.54 [2403]~E(x24031,x24032)+E(f277(x24033,x24031),f277(x24033,x24032))
% 157.76/157.54 [2404]~E(x24041,x24042)+E(f443(x24041,x24043,x24044,x24045),f443(x24042,x24043,x24044,x24045))
% 157.76/157.54 [2405]~E(x24051,x24052)+E(f443(x24053,x24051,x24054,x24055),f443(x24053,x24052,x24054,x24055))
% 157.76/157.54 [2406]~E(x24061,x24062)+E(f443(x24063,x24064,x24061,x24065),f443(x24063,x24064,x24062,x24065))
% 157.76/157.54 [2407]~E(x24071,x24072)+E(f443(x24073,x24074,x24075,x24071),f443(x24073,x24074,x24075,x24072))
% 157.76/157.54 [2408]~E(x24081,x24082)+E(f714(x24081,x24083),f714(x24082,x24083))
% 157.76/157.54 [2409]~E(x24091,x24092)+E(f714(x24093,x24091),f714(x24093,x24092))
% 157.76/157.54 [2410]~E(x24101,x24102)+E(f385(x24101,x24103),f385(x24102,x24103))
% 157.76/157.54 [2411]~E(x24111,x24112)+E(f385(x24113,x24111),f385(x24113,x24112))
% 157.76/157.54 [2412]~E(x24121,x24122)+E(f654(x24121,x24123,x24124,x24125,x24126,x24127),f654(x24122,x24123,x24124,x24125,x24126,x24127))
% 157.76/157.54 [2413]~E(x24131,x24132)+E(f654(x24133,x24131,x24134,x24135,x24136,x24137),f654(x24133,x24132,x24134,x24135,x24136,x24137))
% 157.76/157.54 [2414]~E(x24141,x24142)+E(f654(x24143,x24144,x24141,x24145,x24146,x24147),f654(x24143,x24144,x24142,x24145,x24146,x24147))
% 157.76/157.54 [2415]~E(x24151,x24152)+E(f654(x24153,x24154,x24155,x24151,x24156,x24157),f654(x24153,x24154,x24155,x24152,x24156,x24157))
% 157.76/157.54 [2416]~E(x24161,x24162)+E(f654(x24163,x24164,x24165,x24166,x24161,x24167),f654(x24163,x24164,x24165,x24166,x24162,x24167))
% 157.76/157.54 [2417]~E(x24171,x24172)+E(f654(x24173,x24174,x24175,x24176,x24177,x24171),f654(x24173,x24174,x24175,x24176,x24177,x24172))
% 157.76/157.54 [2418]~E(x24181,x24182)+E(f633(x24181,x24183,x24184),f633(x24182,x24183,x24184))
% 157.76/157.54 [2419]~E(x24191,x24192)+E(f633(x24193,x24191,x24194),f633(x24193,x24192,x24194))
% 157.76/157.54 [2420]~E(x24201,x24202)+E(f633(x24203,x24204,x24201),f633(x24203,x24204,x24202))
% 157.76/157.54 [2421]~E(x24211,x24212)+E(f532(x24211,x24213,x24214,x24215),f532(x24212,x24213,x24214,x24215))
% 157.76/157.54 [2422]~E(x24221,x24222)+E(f532(x24223,x24221,x24224,x24225),f532(x24223,x24222,x24224,x24225))
% 157.76/157.54 [2423]~E(x24231,x24232)+E(f532(x24233,x24234,x24231,x24235),f532(x24233,x24234,x24232,x24235))
% 157.76/157.54 [2424]~E(x24241,x24242)+E(f532(x24243,x24244,x24245,x24241),f532(x24243,x24244,x24245,x24242))
% 157.76/157.54 [2425]~E(x24251,x24252)+E(f823(x24251,x24253,x24254,x24255,x24256,x24257),f823(x24252,x24253,x24254,x24255,x24256,x24257))
% 157.76/157.54 [2426]~E(x24261,x24262)+E(f823(x24263,x24261,x24264,x24265,x24266,x24267),f823(x24263,x24262,x24264,x24265,x24266,x24267))
% 157.76/157.54 [2427]~E(x24271,x24272)+E(f823(x24273,x24274,x24271,x24275,x24276,x24277),f823(x24273,x24274,x24272,x24275,x24276,x24277))
% 157.76/157.54 [2428]~E(x24281,x24282)+E(f823(x24283,x24284,x24285,x24281,x24286,x24287),f823(x24283,x24284,x24285,x24282,x24286,x24287))
% 157.76/157.54 [2429]~E(x24291,x24292)+E(f823(x24293,x24294,x24295,x24296,x24291,x24297),f823(x24293,x24294,x24295,x24296,x24292,x24297))
% 157.76/157.54 [2430]~E(x24301,x24302)+E(f823(x24303,x24304,x24305,x24306,x24307,x24301),f823(x24303,x24304,x24305,x24306,x24307,x24302))
% 157.76/157.54 [2431]~E(x24311,x24312)+E(f490(x24311,x24313,x24314),f490(x24312,x24313,x24314))
% 157.76/157.54 [2432]~E(x24321,x24322)+E(f490(x24323,x24321,x24324),f490(x24323,x24322,x24324))
% 157.76/157.54 [2433]~E(x24331,x24332)+E(f490(x24333,x24334,x24331),f490(x24333,x24334,x24332))
% 157.76/157.54 [2434]~E(x24341,x24342)+E(f234(x24341,x24343,x24344,x24345,x24346),f234(x24342,x24343,x24344,x24345,x24346))
% 157.76/157.54 [2435]~E(x24351,x24352)+E(f234(x24353,x24351,x24354,x24355,x24356),f234(x24353,x24352,x24354,x24355,x24356))
% 157.76/157.54 [2436]~E(x24361,x24362)+E(f234(x24363,x24364,x24361,x24365,x24366),f234(x24363,x24364,x24362,x24365,x24366))
% 157.76/157.54 [2437]~E(x24371,x24372)+E(f234(x24373,x24374,x24375,x24371,x24376),f234(x24373,x24374,x24375,x24372,x24376))
% 157.76/157.54 [2438]~E(x24381,x24382)+E(f234(x24383,x24384,x24385,x24386,x24381),f234(x24383,x24384,x24385,x24386,x24382))
% 157.76/157.54 [2439]~E(x24391,x24392)+E(f49(x24391),f49(x24392))
% 157.76/157.54 [2440]~E(x24401,x24402)+E(f819(x24401),f819(x24402))
% 157.76/157.54 [2441]~E(x24411,x24412)+E(f864(x24411,x24413,x24414),f864(x24412,x24413,x24414))
% 157.76/157.54 [2442]~E(x24421,x24422)+E(f864(x24423,x24421,x24424),f864(x24423,x24422,x24424))
% 157.76/157.54 [2443]~E(x24431,x24432)+E(f864(x24433,x24434,x24431),f864(x24433,x24434,x24432))
% 157.76/157.54 [2444]~E(x24441,x24442)+E(f708(x24441,x24443,x24444,x24445,x24446),f708(x24442,x24443,x24444,x24445,x24446))
% 157.76/157.54 [2445]~E(x24451,x24452)+E(f708(x24453,x24451,x24454,x24455,x24456),f708(x24453,x24452,x24454,x24455,x24456))
% 157.76/157.54 [2446]~E(x24461,x24462)+E(f708(x24463,x24464,x24461,x24465,x24466),f708(x24463,x24464,x24462,x24465,x24466))
% 157.76/157.54 [2447]~E(x24471,x24472)+E(f708(x24473,x24474,x24475,x24471,x24476),f708(x24473,x24474,x24475,x24472,x24476))
% 157.76/157.54 [2448]~E(x24481,x24482)+E(f708(x24483,x24484,x24485,x24486,x24481),f708(x24483,x24484,x24485,x24486,x24482))
% 157.76/157.54 [2449]~E(x24491,x24492)+E(f455(x24491,x24493,x24494,x24495),f455(x24492,x24493,x24494,x24495))
% 157.76/157.54 [2450]~E(x24501,x24502)+E(f455(x24503,x24501,x24504,x24505),f455(x24503,x24502,x24504,x24505))
% 157.76/157.54 [2451]~E(x24511,x24512)+E(f455(x24513,x24514,x24511,x24515),f455(x24513,x24514,x24512,x24515))
% 157.76/157.54 [2452]~E(x24521,x24522)+E(f455(x24523,x24524,x24525,x24521),f455(x24523,x24524,x24525,x24522))
% 157.76/157.54 [2453]~E(x24531,x24532)+E(f677(x24531,x24533,x24534,x24535),f677(x24532,x24533,x24534,x24535))
% 157.76/157.54 [2454]~E(x24541,x24542)+E(f677(x24543,x24541,x24544,x24545),f677(x24543,x24542,x24544,x24545))
% 157.76/157.54 [2455]~E(x24551,x24552)+E(f677(x24553,x24554,x24551,x24555),f677(x24553,x24554,x24552,x24555))
% 157.76/157.54 [2456]~E(x24561,x24562)+E(f677(x24563,x24564,x24565,x24561),f677(x24563,x24564,x24565,x24562))
% 157.76/157.54 [2457]~E(x24571,x24572)+E(f637(x24571,x24573,x24574,x24575,x24576,x24577),f637(x24572,x24573,x24574,x24575,x24576,x24577))
% 157.76/157.54 [2458]~E(x24581,x24582)+E(f637(x24583,x24581,x24584,x24585,x24586,x24587),f637(x24583,x24582,x24584,x24585,x24586,x24587))
% 157.76/157.54 [2459]~E(x24591,x24592)+E(f637(x24593,x24594,x24591,x24595,x24596,x24597),f637(x24593,x24594,x24592,x24595,x24596,x24597))
% 157.76/157.54 [2460]~E(x24601,x24602)+E(f637(x24603,x24604,x24605,x24601,x24606,x24607),f637(x24603,x24604,x24605,x24602,x24606,x24607))
% 157.76/157.54 [2461]~E(x24611,x24612)+E(f637(x24613,x24614,x24615,x24616,x24611,x24617),f637(x24613,x24614,x24615,x24616,x24612,x24617))
% 157.76/157.54 [2462]~E(x24621,x24622)+E(f637(x24623,x24624,x24625,x24626,x24627,x24621),f637(x24623,x24624,x24625,x24626,x24627,x24622))
% 157.76/157.54 [2463]~E(x24631,x24632)+E(f285(x24631,x24633,x24634,x24635),f285(x24632,x24633,x24634,x24635))
% 157.76/157.54 [2464]~E(x24641,x24642)+E(f285(x24643,x24641,x24644,x24645),f285(x24643,x24642,x24644,x24645))
% 157.76/157.54 [2465]~E(x24651,x24652)+E(f285(x24653,x24654,x24651,x24655),f285(x24653,x24654,x24652,x24655))
% 157.76/157.54 [2466]~E(x24661,x24662)+E(f285(x24663,x24664,x24665,x24661),f285(x24663,x24664,x24665,x24662))
% 157.76/157.54 [2467]~E(x24671,x24672)+E(f696(x24671,x24673,x24674,x24675),f696(x24672,x24673,x24674,x24675))
% 157.76/157.54 [2468]~E(x24681,x24682)+E(f696(x24683,x24681,x24684,x24685),f696(x24683,x24682,x24684,x24685))
% 157.76/157.54 [2469]~E(x24691,x24692)+E(f696(x24693,x24694,x24691,x24695),f696(x24693,x24694,x24692,x24695))
% 157.76/157.54 [2470]~E(x24701,x24702)+E(f696(x24703,x24704,x24705,x24701),f696(x24703,x24704,x24705,x24702))
% 157.76/157.54 [2471]~E(x24711,x24712)+E(f440(x24711,x24713,x24714),f440(x24712,x24713,x24714))
% 157.76/157.54 [2472]~E(x24721,x24722)+E(f440(x24723,x24721,x24724),f440(x24723,x24722,x24724))
% 157.76/157.54 [2473]~E(x24731,x24732)+E(f440(x24733,x24734,x24731),f440(x24733,x24734,x24732))
% 157.76/157.54 [2474]~E(x24741,x24742)+E(f775(x24741,x24743,x24744),f775(x24742,x24743,x24744))
% 157.76/157.54 [2475]~E(x24751,x24752)+E(f775(x24753,x24751,x24754),f775(x24753,x24752,x24754))
% 157.76/157.54 [2476]~E(x24761,x24762)+E(f775(x24763,x24764,x24761),f775(x24763,x24764,x24762))
% 157.76/157.54 [2477]~E(x24771,x24772)+E(f468(x24771,x24773,x24774),f468(x24772,x24773,x24774))
% 157.76/157.54 [2478]~E(x24781,x24782)+E(f468(x24783,x24781,x24784),f468(x24783,x24782,x24784))
% 157.76/157.54 [2479]~E(x24791,x24792)+E(f468(x24793,x24794,x24791),f468(x24793,x24794,x24792))
% 157.76/157.54 [2480]~E(x24801,x24802)+E(f859(x24801,x24803,x24804,x24805,x24806,x24807),f859(x24802,x24803,x24804,x24805,x24806,x24807))
% 157.76/157.54 [2481]~E(x24811,x24812)+E(f859(x24813,x24811,x24814,x24815,x24816,x24817),f859(x24813,x24812,x24814,x24815,x24816,x24817))
% 157.76/157.54 [2482]~E(x24821,x24822)+E(f859(x24823,x24824,x24821,x24825,x24826,x24827),f859(x24823,x24824,x24822,x24825,x24826,x24827))
% 157.76/157.54 [2483]~E(x24831,x24832)+E(f859(x24833,x24834,x24835,x24831,x24836,x24837),f859(x24833,x24834,x24835,x24832,x24836,x24837))
% 157.76/157.54 [2484]~E(x24841,x24842)+E(f859(x24843,x24844,x24845,x24846,x24841,x24847),f859(x24843,x24844,x24845,x24846,x24842,x24847))
% 157.76/157.54 [2485]~E(x24851,x24852)+E(f859(x24853,x24854,x24855,x24856,x24857,x24851),f859(x24853,x24854,x24855,x24856,x24857,x24852))
% 157.76/157.54 [2486]~E(x24861,x24862)+E(f658(x24861,x24863),f658(x24862,x24863))
% 157.76/157.54 [2487]~E(x24871,x24872)+E(f658(x24873,x24871),f658(x24873,x24872))
% 157.76/157.54 [2488]~E(x24881,x24882)+E(f910(x24881,x24883,x24884),f910(x24882,x24883,x24884))
% 157.76/157.54 [2489]~E(x24891,x24892)+E(f910(x24893,x24891,x24894),f910(x24893,x24892,x24894))
% 157.76/157.54 [2490]~E(x24901,x24902)+E(f910(x24903,x24904,x24901),f910(x24903,x24904,x24902))
% 157.76/157.54 [2491]~E(x24911,x24912)+E(f869(x24911,x24913),f869(x24912,x24913))
% 157.76/157.54 [2492]~E(x24921,x24922)+E(f869(x24923,x24921),f869(x24923,x24922))
% 157.76/157.54 [2493]~E(x24931,x24932)+E(f353(x24931,x24933,x24934,x24935,x24936),f353(x24932,x24933,x24934,x24935,x24936))
% 157.76/157.54 [2494]~E(x24941,x24942)+E(f353(x24943,x24941,x24944,x24945,x24946),f353(x24943,x24942,x24944,x24945,x24946))
% 157.76/157.54 [2495]~E(x24951,x24952)+E(f353(x24953,x24954,x24951,x24955,x24956),f353(x24953,x24954,x24952,x24955,x24956))
% 157.76/157.54 [2496]~E(x24961,x24962)+E(f353(x24963,x24964,x24965,x24961,x24966),f353(x24963,x24964,x24965,x24962,x24966))
% 157.76/157.54 [2497]~E(x24971,x24972)+E(f353(x24973,x24974,x24975,x24976,x24971),f353(x24973,x24974,x24975,x24976,x24972))
% 157.76/157.54 [2498]~E(x24981,x24982)+E(f897(x24981,x24983,x24984,x24985),f897(x24982,x24983,x24984,x24985))
% 157.76/157.54 [2499]~E(x24991,x24992)+E(f897(x24993,x24991,x24994,x24995),f897(x24993,x24992,x24994,x24995))
% 157.76/157.54 [2500]~E(x25001,x25002)+E(f897(x25003,x25004,x25001,x25005),f897(x25003,x25004,x25002,x25005))
% 157.76/157.54 [2501]~E(x25011,x25012)+E(f897(x25013,x25014,x25015,x25011),f897(x25013,x25014,x25015,x25012))
% 157.76/157.54 [2502]~E(x25021,x25022)+E(f747(x25021,x25023),f747(x25022,x25023))
% 157.76/157.54 [2503]~E(x25031,x25032)+E(f747(x25033,x25031),f747(x25033,x25032))
% 157.76/157.54 [2504]~E(x25041,x25042)+E(f603(x25041,x25043,x25044,x25045),f603(x25042,x25043,x25044,x25045))
% 157.76/157.54 [2505]~E(x25051,x25052)+E(f603(x25053,x25051,x25054,x25055),f603(x25053,x25052,x25054,x25055))
% 157.76/157.54 [2506]~E(x25061,x25062)+E(f603(x25063,x25064,x25061,x25065),f603(x25063,x25064,x25062,x25065))
% 157.76/157.54 [2507]~E(x25071,x25072)+E(f603(x25073,x25074,x25075,x25071),f603(x25073,x25074,x25075,x25072))
% 157.76/157.54 [2508]~E(x25081,x25082)+E(f751(x25081,x25083,x25084,x25085,x25086),f751(x25082,x25083,x25084,x25085,x25086))
% 157.76/157.54 [2509]~E(x25091,x25092)+E(f751(x25093,x25091,x25094,x25095,x25096),f751(x25093,x25092,x25094,x25095,x25096))
% 157.76/157.54 [2510]~E(x25101,x25102)+E(f751(x25103,x25104,x25101,x25105,x25106),f751(x25103,x25104,x25102,x25105,x25106))
% 157.76/157.54 [2511]~E(x25111,x25112)+E(f751(x25113,x25114,x25115,x25111,x25116),f751(x25113,x25114,x25115,x25112,x25116))
% 157.76/157.54 [2512]~E(x25121,x25122)+E(f751(x25123,x25124,x25125,x25126,x25121),f751(x25123,x25124,x25125,x25126,x25122))
% 157.76/157.54 [2513]~E(x25131,x25132)+E(f495(x25131,x25133,x25134),f495(x25132,x25133,x25134))
% 157.76/157.54 [2514]~E(x25141,x25142)+E(f495(x25143,x25141,x25144),f495(x25143,x25142,x25144))
% 157.76/157.54 [2515]~E(x25151,x25152)+E(f495(x25153,x25154,x25151),f495(x25153,x25154,x25152))
% 157.76/157.54 [2516]~E(x25161,x25162)+E(f380(x25161,x25163,x25164),f380(x25162,x25163,x25164))
% 157.76/157.54 [2517]~E(x25171,x25172)+E(f380(x25173,x25171,x25174),f380(x25173,x25172,x25174))
% 157.76/157.54 [2518]~E(x25181,x25182)+E(f380(x25183,x25184,x25181),f380(x25183,x25184,x25182))
% 157.76/157.54 [2519]~E(x25191,x25192)+E(f397(x25191,x25193,x25194,x25195,x25196),f397(x25192,x25193,x25194,x25195,x25196))
% 157.76/157.54 [2520]~E(x25201,x25202)+E(f397(x25203,x25201,x25204,x25205,x25206),f397(x25203,x25202,x25204,x25205,x25206))
% 157.76/157.54 [2521]~E(x25211,x25212)+E(f397(x25213,x25214,x25211,x25215,x25216),f397(x25213,x25214,x25212,x25215,x25216))
% 157.76/157.54 [2522]~E(x25221,x25222)+E(f397(x25223,x25224,x25225,x25221,x25226),f397(x25223,x25224,x25225,x25222,x25226))
% 157.76/157.54 [2523]~E(x25231,x25232)+E(f397(x25233,x25234,x25235,x25236,x25231),f397(x25233,x25234,x25235,x25236,x25232))
% 157.76/157.54 [2524]~E(x25241,x25242)+E(f348(x25241,x25243,x25244),f348(x25242,x25243,x25244))
% 157.76/157.54 [2525]~E(x25251,x25252)+E(f348(x25253,x25251,x25254),f348(x25253,x25252,x25254))
% 157.76/157.54 [2526]~E(x25261,x25262)+E(f348(x25263,x25264,x25261),f348(x25263,x25264,x25262))
% 157.76/157.54 [2527]~E(x25271,x25272)+E(f437(x25271,x25273,x25274,x25275),f437(x25272,x25273,x25274,x25275))
% 157.76/157.54 [2528]~E(x25281,x25282)+E(f437(x25283,x25281,x25284,x25285),f437(x25283,x25282,x25284,x25285))
% 157.76/157.54 [2529]~E(x25291,x25292)+E(f437(x25293,x25294,x25291,x25295),f437(x25293,x25294,x25292,x25295))
% 157.76/157.54 [2530]~E(x25301,x25302)+E(f437(x25303,x25304,x25305,x25301),f437(x25303,x25304,x25305,x25302))
% 157.76/157.54 [2531]~E(x25311,x25312)+E(f591(x25311,x25313),f591(x25312,x25313))
% 157.76/157.54 [2532]~E(x25321,x25322)+E(f591(x25323,x25321),f591(x25323,x25322))
% 157.76/157.54 [2533]~E(x25331,x25332)+E(f475(x25331,x25333,x25334,x25335,x25336),f475(x25332,x25333,x25334,x25335,x25336))
% 157.76/157.54 [2534]~E(x25341,x25342)+E(f475(x25343,x25341,x25344,x25345,x25346),f475(x25343,x25342,x25344,x25345,x25346))
% 157.76/157.54 [2535]~E(x25351,x25352)+E(f475(x25353,x25354,x25351,x25355,x25356),f475(x25353,x25354,x25352,x25355,x25356))
% 157.76/157.54 [2536]~E(x25361,x25362)+E(f475(x25363,x25364,x25365,x25361,x25366),f475(x25363,x25364,x25365,x25362,x25366))
% 157.76/157.54 [2537]~E(x25371,x25372)+E(f475(x25373,x25374,x25375,x25376,x25371),f475(x25373,x25374,x25375,x25376,x25372))
% 157.76/157.54 [2538]~E(x25381,x25382)+E(f803(x25381,x25383),f803(x25382,x25383))
% 157.76/157.54 [2539]~E(x25391,x25392)+E(f803(x25393,x25391),f803(x25393,x25392))
% 157.76/157.54 [2540]~E(x25401,x25402)+E(f812(x25401,x25403),f812(x25402,x25403))
% 157.76/157.54 [2541]~E(x25411,x25412)+E(f812(x25413,x25411),f812(x25413,x25412))
% 157.76/157.54 [2542]~E(x25421,x25422)+E(f638(x25421,x25423,x25424,x25425,x25426,x25427,x25428),f638(x25422,x25423,x25424,x25425,x25426,x25427,x25428))
% 157.76/157.54 [2543]~E(x25431,x25432)+E(f638(x25433,x25431,x25434,x25435,x25436,x25437,x25438),f638(x25433,x25432,x25434,x25435,x25436,x25437,x25438))
% 157.76/157.54 [2544]~E(x25441,x25442)+E(f638(x25443,x25444,x25441,x25445,x25446,x25447,x25448),f638(x25443,x25444,x25442,x25445,x25446,x25447,x25448))
% 157.76/157.54 [2545]~E(x25451,x25452)+E(f638(x25453,x25454,x25455,x25451,x25456,x25457,x25458),f638(x25453,x25454,x25455,x25452,x25456,x25457,x25458))
% 157.76/157.54 [2546]~E(x25461,x25462)+E(f638(x25463,x25464,x25465,x25466,x25461,x25467,x25468),f638(x25463,x25464,x25465,x25466,x25462,x25467,x25468))
% 157.76/157.54 [2547]~E(x25471,x25472)+E(f638(x25473,x25474,x25475,x25476,x25477,x25471,x25478),f638(x25473,x25474,x25475,x25476,x25477,x25472,x25478))
% 157.76/157.54 [2548]~E(x25481,x25482)+E(f638(x25483,x25484,x25485,x25486,x25487,x25488,x25481),f638(x25483,x25484,x25485,x25486,x25487,x25488,x25482))
% 157.76/157.54 [2549]~E(x25491,x25492)+E(f777(x25491,x25493,x25494),f777(x25492,x25493,x25494))
% 157.76/157.54 [2550]~E(x25501,x25502)+E(f777(x25503,x25501,x25504),f777(x25503,x25502,x25504))
% 157.76/157.54 [2551]~E(x25511,x25512)+E(f777(x25513,x25514,x25511),f777(x25513,x25514,x25512))
% 157.76/157.54 [2552]~E(x25521,x25522)+E(f899(x25521,x25523,x25524,x25525,x25526),f899(x25522,x25523,x25524,x25525,x25526))
% 157.76/157.54 [2553]~E(x25531,x25532)+E(f899(x25533,x25531,x25534,x25535,x25536),f899(x25533,x25532,x25534,x25535,x25536))
% 157.76/157.54 [2554]~E(x25541,x25542)+E(f899(x25543,x25544,x25541,x25545,x25546),f899(x25543,x25544,x25542,x25545,x25546))
% 157.76/157.54 [2555]~E(x25551,x25552)+E(f899(x25553,x25554,x25555,x25551,x25556),f899(x25553,x25554,x25555,x25552,x25556))
% 157.76/157.54 [2556]~E(x25561,x25562)+E(f899(x25563,x25564,x25565,x25566,x25561),f899(x25563,x25564,x25565,x25566,x25562))
% 157.76/157.54 [2557]~E(x25571,x25572)+E(f890(x25571,x25573,x25574,x25575),f890(x25572,x25573,x25574,x25575))
% 157.76/157.54 [2558]~E(x25581,x25582)+E(f890(x25583,x25581,x25584,x25585),f890(x25583,x25582,x25584,x25585))
% 157.76/157.54 [2559]~E(x25591,x25592)+E(f890(x25593,x25594,x25591,x25595),f890(x25593,x25594,x25592,x25595))
% 157.76/157.54 [2560]~E(x25601,x25602)+E(f890(x25603,x25604,x25605,x25601),f890(x25603,x25604,x25605,x25602))
% 157.76/157.54 [2561]~E(x25611,x25612)+E(f101(x25611,x25613,x25614,x25615),f101(x25612,x25613,x25614,x25615))
% 157.76/157.54 [2562]~E(x25621,x25622)+E(f101(x25623,x25621,x25624,x25625),f101(x25623,x25622,x25624,x25625))
% 157.76/157.54 [2563]~E(x25631,x25632)+E(f101(x25633,x25634,x25631,x25635),f101(x25633,x25634,x25632,x25635))
% 157.76/157.54 [2564]~E(x25641,x25642)+E(f101(x25643,x25644,x25645,x25641),f101(x25643,x25644,x25645,x25642))
% 157.76/157.54 [2565]~E(x25651,x25652)+E(f860(x25651,x25653,x25654,x25655,x25656,x25657),f860(x25652,x25653,x25654,x25655,x25656,x25657))
% 157.76/157.54 [2566]~E(x25661,x25662)+E(f860(x25663,x25661,x25664,x25665,x25666,x25667),f860(x25663,x25662,x25664,x25665,x25666,x25667))
% 157.76/157.54 [2567]~E(x25671,x25672)+E(f860(x25673,x25674,x25671,x25675,x25676,x25677),f860(x25673,x25674,x25672,x25675,x25676,x25677))
% 157.76/157.54 [2568]~E(x25681,x25682)+E(f860(x25683,x25684,x25685,x25681,x25686,x25687),f860(x25683,x25684,x25685,x25682,x25686,x25687))
% 157.76/157.54 [2569]~E(x25691,x25692)+E(f860(x25693,x25694,x25695,x25696,x25691,x25697),f860(x25693,x25694,x25695,x25696,x25692,x25697))
% 157.76/157.54 [2570]~E(x25701,x25702)+E(f860(x25703,x25704,x25705,x25706,x25707,x25701),f860(x25703,x25704,x25705,x25706,x25707,x25702))
% 157.76/157.54 [2571]~E(x25711,x25712)+E(f381(x25711,x25713,x25714),f381(x25712,x25713,x25714))
% 157.76/157.54 [2572]~E(x25721,x25722)+E(f381(x25723,x25721,x25724),f381(x25723,x25722,x25724))
% 157.76/157.54 [2573]~E(x25731,x25732)+E(f381(x25733,x25734,x25731),f381(x25733,x25734,x25732))
% 157.76/157.54 [2574]~E(x25741,x25742)+E(f238(x25741,x25743,x25744,x25745),f238(x25742,x25743,x25744,x25745))
% 157.76/157.54 [2575]~E(x25751,x25752)+E(f238(x25753,x25751,x25754,x25755),f238(x25753,x25752,x25754,x25755))
% 157.76/157.54 [2576]~E(x25761,x25762)+E(f238(x25763,x25764,x25761,x25765),f238(x25763,x25764,x25762,x25765))
% 157.76/157.54 [2577]~E(x25771,x25772)+E(f238(x25773,x25774,x25775,x25771),f238(x25773,x25774,x25775,x25772))
% 157.76/157.54 [2578]~E(x25781,x25782)+E(f240(x25781,x25783,x25784,x25785),f240(x25782,x25783,x25784,x25785))
% 157.76/157.54 [2579]~E(x25791,x25792)+E(f240(x25793,x25791,x25794,x25795),f240(x25793,x25792,x25794,x25795))
% 157.76/157.54 [2580]~E(x25801,x25802)+E(f240(x25803,x25804,x25801,x25805),f240(x25803,x25804,x25802,x25805))
% 157.76/157.54 [2581]~E(x25811,x25812)+E(f240(x25813,x25814,x25815,x25811),f240(x25813,x25814,x25815,x25812))
% 157.76/157.54 [2582]~E(x25821,x25822)+E(f635(x25821,x25823,x25824,x25825),f635(x25822,x25823,x25824,x25825))
% 157.76/157.54 [2583]~E(x25831,x25832)+E(f635(x25833,x25831,x25834,x25835),f635(x25833,x25832,x25834,x25835))
% 157.76/157.54 [2584]~E(x25841,x25842)+E(f635(x25843,x25844,x25841,x25845),f635(x25843,x25844,x25842,x25845))
% 157.76/157.54 [2585]~E(x25851,x25852)+E(f635(x25853,x25854,x25855,x25851),f635(x25853,x25854,x25855,x25852))
% 157.76/157.54 [2586]~E(x25861,x25862)+E(f407(x25861,x25863),f407(x25862,x25863))
% 157.76/157.54 [2587]~E(x25871,x25872)+E(f407(x25873,x25871),f407(x25873,x25872))
% 157.76/157.54 [2588]~E(x25881,x25882)+E(f576(x25881,x25883,x25884,x25885,x25886),f576(x25882,x25883,x25884,x25885,x25886))
% 157.76/157.54 [2589]~E(x25891,x25892)+E(f576(x25893,x25891,x25894,x25895,x25896),f576(x25893,x25892,x25894,x25895,x25896))
% 157.76/157.54 [2590]~E(x25901,x25902)+E(f576(x25903,x25904,x25901,x25905,x25906),f576(x25903,x25904,x25902,x25905,x25906))
% 157.76/157.54 [2591]~E(x25911,x25912)+E(f576(x25913,x25914,x25915,x25911,x25916),f576(x25913,x25914,x25915,x25912,x25916))
% 157.76/157.54 [2592]~E(x25921,x25922)+E(f576(x25923,x25924,x25925,x25926,x25921),f576(x25923,x25924,x25925,x25926,x25922))
% 157.76/157.54 [2593]~E(x25931,x25932)+E(f787(x25931,x25933,x25934,x25935),f787(x25932,x25933,x25934,x25935))
% 157.76/157.54 [2594]~E(x25941,x25942)+E(f787(x25943,x25941,x25944,x25945),f787(x25943,x25942,x25944,x25945))
% 157.76/157.54 [2595]~E(x25951,x25952)+E(f787(x25953,x25954,x25951,x25955),f787(x25953,x25954,x25952,x25955))
% 157.76/157.54 [2596]~E(x25961,x25962)+E(f787(x25963,x25964,x25965,x25961),f787(x25963,x25964,x25965,x25962))
% 157.76/157.54 [2597]~E(x25971,x25972)+E(f411(x25971,x25973),f411(x25972,x25973))
% 157.76/157.54 [2598]~E(x25981,x25982)+E(f411(x25983,x25981),f411(x25983,x25982))
% 157.76/157.54 [2599]~E(x25991,x25992)+E(f716(x25991,x25993),f716(x25992,x25993))
% 157.76/157.54 [2600]~E(x26001,x26002)+E(f716(x26003,x26001),f716(x26003,x26002))
% 157.76/157.54 [2601]~E(x26011,x26012)+E(f518(x26011,x26013,x26014),f518(x26012,x26013,x26014))
% 157.76/157.54 [2602]~E(x26021,x26022)+E(f518(x26023,x26021,x26024),f518(x26023,x26022,x26024))
% 157.76/157.54 [2603]~E(x26031,x26032)+E(f518(x26033,x26034,x26031),f518(x26033,x26034,x26032))
% 157.76/157.54 [2604]~E(x26041,x26042)+E(f534(x26041,x26043,x26044,x26045,x26046,x26047),f534(x26042,x26043,x26044,x26045,x26046,x26047))
% 157.76/157.54 [2605]~E(x26051,x26052)+E(f534(x26053,x26051,x26054,x26055,x26056,x26057),f534(x26053,x26052,x26054,x26055,x26056,x26057))
% 157.76/157.54 [2606]~E(x26061,x26062)+E(f534(x26063,x26064,x26061,x26065,x26066,x26067),f534(x26063,x26064,x26062,x26065,x26066,x26067))
% 157.76/157.54 [2607]~E(x26071,x26072)+E(f534(x26073,x26074,x26075,x26071,x26076,x26077),f534(x26073,x26074,x26075,x26072,x26076,x26077))
% 157.76/157.54 [2608]~E(x26081,x26082)+E(f534(x26083,x26084,x26085,x26086,x26081,x26087),f534(x26083,x26084,x26085,x26086,x26082,x26087))
% 157.76/157.54 [2609]~E(x26091,x26092)+E(f534(x26093,x26094,x26095,x26096,x26097,x26091),f534(x26093,x26094,x26095,x26096,x26097,x26092))
% 157.76/157.54 [2610]~E(x26101,x26102)+E(f386(x26101,x26103),f386(x26102,x26103))
% 157.76/157.54 [2611]~E(x26111,x26112)+E(f386(x26113,x26111),f386(x26113,x26112))
% 157.76/157.54 [2612]~E(x26121,x26122)+E(f282(x26121,x26123,x26124),f282(x26122,x26123,x26124))
% 157.76/157.54 [2613]~E(x26131,x26132)+E(f282(x26133,x26131,x26134),f282(x26133,x26132,x26134))
% 157.76/157.54 [2614]~E(x26141,x26142)+E(f282(x26143,x26144,x26141),f282(x26143,x26144,x26142))
% 157.76/157.54 [2615]~E(x26151,x26152)+E(f645(x26151,x26153,x26154),f645(x26152,x26153,x26154))
% 157.76/157.54 [2616]~E(x26161,x26162)+E(f645(x26163,x26161,x26164),f645(x26163,x26162,x26164))
% 157.76/157.54 [2617]~E(x26171,x26172)+E(f645(x26173,x26174,x26171),f645(x26173,x26174,x26172))
% 157.76/157.54 [2618]~E(x26181,x26182)+E(f863(x26181,x26183,x26184),f863(x26182,x26183,x26184))
% 157.76/157.54 [2619]~E(x26191,x26192)+E(f863(x26193,x26191,x26194),f863(x26193,x26192,x26194))
% 157.76/157.54 [2620]~E(x26201,x26202)+E(f863(x26203,x26204,x26201),f863(x26203,x26204,x26202))
% 157.76/157.54 [2621]~E(x26211,x26212)+E(f347(x26211,x26213),f347(x26212,x26213))
% 157.76/157.54 [2622]~E(x26221,x26222)+E(f347(x26223,x26221),f347(x26223,x26222))
% 157.76/157.54 [2623]~E(x26231,x26232)+E(f377(x26231,x26233),f377(x26232,x26233))
% 157.76/157.54 [2624]~E(x26241,x26242)+E(f377(x26243,x26241),f377(x26243,x26242))
% 157.76/157.54 [2625]~E(x26251,x26252)+E(f227(x26251,x26253),f227(x26252,x26253))
% 157.76/157.54 [2626]~E(x26261,x26262)+E(f227(x26263,x26261),f227(x26263,x26262))
% 157.76/157.54 [2627]~E(x26271,x26272)+E(f760(x26271,x26273,x26274),f760(x26272,x26273,x26274))
% 157.76/157.54 [2628]~E(x26281,x26282)+E(f760(x26283,x26281,x26284),f760(x26283,x26282,x26284))
% 157.76/157.54 [2629]~E(x26291,x26292)+E(f760(x26293,x26294,x26291),f760(x26293,x26294,x26292))
% 157.76/157.54 [2630]~E(x26301,x26302)+E(f784(x26301,x26303,x26304,x26305,x26306),f784(x26302,x26303,x26304,x26305,x26306))
% 157.76/157.54 [2631]~E(x26311,x26312)+E(f784(x26313,x26311,x26314,x26315,x26316),f784(x26313,x26312,x26314,x26315,x26316))
% 157.76/157.54 [2632]~E(x26321,x26322)+E(f784(x26323,x26324,x26321,x26325,x26326),f784(x26323,x26324,x26322,x26325,x26326))
% 157.76/157.54 [2633]~E(x26331,x26332)+E(f784(x26333,x26334,x26335,x26331,x26336),f784(x26333,x26334,x26335,x26332,x26336))
% 157.76/157.54 [2634]~E(x26341,x26342)+E(f784(x26343,x26344,x26345,x26346,x26341),f784(x26343,x26344,x26345,x26346,x26342))
% 157.76/157.54 [2635]~E(x26351,x26352)+E(f231(x26351,x26353,x26354),f231(x26352,x26353,x26354))
% 157.76/157.54 [2636]~E(x26361,x26362)+E(f231(x26363,x26361,x26364),f231(x26363,x26362,x26364))
% 157.76/157.54 [2637]~E(x26371,x26372)+E(f231(x26373,x26374,x26371),f231(x26373,x26374,x26372))
% 157.76/157.54 [2638]~E(x26381,x26382)+E(f541(x26381,x26383,x26384,x26385,x26386),f541(x26382,x26383,x26384,x26385,x26386))
% 157.76/157.54 [2639]~E(x26391,x26392)+E(f541(x26393,x26391,x26394,x26395,x26396),f541(x26393,x26392,x26394,x26395,x26396))
% 157.76/157.54 [2640]~E(x26401,x26402)+E(f541(x26403,x26404,x26401,x26405,x26406),f541(x26403,x26404,x26402,x26405,x26406))
% 157.76/157.54 [2641]~E(x26411,x26412)+E(f541(x26413,x26414,x26415,x26411,x26416),f541(x26413,x26414,x26415,x26412,x26416))
% 157.76/157.54 [2642]~E(x26421,x26422)+E(f541(x26423,x26424,x26425,x26426,x26421),f541(x26423,x26424,x26425,x26426,x26422))
% 157.76/157.54 [2643]~E(x26431,x26432)+E(f848(x26431,x26433,x26434,x26435,x26436,x26437,x26438),f848(x26432,x26433,x26434,x26435,x26436,x26437,x26438))
% 157.76/157.54 [2644]~E(x26441,x26442)+E(f848(x26443,x26441,x26444,x26445,x26446,x26447,x26448),f848(x26443,x26442,x26444,x26445,x26446,x26447,x26448))
% 157.76/157.54 [2645]~E(x26451,x26452)+E(f848(x26453,x26454,x26451,x26455,x26456,x26457,x26458),f848(x26453,x26454,x26452,x26455,x26456,x26457,x26458))
% 157.76/157.54 [2646]~E(x26461,x26462)+E(f848(x26463,x26464,x26465,x26461,x26466,x26467,x26468),f848(x26463,x26464,x26465,x26462,x26466,x26467,x26468))
% 157.76/157.54 [2647]~E(x26471,x26472)+E(f848(x26473,x26474,x26475,x26476,x26471,x26477,x26478),f848(x26473,x26474,x26475,x26476,x26472,x26477,x26478))
% 157.76/157.54 [2648]~E(x26481,x26482)+E(f848(x26483,x26484,x26485,x26486,x26487,x26481,x26488),f848(x26483,x26484,x26485,x26486,x26487,x26482,x26488))
% 157.76/157.54 [2649]~E(x26491,x26492)+E(f848(x26493,x26494,x26495,x26496,x26497,x26498,x26491),f848(x26493,x26494,x26495,x26496,x26497,x26498,x26492))
% 157.76/157.54 [2650]~E(x26501,x26502)+E(f883(x26501,x26503,x26504,x26505),f883(x26502,x26503,x26504,x26505))
% 157.76/157.54 [2651]~E(x26511,x26512)+E(f883(x26513,x26511,x26514,x26515),f883(x26513,x26512,x26514,x26515))
% 157.76/157.54 [2652]~E(x26521,x26522)+E(f883(x26523,x26524,x26521,x26525),f883(x26523,x26524,x26522,x26525))
% 157.76/157.54 [2653]~E(x26531,x26532)+E(f883(x26533,x26534,x26535,x26531),f883(x26533,x26534,x26535,x26532))
% 157.76/157.54 [2654]~E(x26541,x26542)+E(f629(x26541,x26543,x26544),f629(x26542,x26543,x26544))
% 157.76/157.54 [2655]~E(x26551,x26552)+E(f629(x26553,x26551,x26554),f629(x26553,x26552,x26554))
% 157.76/157.54 [2656]~E(x26561,x26562)+E(f629(x26563,x26564,x26561),f629(x26563,x26564,x26562))
% 157.76/157.54 [2657]~E(x26571,x26572)+E(f904(x26571,x26573,x26574),f904(x26572,x26573,x26574))
% 157.76/157.54 [2658]~E(x26581,x26582)+E(f904(x26583,x26581,x26584),f904(x26583,x26582,x26584))
% 157.76/157.54 [2659]~E(x26591,x26592)+E(f904(x26593,x26594,x26591),f904(x26593,x26594,x26592))
% 157.76/157.54 [2660]~E(x26601,x26602)+E(f363(x26601,x26603),f363(x26602,x26603))
% 157.76/157.54 [2661]~E(x26611,x26612)+E(f363(x26613,x26611),f363(x26613,x26612))
% 157.76/157.54 [2662]~E(x26621,x26622)+E(f790(x26621,x26623,x26624),f790(x26622,x26623,x26624))
% 157.76/157.54 [2663]~E(x26631,x26632)+E(f790(x26633,x26631,x26634),f790(x26633,x26632,x26634))
% 157.76/157.54 [2664]~E(x26641,x26642)+E(f790(x26643,x26644,x26641),f790(x26643,x26644,x26642))
% 157.76/157.54 [2665]~E(x26651,x26652)+E(f804(x26651),f804(x26652))
% 157.76/157.54 [2666]~E(x26661,x26662)+E(f843(x26661,x26663,x26664),f843(x26662,x26663,x26664))
% 157.76/157.54 [2667]~E(x26671,x26672)+E(f843(x26673,x26671,x26674),f843(x26673,x26672,x26674))
% 157.76/157.54 [2668]~E(x26681,x26682)+E(f843(x26683,x26684,x26681),f843(x26683,x26684,x26682))
% 157.76/157.54 [2669]~E(x26691,x26692)+E(f680(x26691,x26693,x26694),f680(x26692,x26693,x26694))
% 157.76/157.54 [2670]~E(x26701,x26702)+E(f680(x26703,x26701,x26704),f680(x26703,x26702,x26704))
% 157.76/157.54 [2671]~E(x26711,x26712)+E(f680(x26713,x26714,x26711),f680(x26713,x26714,x26712))
% 157.76/157.54 [2672]~E(x26721,x26722)+E(f853(x26721,x26723,x26724,x26725,x26726,x26727,x26728,x26729),f853(x26722,x26723,x26724,x26725,x26726,x26727,x26728,x26729))
% 157.76/157.54 [2673]~E(x26731,x26732)+E(f853(x26733,x26731,x26734,x26735,x26736,x26737,x26738,x26739),f853(x26733,x26732,x26734,x26735,x26736,x26737,x26738,x26739))
% 157.76/157.54 [2674]~E(x26741,x26742)+E(f853(x26743,x26744,x26741,x26745,x26746,x26747,x26748,x26749),f853(x26743,x26744,x26742,x26745,x26746,x26747,x26748,x26749))
% 157.76/157.54 [2675]~E(x26751,x26752)+E(f853(x26753,x26754,x26755,x26751,x26756,x26757,x26758,x26759),f853(x26753,x26754,x26755,x26752,x26756,x26757,x26758,x26759))
% 157.76/157.54 [2676]~E(x26761,x26762)+E(f853(x26763,x26764,x26765,x26766,x26761,x26767,x26768,x26769),f853(x26763,x26764,x26765,x26766,x26762,x26767,x26768,x26769))
% 157.76/157.54 [2677]~E(x26771,x26772)+E(f853(x26773,x26774,x26775,x26776,x26777,x26771,x26778,x26779),f853(x26773,x26774,x26775,x26776,x26777,x26772,x26778,x26779))
% 157.76/157.54 [2678]~E(x26781,x26782)+E(f853(x26783,x26784,x26785,x26786,x26787,x26788,x26781,x26789),f853(x26783,x26784,x26785,x26786,x26787,x26788,x26782,x26789))
% 157.76/157.54 [2679]~E(x26791,x26792)+E(f853(x26793,x26794,x26795,x26796,x26797,x26798,x26799,x26791),f853(x26793,x26794,x26795,x26796,x26797,x26798,x26799,x26792))
% 157.76/157.54 [2680]~E(x26801,x26802)+E(f651(x26801,x26803,x26804),f651(x26802,x26803,x26804))
% 157.76/157.54 [2681]~E(x26811,x26812)+E(f651(x26813,x26811,x26814),f651(x26813,x26812,x26814))
% 157.76/157.54 [2682]~E(x26821,x26822)+E(f651(x26823,x26824,x26821),f651(x26823,x26824,x26822))
% 157.76/157.54 [2683]~E(x26831,x26832)+E(f785(x26831,x26833,x26834,x26835,x26836),f785(x26832,x26833,x26834,x26835,x26836))
% 157.76/157.54 [2684]~E(x26841,x26842)+E(f785(x26843,x26841,x26844,x26845,x26846),f785(x26843,x26842,x26844,x26845,x26846))
% 157.76/157.54 [2685]~E(x26851,x26852)+E(f785(x26853,x26854,x26851,x26855,x26856),f785(x26853,x26854,x26852,x26855,x26856))
% 157.76/157.54 [2686]~E(x26861,x26862)+E(f785(x26863,x26864,x26865,x26861,x26866),f785(x26863,x26864,x26865,x26862,x26866))
% 157.76/157.54 [2687]~E(x26871,x26872)+E(f785(x26873,x26874,x26875,x26876,x26871),f785(x26873,x26874,x26875,x26876,x26872))
% 157.76/157.54 [2688]~E(x26881,x26882)+E(f217(x26881,x26883,x26884,x26885,x26886,x26887,x26888),f217(x26882,x26883,x26884,x26885,x26886,x26887,x26888))
% 157.76/157.54 [2689]~E(x26891,x26892)+E(f217(x26893,x26891,x26894,x26895,x26896,x26897,x26898),f217(x26893,x26892,x26894,x26895,x26896,x26897,x26898))
% 157.76/157.54 [2690]~E(x26901,x26902)+E(f217(x26903,x26904,x26901,x26905,x26906,x26907,x26908),f217(x26903,x26904,x26902,x26905,x26906,x26907,x26908))
% 157.76/157.54 [2691]~E(x26911,x26912)+E(f217(x26913,x26914,x26915,x26911,x26916,x26917,x26918),f217(x26913,x26914,x26915,x26912,x26916,x26917,x26918))
% 157.76/157.54 [2692]~E(x26921,x26922)+E(f217(x26923,x26924,x26925,x26926,x26921,x26927,x26928),f217(x26923,x26924,x26925,x26926,x26922,x26927,x26928))
% 157.76/157.54 [2693]~E(x26931,x26932)+E(f217(x26933,x26934,x26935,x26936,x26937,x26931,x26938),f217(x26933,x26934,x26935,x26936,x26937,x26932,x26938))
% 157.76/157.54 [2694]~E(x26941,x26942)+E(f217(x26943,x26944,x26945,x26946,x26947,x26948,x26941),f217(x26943,x26944,x26945,x26946,x26947,x26948,x26942))
% 157.76/157.54 [2695]~E(x26951,x26952)+E(f392(x26951,x26953,x26954),f392(x26952,x26953,x26954))
% 157.76/157.54 [2696]~E(x26961,x26962)+E(f392(x26963,x26961,x26964),f392(x26963,x26962,x26964))
% 157.76/157.54 [2697]~E(x26971,x26972)+E(f392(x26973,x26974,x26971),f392(x26973,x26974,x26972))
% 157.76/157.54 [2698]~E(x26981,x26982)+E(f405(x26981,x26983,x26984,x26985,x26986,x26987),f405(x26982,x26983,x26984,x26985,x26986,x26987))
% 157.76/157.54 [2699]~E(x26991,x26992)+E(f405(x26993,x26991,x26994,x26995,x26996,x26997),f405(x26993,x26992,x26994,x26995,x26996,x26997))
% 157.76/157.54 [2700]~E(x27001,x27002)+E(f405(x27003,x27004,x27001,x27005,x27006,x27007),f405(x27003,x27004,x27002,x27005,x27006,x27007))
% 157.76/157.54 [2701]~E(x27011,x27012)+E(f405(x27013,x27014,x27015,x27011,x27016,x27017),f405(x27013,x27014,x27015,x27012,x27016,x27017))
% 157.76/157.54 [2702]~E(x27021,x27022)+E(f405(x27023,x27024,x27025,x27026,x27021,x27027),f405(x27023,x27024,x27025,x27026,x27022,x27027))
% 157.76/157.54 [2703]~E(x27031,x27032)+E(f405(x27033,x27034,x27035,x27036,x27037,x27031),f405(x27033,x27034,x27035,x27036,x27037,x27032))
% 157.76/157.54 [2704]~E(x27041,x27042)+E(f589(x27041,x27043),f589(x27042,x27043))
% 157.76/157.54 [2705]~E(x27051,x27052)+E(f589(x27053,x27051),f589(x27053,x27052))
% 157.76/157.54 [2706]~E(x27061,x27062)+E(f830(x27061,x27063),f830(x27062,x27063))
% 157.76/157.54 [2707]~E(x27071,x27072)+E(f830(x27073,x27071),f830(x27073,x27072))
% 157.76/157.54 [2708]~E(x27081,x27082)+E(f488(x27081,x27083,x27084),f488(x27082,x27083,x27084))
% 157.76/157.54 [2709]~E(x27091,x27092)+E(f488(x27093,x27091,x27094),f488(x27093,x27092,x27094))
% 157.76/157.54 [2710]~E(x27101,x27102)+E(f488(x27103,x27104,x27101),f488(x27103,x27104,x27102))
% 157.76/157.54 [2711]~E(x27111,x27112)+E(f516(x27111,x27113),f516(x27112,x27113))
% 157.76/157.54 [2712]~E(x27121,x27122)+E(f516(x27123,x27121),f516(x27123,x27122))
% 157.76/157.54 [2713]~E(x27131,x27132)+E(f527(x27131,x27133),f527(x27132,x27133))
% 157.76/157.54 [2714]~E(x27141,x27142)+E(f527(x27143,x27141),f527(x27143,x27142))
% 157.76/157.54 [2715]~E(x27151,x27152)+E(f388(x27151,x27153,x27154),f388(x27152,x27153,x27154))
% 157.76/157.54 [2716]~E(x27161,x27162)+E(f388(x27163,x27161,x27164),f388(x27163,x27162,x27164))
% 157.76/157.54 [2717]~E(x27171,x27172)+E(f388(x27173,x27174,x27171),f388(x27173,x27174,x27172))
% 157.76/157.54 [2718]~E(x27181,x27182)+E(f884(x27181,x27183,x27184,x27185,x27186,x27187),f884(x27182,x27183,x27184,x27185,x27186,x27187))
% 157.76/157.54 [2719]~E(x27191,x27192)+E(f884(x27193,x27191,x27194,x27195,x27196,x27197),f884(x27193,x27192,x27194,x27195,x27196,x27197))
% 157.76/157.54 [2720]~E(x27201,x27202)+E(f884(x27203,x27204,x27201,x27205,x27206,x27207),f884(x27203,x27204,x27202,x27205,x27206,x27207))
% 157.76/157.54 [2721]~E(x27211,x27212)+E(f884(x27213,x27214,x27215,x27211,x27216,x27217),f884(x27213,x27214,x27215,x27212,x27216,x27217))
% 157.76/157.54 [2722]~E(x27221,x27222)+E(f884(x27223,x27224,x27225,x27226,x27221,x27227),f884(x27223,x27224,x27225,x27226,x27222,x27227))
% 157.76/157.54 [2723]~E(x27231,x27232)+E(f884(x27233,x27234,x27235,x27236,x27237,x27231),f884(x27233,x27234,x27235,x27236,x27237,x27232))
% 157.76/157.54 [2724]~E(x27241,x27242)+E(f704(x27241,x27243),f704(x27242,x27243))
% 157.76/157.54 [2725]~E(x27251,x27252)+E(f704(x27253,x27251),f704(x27253,x27252))
% 157.76/157.54 [2726]~E(x27261,x27262)+E(f903(x27261,x27263,x27264,x27265,x27266,x27267,x27268),f903(x27262,x27263,x27264,x27265,x27266,x27267,x27268))
% 157.76/157.54 [2727]~E(x27271,x27272)+E(f903(x27273,x27271,x27274,x27275,x27276,x27277,x27278),f903(x27273,x27272,x27274,x27275,x27276,x27277,x27278))
% 157.76/157.54 [2728]~E(x27281,x27282)+E(f903(x27283,x27284,x27281,x27285,x27286,x27287,x27288),f903(x27283,x27284,x27282,x27285,x27286,x27287,x27288))
% 157.76/157.54 [2729]~E(x27291,x27292)+E(f903(x27293,x27294,x27295,x27291,x27296,x27297,x27298),f903(x27293,x27294,x27295,x27292,x27296,x27297,x27298))
% 157.76/157.54 [2730]~E(x27301,x27302)+E(f903(x27303,x27304,x27305,x27306,x27301,x27307,x27308),f903(x27303,x27304,x27305,x27306,x27302,x27307,x27308))
% 157.76/157.54 [2731]~E(x27311,x27312)+E(f903(x27313,x27314,x27315,x27316,x27317,x27311,x27318),f903(x27313,x27314,x27315,x27316,x27317,x27312,x27318))
% 157.76/157.54 [2732]~E(x27321,x27322)+E(f903(x27323,x27324,x27325,x27326,x27327,x27328,x27321),f903(x27323,x27324,x27325,x27326,x27327,x27328,x27322))
% 157.76/157.54 [2733]~E(x27331,x27332)+E(f765(x27331,x27333,x27334),f765(x27332,x27333,x27334))
% 157.76/157.54 [2734]~E(x27341,x27342)+E(f765(x27343,x27341,x27344),f765(x27343,x27342,x27344))
% 157.76/157.54 [2735]~E(x27351,x27352)+E(f765(x27353,x27354,x27351),f765(x27353,x27354,x27352))
% 157.76/157.54 [2736]~E(x27361,x27362)+E(f881(x27361,x27363,x27364,x27365),f881(x27362,x27363,x27364,x27365))
% 157.76/157.54 [2737]~E(x27371,x27372)+E(f881(x27373,x27371,x27374,x27375),f881(x27373,x27372,x27374,x27375))
% 157.76/157.54 [2738]~E(x27381,x27382)+E(f881(x27383,x27384,x27381,x27385),f881(x27383,x27384,x27382,x27385))
% 157.76/157.54 [2739]~E(x27391,x27392)+E(f881(x27393,x27394,x27395,x27391),f881(x27393,x27394,x27395,x27392))
% 157.76/157.54 [2740]~E(x27401,x27402)+E(f369(x27401,x27403,x27404),f369(x27402,x27403,x27404))
% 157.76/157.54 [2741]~E(x27411,x27412)+E(f369(x27413,x27411,x27414),f369(x27413,x27412,x27414))
% 157.76/157.54 [2742]~E(x27421,x27422)+E(f369(x27423,x27424,x27421),f369(x27423,x27424,x27422))
% 157.76/157.54 [2743]~E(x27431,x27432)+E(f288(x27431,x27433,x27434,x27435),f288(x27432,x27433,x27434,x27435))
% 157.76/157.54 [2744]~E(x27441,x27442)+E(f288(x27443,x27441,x27444,x27445),f288(x27443,x27442,x27444,x27445))
% 157.76/157.54 [2745]~E(x27451,x27452)+E(f288(x27453,x27454,x27451,x27455),f288(x27453,x27454,x27452,x27455))
% 157.76/157.54 [2746]~E(x27461,x27462)+E(f288(x27463,x27464,x27465,x27461),f288(x27463,x27464,x27465,x27462))
% 157.76/157.54 [2747]~E(x27471,x27472)+E(f19(x27471,x27473,x27474,x27475),f19(x27472,x27473,x27474,x27475))
% 157.76/157.54 [2748]~E(x27481,x27482)+E(f19(x27483,x27481,x27484,x27485),f19(x27483,x27482,x27484,x27485))
% 157.76/157.54 [2749]~E(x27491,x27492)+E(f19(x27493,x27494,x27491,x27495),f19(x27493,x27494,x27492,x27495))
% 157.76/157.54 [2750]~E(x27501,x27502)+E(f19(x27503,x27504,x27505,x27501),f19(x27503,x27504,x27505,x27502))
% 157.76/157.54 [2751]~E(x27511,x27512)+E(f36(x27511,x27513,x27514,x27515),f36(x27512,x27513,x27514,x27515))
% 157.76/157.54 [2752]~E(x27521,x27522)+E(f36(x27523,x27521,x27524,x27525),f36(x27523,x27522,x27524,x27525))
% 157.76/157.54 [2753]~E(x27531,x27532)+E(f36(x27533,x27534,x27531,x27535),f36(x27533,x27534,x27532,x27535))
% 157.76/157.54 [2754]~E(x27541,x27542)+E(f36(x27543,x27544,x27545,x27541),f36(x27543,x27544,x27545,x27542))
% 157.76/157.54 [2755]~E(x27551,x27552)+E(f761(x27551,x27553,x27554,x27555),f761(x27552,x27553,x27554,x27555))
% 157.76/157.54 [2756]~E(x27561,x27562)+E(f761(x27563,x27561,x27564,x27565),f761(x27563,x27562,x27564,x27565))
% 157.76/157.54 [2757]~E(x27571,x27572)+E(f761(x27573,x27574,x27571,x27575),f761(x27573,x27574,x27572,x27575))
% 157.76/157.54 [2758]~E(x27581,x27582)+E(f761(x27583,x27584,x27585,x27581),f761(x27583,x27584,x27585,x27582))
% 157.76/157.54 [2759]~E(x27591,x27592)+E(f517(x27591,x27593,x27594),f517(x27592,x27593,x27594))
% 157.76/157.54 [2760]~E(x27601,x27602)+E(f517(x27603,x27601,x27604),f517(x27603,x27602,x27604))
% 157.76/157.54 [2761]~E(x27611,x27612)+E(f517(x27613,x27614,x27611),f517(x27613,x27614,x27612))
% 157.76/157.54 [2762]~E(x27621,x27622)+E(f284(x27621,x27623,x27624,x27625),f284(x27622,x27623,x27624,x27625))
% 157.76/157.54 [2763]~E(x27631,x27632)+E(f284(x27633,x27631,x27634,x27635),f284(x27633,x27632,x27634,x27635))
% 157.76/157.54 [2764]~E(x27641,x27642)+E(f284(x27643,x27644,x27641,x27645),f284(x27643,x27644,x27642,x27645))
% 157.76/157.54 [2765]~E(x27651,x27652)+E(f284(x27653,x27654,x27655,x27651),f284(x27653,x27654,x27655,x27652))
% 157.76/157.54 [2766]~E(x27661,x27662)+E(f525(x27661,x27663),f525(x27662,x27663))
% 157.76/157.54 [2767]~E(x27671,x27672)+E(f525(x27673,x27671),f525(x27673,x27672))
% 157.76/157.54 [2768]~E(x27681,x27682)+E(f856(x27681,x27683,x27684,x27685,x27686),f856(x27682,x27683,x27684,x27685,x27686))
% 157.76/157.54 [2769]~E(x27691,x27692)+E(f856(x27693,x27691,x27694,x27695,x27696),f856(x27693,x27692,x27694,x27695,x27696))
% 157.76/157.54 [2770]~E(x27701,x27702)+E(f856(x27703,x27704,x27701,x27705,x27706),f856(x27703,x27704,x27702,x27705,x27706))
% 157.76/157.54 [2771]~E(x27711,x27712)+E(f856(x27713,x27714,x27715,x27711,x27716),f856(x27713,x27714,x27715,x27712,x27716))
% 157.76/157.54 [2772]~E(x27721,x27722)+E(f856(x27723,x27724,x27725,x27726,x27721),f856(x27723,x27724,x27725,x27726,x27722))
% 157.76/157.54 [2773]~E(x27731,x27732)+E(f535(x27731,x27733,x27734,x27735,x27736,x27737),f535(x27732,x27733,x27734,x27735,x27736,x27737))
% 157.76/157.54 [2774]~E(x27741,x27742)+E(f535(x27743,x27741,x27744,x27745,x27746,x27747),f535(x27743,x27742,x27744,x27745,x27746,x27747))
% 157.76/157.54 [2775]~E(x27751,x27752)+E(f535(x27753,x27754,x27751,x27755,x27756,x27757),f535(x27753,x27754,x27752,x27755,x27756,x27757))
% 157.76/157.54 [2776]~E(x27761,x27762)+E(f535(x27763,x27764,x27765,x27761,x27766,x27767),f535(x27763,x27764,x27765,x27762,x27766,x27767))
% 157.76/157.54 [2777]~E(x27771,x27772)+E(f535(x27773,x27774,x27775,x27776,x27771,x27777),f535(x27773,x27774,x27775,x27776,x27772,x27777))
% 157.76/157.54 [2778]~E(x27781,x27782)+E(f535(x27783,x27784,x27785,x27786,x27787,x27781),f535(x27783,x27784,x27785,x27786,x27787,x27782))
% 157.76/157.54 [2779]~E(x27791,x27792)+E(f571(x27791,x27793,x27794),f571(x27792,x27793,x27794))
% 157.76/157.54 [2780]~E(x27801,x27802)+E(f571(x27803,x27801,x27804),f571(x27803,x27802,x27804))
% 157.76/157.54 [2781]~E(x27811,x27812)+E(f571(x27813,x27814,x27811),f571(x27813,x27814,x27812))
% 157.76/157.54 [2782]~E(x27821,x27822)+E(f832(x27821,x27823,x27824,x27825),f832(x27822,x27823,x27824,x27825))
% 157.76/157.54 [2783]~E(x27831,x27832)+E(f832(x27833,x27831,x27834,x27835),f832(x27833,x27832,x27834,x27835))
% 157.76/157.54 [2784]~E(x27841,x27842)+E(f832(x27843,x27844,x27841,x27845),f832(x27843,x27844,x27842,x27845))
% 157.76/157.54 [2785]~E(x27851,x27852)+E(f832(x27853,x27854,x27855,x27851),f832(x27853,x27854,x27855,x27852))
% 157.76/157.54 [2786]~E(x27861,x27862)+E(f766(x27861,x27863,x27864),f766(x27862,x27863,x27864))
% 157.76/157.54 [2787]~E(x27871,x27872)+E(f766(x27873,x27871,x27874),f766(x27873,x27872,x27874))
% 157.76/157.54 [2788]~E(x27881,x27882)+E(f766(x27883,x27884,x27881),f766(x27883,x27884,x27882))
% 157.76/157.54 [2789]~E(x27891,x27892)+E(f722(x27891,x27893,x27894),f722(x27892,x27893,x27894))
% 157.76/157.54 [2790]~E(x27901,x27902)+E(f722(x27903,x27901,x27904),f722(x27903,x27902,x27904))
% 157.76/157.54 [2791]~E(x27911,x27912)+E(f722(x27913,x27914,x27911),f722(x27913,x27914,x27912))
% 157.76/157.54 [2792]~E(x27921,x27922)+E(f529(x27921,x27923,x27924,x27925),f529(x27922,x27923,x27924,x27925))
% 157.76/157.54 [2793]~E(x27931,x27932)+E(f529(x27933,x27931,x27934,x27935),f529(x27933,x27932,x27934,x27935))
% 157.76/157.54 [2794]~E(x27941,x27942)+E(f529(x27943,x27944,x27941,x27945),f529(x27943,x27944,x27942,x27945))
% 157.76/157.54 [2795]~E(x27951,x27952)+E(f529(x27953,x27954,x27955,x27951),f529(x27953,x27954,x27955,x27952))
% 157.76/157.54 [2796]~E(x27961,x27962)+E(f582(x27961,x27963,x27964,x27965,x27966),f582(x27962,x27963,x27964,x27965,x27966))
% 157.76/157.54 [2797]~E(x27971,x27972)+E(f582(x27973,x27971,x27974,x27975,x27976),f582(x27973,x27972,x27974,x27975,x27976))
% 157.76/157.54 [2798]~E(x27981,x27982)+E(f582(x27983,x27984,x27981,x27985,x27986),f582(x27983,x27984,x27982,x27985,x27986))
% 157.76/157.54 [2799]~E(x27991,x27992)+E(f582(x27993,x27994,x27995,x27991,x27996),f582(x27993,x27994,x27995,x27992,x27996))
% 157.76/157.54 [2800]~E(x28001,x28002)+E(f582(x28003,x28004,x28005,x28006,x28001),f582(x28003,x28004,x28005,x28006,x28002))
% 157.76/157.54 [2801]~E(x28011,x28012)+E(f776(x28011,x28013,x28014),f776(x28012,x28013,x28014))
% 157.76/157.54 [2802]~E(x28021,x28022)+E(f776(x28023,x28021,x28024),f776(x28023,x28022,x28024))
% 157.76/157.54 [2803]~E(x28031,x28032)+E(f776(x28033,x28034,x28031),f776(x28033,x28034,x28032))
% 157.76/157.54 [2804]~E(x28041,x28042)+E(f820(x28041,x28043),f820(x28042,x28043))
% 157.76/157.54 [2805]~E(x28051,x28052)+E(f820(x28053,x28051),f820(x28053,x28052))
% 157.76/157.54 [2806]~E(x28061,x28062)+E(f759(x28061),f759(x28062))
% 157.76/157.54 [2807]~E(x28071,x28072)+E(f831(x28071,x28073),f831(x28072,x28073))
% 157.76/157.54 [2808]~E(x28081,x28082)+E(f831(x28083,x28081),f831(x28083,x28082))
% 157.76/157.54 [2809]~E(x28091,x28092)+E(f902(x28091,x28093),f902(x28092,x28093))
% 157.76/157.54 [2810]~E(x28101,x28102)+E(f902(x28103,x28101),f902(x28103,x28102))
% 157.76/157.54 [2811]~E(x28111,x28112)+E(f21(x28111,x28113),f21(x28112,x28113))
% 157.76/157.54 [2812]~E(x28121,x28122)+E(f21(x28123,x28121),f21(x28123,x28122))
% 157.76/157.54 [2813]~E(x28131,x28132)+E(f537(x28131,x28133),f537(x28132,x28133))
% 157.76/157.54 [2814]~E(x28141,x28142)+E(f537(x28143,x28141),f537(x28143,x28142))
% 157.76/157.54 [2815]~E(x28151,x28152)+E(f399(x28151),f399(x28152))
% 157.76/157.54 [2816]~E(x28161,x28162)+E(f235(x28161,x28163,x28164,x28165,x28166),f235(x28162,x28163,x28164,x28165,x28166))
% 157.76/157.54 [2817]~E(x28171,x28172)+E(f235(x28173,x28171,x28174,x28175,x28176),f235(x28173,x28172,x28174,x28175,x28176))
% 157.76/157.54 [2818]~E(x28181,x28182)+E(f235(x28183,x28184,x28181,x28185,x28186),f235(x28183,x28184,x28182,x28185,x28186))
% 157.76/157.54 [2819]~E(x28191,x28192)+E(f235(x28193,x28194,x28195,x28191,x28196),f235(x28193,x28194,x28195,x28192,x28196))
% 157.76/157.54 [2820]~E(x28201,x28202)+E(f235(x28203,x28204,x28205,x28206,x28201),f235(x28203,x28204,x28205,x28206,x28202))
% 157.76/157.54 [2821]~E(x28211,x28212)+E(f584(x28211,x28213,x28214),f584(x28212,x28213,x28214))
% 157.76/157.54 [2822]~E(x28221,x28222)+E(f584(x28223,x28221,x28224),f584(x28223,x28222,x28224))
% 157.76/157.54 [2823]~E(x28231,x28232)+E(f584(x28233,x28234,x28231),f584(x28233,x28234,x28232))
% 157.76/157.54 [2824]~E(x28241,x28242)+E(f269(x28241,x28243,x28244,x28245,x28246),f269(x28242,x28243,x28244,x28245,x28246))
% 157.76/157.54 [2825]~E(x28251,x28252)+E(f269(x28253,x28251,x28254,x28255,x28256),f269(x28253,x28252,x28254,x28255,x28256))
% 157.76/157.54 [2826]~E(x28261,x28262)+E(f269(x28263,x28264,x28261,x28265,x28266),f269(x28263,x28264,x28262,x28265,x28266))
% 157.76/157.54 [2827]~E(x28271,x28272)+E(f269(x28273,x28274,x28275,x28271,x28276),f269(x28273,x28274,x28275,x28272,x28276))
% 157.76/157.54 [2828]~E(x28281,x28282)+E(f269(x28283,x28284,x28285,x28286,x28281),f269(x28283,x28284,x28285,x28286,x28282))
% 157.76/157.54 [2829]~E(x28291,x28292)+E(f540(x28291,x28293,x28294,x28295),f540(x28292,x28293,x28294,x28295))
% 157.76/157.54 [2830]~E(x28301,x28302)+E(f540(x28303,x28301,x28304,x28305),f540(x28303,x28302,x28304,x28305))
% 157.76/157.54 [2831]~E(x28311,x28312)+E(f540(x28313,x28314,x28311,x28315),f540(x28313,x28314,x28312,x28315))
% 157.76/157.54 [2832]~E(x28321,x28322)+E(f540(x28323,x28324,x28325,x28321),f540(x28323,x28324,x28325,x28322))
% 157.76/157.54 [2833]~E(x28331,x28332)+E(f237(x28331,x28333,x28334),f237(x28332,x28333,x28334))
% 157.76/157.54 [2834]~E(x28341,x28342)+E(f237(x28343,x28341,x28344),f237(x28343,x28342,x28344))
% 157.76/157.54 [2835]~E(x28351,x28352)+E(f237(x28353,x28354,x28351),f237(x28353,x28354,x28352))
% 157.76/157.54 [2836]~E(x28361,x28362)+E(f287(x28361,x28363,x28364,x28365),f287(x28362,x28363,x28364,x28365))
% 157.76/157.54 [2837]~E(x28371,x28372)+E(f287(x28373,x28371,x28374,x28375),f287(x28373,x28372,x28374,x28375))
% 157.76/157.54 [2838]~E(x28381,x28382)+E(f287(x28383,x28384,x28381,x28385),f287(x28383,x28384,x28382,x28385))
% 157.76/157.54 [2839]~E(x28391,x28392)+E(f287(x28393,x28394,x28395,x28391),f287(x28393,x28394,x28395,x28392))
% 157.76/157.54 [2840]~E(x28401,x28402)+E(f763(x28401,x28403,x28404),f763(x28402,x28403,x28404))
% 157.76/157.54 [2841]~E(x28411,x28412)+E(f763(x28413,x28411,x28414),f763(x28413,x28412,x28414))
% 157.76/157.54 [2842]~E(x28421,x28422)+E(f763(x28423,x28424,x28421),f763(x28423,x28424,x28422))
% 157.76/157.54 [2843]~E(x28431,x28432)+E(f898(x28431,x28433,x28434,x28435,x28436),f898(x28432,x28433,x28434,x28435,x28436))
% 157.76/157.54 [2844]~E(x28441,x28442)+E(f898(x28443,x28441,x28444,x28445,x28446),f898(x28443,x28442,x28444,x28445,x28446))
% 157.76/157.54 [2845]~E(x28451,x28452)+E(f898(x28453,x28454,x28451,x28455,x28456),f898(x28453,x28454,x28452,x28455,x28456))
% 157.76/157.54 [2846]~E(x28461,x28462)+E(f898(x28463,x28464,x28465,x28461,x28466),f898(x28463,x28464,x28465,x28462,x28466))
% 157.76/157.54 [2847]~E(x28471,x28472)+E(f898(x28473,x28474,x28475,x28476,x28471),f898(x28473,x28474,x28475,x28476,x28472))
% 157.76/157.54 [2848]~E(x28481,x28482)+E(f538(x28481,x28483,x28484,x28485),f538(x28482,x28483,x28484,x28485))
% 157.76/157.54 [2849]~E(x28491,x28492)+E(f538(x28493,x28491,x28494,x28495),f538(x28493,x28492,x28494,x28495))
% 157.76/157.54 [2850]~E(x28501,x28502)+E(f538(x28503,x28504,x28501,x28505),f538(x28503,x28504,x28502,x28505))
% 157.76/157.54 [2851]~E(x28511,x28512)+E(f538(x28513,x28514,x28515,x28511),f538(x28513,x28514,x28515,x28512))
% 157.76/157.54 [2852]~E(x28521,x28522)+E(f341(x28521),f341(x28522))
% 157.76/157.54 [2853]~E(x28531,x28532)+E(f919(x28531,x28533,x28534,x28535,x28536),f919(x28532,x28533,x28534,x28535,x28536))
% 157.76/157.54 [2854]~E(x28541,x28542)+E(f919(x28543,x28541,x28544,x28545,x28546),f919(x28543,x28542,x28544,x28545,x28546))
% 157.76/157.54 [2855]~E(x28551,x28552)+E(f919(x28553,x28554,x28551,x28555,x28556),f919(x28553,x28554,x28552,x28555,x28556))
% 157.76/157.54 [2856]~E(x28561,x28562)+E(f919(x28563,x28564,x28565,x28561,x28566),f919(x28563,x28564,x28565,x28562,x28566))
% 157.76/157.54 [2857]~E(x28571,x28572)+E(f919(x28573,x28574,x28575,x28576,x28571),f919(x28573,x28574,x28575,x28576,x28572))
% 157.76/157.54 [2858]~E(x28581,x28582)+E(f666(x28581,x28583,x28584),f666(x28582,x28583,x28584))
% 157.76/157.54 [2859]~E(x28591,x28592)+E(f666(x28593,x28591,x28594),f666(x28593,x28592,x28594))
% 157.76/157.54 [2860]~E(x28601,x28602)+E(f666(x28603,x28604,x28601),f666(x28603,x28604,x28602))
% 157.76/157.54 [2861]~E(x28611,x28612)+E(f822(x28611,x28613),f822(x28612,x28613))
% 157.76/157.54 [2862]~E(x28621,x28622)+E(f822(x28623,x28621),f822(x28623,x28622))
% 157.76/157.54 [2863]~E(x28631,x28632)+E(f130(x28631),f130(x28632))
% 157.76/157.54 [2864]~E(x28641,x28642)+E(f861(x28641,x28643,x28644),f861(x28642,x28643,x28644))
% 157.76/157.54 [2865]~E(x28651,x28652)+E(f861(x28653,x28651,x28654),f861(x28653,x28652,x28654))
% 157.76/157.54 [2866]~E(x28661,x28662)+E(f861(x28663,x28664,x28661),f861(x28663,x28664,x28662))
% 157.76/157.54 [2867]~E(x28671,x28672)+E(f220(x28671,x28673,x28674,x28675,x28676,x28677,x28678),f220(x28672,x28673,x28674,x28675,x28676,x28677,x28678))
% 157.76/157.54 [2868]~E(x28681,x28682)+E(f220(x28683,x28681,x28684,x28685,x28686,x28687,x28688),f220(x28683,x28682,x28684,x28685,x28686,x28687,x28688))
% 157.76/157.54 [2869]~E(x28691,x28692)+E(f220(x28693,x28694,x28691,x28695,x28696,x28697,x28698),f220(x28693,x28694,x28692,x28695,x28696,x28697,x28698))
% 157.76/157.54 [2870]~E(x28701,x28702)+E(f220(x28703,x28704,x28705,x28701,x28706,x28707,x28708),f220(x28703,x28704,x28705,x28702,x28706,x28707,x28708))
% 157.76/157.54 [2871]~E(x28711,x28712)+E(f220(x28713,x28714,x28715,x28716,x28711,x28717,x28718),f220(x28713,x28714,x28715,x28716,x28712,x28717,x28718))
% 157.76/157.54 [2872]~E(x28721,x28722)+E(f220(x28723,x28724,x28725,x28726,x28727,x28721,x28728),f220(x28723,x28724,x28725,x28726,x28727,x28722,x28728))
% 157.76/157.54 [2873]~E(x28731,x28732)+E(f220(x28733,x28734,x28735,x28736,x28737,x28738,x28731),f220(x28733,x28734,x28735,x28736,x28737,x28738,x28732))
% 157.76/157.54 [2874]~P1(x28741)+P1(x28742)+~E(x28741,x28742)
% 157.76/157.54 [2875]~P107(x28751)+P107(x28752)+~E(x28751,x28752)
% 157.76/157.54 [2876]P12(x28762,x28763,x28764,x28765,x28766,x28767)+~E(x28761,x28762)+~P12(x28761,x28763,x28764,x28765,x28766,x28767)
% 157.76/157.54 [2877]P12(x28773,x28772,x28774,x28775,x28776,x28777)+~E(x28771,x28772)+~P12(x28773,x28771,x28774,x28775,x28776,x28777)
% 157.76/157.54 [2878]P12(x28783,x28784,x28782,x28785,x28786,x28787)+~E(x28781,x28782)+~P12(x28783,x28784,x28781,x28785,x28786,x28787)
% 157.76/157.54 [2879]P12(x28793,x28794,x28795,x28792,x28796,x28797)+~E(x28791,x28792)+~P12(x28793,x28794,x28795,x28791,x28796,x28797)
% 157.76/157.54 [2880]P12(x28803,x28804,x28805,x28806,x28802,x28807)+~E(x28801,x28802)+~P12(x28803,x28804,x28805,x28806,x28801,x28807)
% 157.76/157.54 [2881]P12(x28813,x28814,x28815,x28816,x28817,x28812)+~E(x28811,x28812)+~P12(x28813,x28814,x28815,x28816,x28817,x28811)
% 157.76/157.54 [2882]~P108(x28821)+P108(x28822)+~E(x28821,x28822)
% 157.76/157.54 [2883]~P87(x28831)+P87(x28832)+~E(x28831,x28832)
% 157.76/157.54 [2884]~P110(x28841)+P110(x28842)+~E(x28841,x28842)
% 157.76/157.54 [2885]P57(x28852,x28853,x28854)+~E(x28851,x28852)+~P57(x28851,x28853,x28854)
% 157.76/157.54 [2886]P57(x28863,x28862,x28864)+~E(x28861,x28862)+~P57(x28863,x28861,x28864)
% 157.76/157.54 [2887]P57(x28873,x28874,x28872)+~E(x28871,x28872)+~P57(x28873,x28874,x28871)
% 157.76/157.54 [2888]~P109(x28881)+P109(x28882)+~E(x28881,x28882)
% 157.76/157.54 [2889]P24(x28892,x28893,x28894)+~E(x28891,x28892)+~P24(x28891,x28893,x28894)
% 157.76/157.54 [2890]P24(x28903,x28902,x28904)+~E(x28901,x28902)+~P24(x28903,x28901,x28904)
% 157.76/157.54 [2891]P24(x28913,x28914,x28912)+~E(x28911,x28912)+~P24(x28913,x28914,x28911)
% 157.76/157.54 [2892]P150(x28922,x28923,x28924)+~E(x28921,x28922)+~P150(x28921,x28923,x28924)
% 157.76/157.54 [2893]P150(x28933,x28932,x28934)+~E(x28931,x28932)+~P150(x28933,x28931,x28934)
% 157.76/157.54 [2894]P150(x28943,x28944,x28942)+~E(x28941,x28942)+~P150(x28943,x28944,x28941)
% 157.76/157.54 [2895]~P62(x28951)+P62(x28952)+~E(x28951,x28952)
% 157.76/157.54 [2896]P37(x28962,x28963)+~E(x28961,x28962)+~P37(x28961,x28963)
% 157.76/157.54 [2897]P37(x28973,x28972)+~E(x28971,x28972)+~P37(x28973,x28971)
% 157.76/157.54 [2898]~P128(x28981)+P128(x28982)+~E(x28981,x28982)
% 157.76/157.54 [2899]P18(x28992,x28993,x28994)+~E(x28991,x28992)+~P18(x28991,x28993,x28994)
% 157.76/157.54 [2900]P18(x29003,x29002,x29004)+~E(x29001,x29002)+~P18(x29003,x29001,x29004)
% 157.76/157.54 [2901]P18(x29013,x29014,x29012)+~E(x29011,x29012)+~P18(x29013,x29014,x29011)
% 157.76/157.54 [2902]~P111(x29021)+P111(x29022)+~E(x29021,x29022)
% 157.76/157.54 [2903]~P67(x29031)+P67(x29032)+~E(x29031,x29032)
% 157.76/157.54 [2904]~P83(x29041)+P83(x29042)+~E(x29041,x29042)
% 157.76/157.54 [2905]P13(x29052,x29053)+~E(x29051,x29052)+~P13(x29051,x29053)
% 157.76/157.54 [2906]P13(x29063,x29062)+~E(x29061,x29062)+~P13(x29063,x29061)
% 157.76/157.54 [2907]~P2(x29071)+P2(x29072)+~E(x29071,x29072)
% 157.76/157.54 [2908]~P71(x29081)+P71(x29082)+~E(x29081,x29082)
% 157.76/157.54 [2909]~P6(x29091)+P6(x29092)+~E(x29091,x29092)
% 157.76/157.54 [2910]P39(x29102,x29103)+~E(x29101,x29102)+~P39(x29101,x29103)
% 157.76/157.54 [2911]P39(x29113,x29112)+~E(x29111,x29112)+~P39(x29113,x29111)
% 157.76/157.54 [2912]~P79(x29121)+P79(x29122)+~E(x29121,x29122)
% 157.76/157.54 [2913]~P3(x29131)+P3(x29132)+~E(x29131,x29132)
% 157.76/157.54 [2914]~P69(x29141)+P69(x29142)+~E(x29141,x29142)
% 157.76/157.54 [2915]~P89(x29151)+P89(x29152)+~E(x29151,x29152)
% 157.76/157.54 [2916]~P120(x29161)+P120(x29162)+~E(x29161,x29162)
% 157.76/157.54 [2917]~P112(x29171)+P112(x29172)+~E(x29171,x29172)
% 157.76/157.54 [2918]P25(x29182,x29183,x29184,x29185)+~E(x29181,x29182)+~P25(x29181,x29183,x29184,x29185)
% 157.76/157.54 [2919]P25(x29193,x29192,x29194,x29195)+~E(x29191,x29192)+~P25(x29193,x29191,x29194,x29195)
% 157.76/157.54 [2920]P25(x29203,x29204,x29202,x29205)+~E(x29201,x29202)+~P25(x29203,x29204,x29201,x29205)
% 157.76/157.54 [2921]P25(x29213,x29214,x29215,x29212)+~E(x29211,x29212)+~P25(x29213,x29214,x29215,x29211)
% 157.76/157.54 [2922]P16(x29222,x29223,x29224)+~E(x29221,x29222)+~P16(x29221,x29223,x29224)
% 157.76/157.54 [2923]P16(x29233,x29232,x29234)+~E(x29231,x29232)+~P16(x29233,x29231,x29234)
% 157.76/157.54 [2924]P16(x29243,x29244,x29242)+~E(x29241,x29242)+~P16(x29243,x29244,x29241)
% 157.76/157.54 [2925]~P65(x29251)+P65(x29252)+~E(x29251,x29252)
% 157.76/157.54 [2926]~P102(x29261)+P102(x29262)+~E(x29261,x29262)
% 157.76/157.54 [2927]P55(x29272,x29273,x29274)+~E(x29271,x29272)+~P55(x29271,x29273,x29274)
% 157.76/157.54 [2928]P55(x29283,x29282,x29284)+~E(x29281,x29282)+~P55(x29283,x29281,x29284)
% 157.76/157.54 [2929]P55(x29293,x29294,x29292)+~E(x29291,x29292)+~P55(x29293,x29294,x29291)
% 157.76/157.54 [2930]P26(x29302,x29303,x29304,x29305,x29306)+~E(x29301,x29302)+~P26(x29301,x29303,x29304,x29305,x29306)
% 157.76/157.54 [2931]P26(x29313,x29312,x29314,x29315,x29316)+~E(x29311,x29312)+~P26(x29313,x29311,x29314,x29315,x29316)
% 157.76/157.54 [2932]P26(x29323,x29324,x29322,x29325,x29326)+~E(x29321,x29322)+~P26(x29323,x29324,x29321,x29325,x29326)
% 157.76/157.54 [2933]P26(x29333,x29334,x29335,x29332,x29336)+~E(x29331,x29332)+~P26(x29333,x29334,x29335,x29331,x29336)
% 157.76/157.54 [2934]P26(x29343,x29344,x29345,x29346,x29342)+~E(x29341,x29342)+~P26(x29343,x29344,x29345,x29346,x29341)
% 157.76/157.54 [2935]~P84(x29351)+P84(x29352)+~E(x29351,x29352)
% 157.76/157.54 [2936]~P4(x29361)+P4(x29362)+~E(x29361,x29362)
% 157.76/157.54 [2937]~P96(x29371)+P96(x29372)+~E(x29371,x29372)
% 157.76/157.54 [2938]~P85(x29381)+P85(x29382)+~E(x29381,x29382)
% 157.76/157.54 [2939]~P5(x29391)+P5(x29392)+~E(x29391,x29392)
% 157.76/157.54 [2940]~P80(x29401)+P80(x29402)+~E(x29401,x29402)
% 157.76/157.54 [2941]P7(x29412,x29413)+~E(x29411,x29412)+~P7(x29411,x29413)
% 157.76/157.54 [2942]P7(x29423,x29422)+~E(x29421,x29422)+~P7(x29423,x29421)
% 157.76/157.54 [2943]~P40(x29431)+P40(x29432)+~E(x29431,x29432)
% 157.76/157.54 [2944]~P68(x29441)+P68(x29442)+~E(x29441,x29442)
% 157.76/157.54 [2945]~P135(x29451)+P135(x29452)+~E(x29451,x29452)
% 157.76/157.54 [2946]P31(x29462,x29463,x29464)+~E(x29461,x29462)+~P31(x29461,x29463,x29464)
% 157.76/157.54 [2947]P31(x29473,x29472,x29474)+~E(x29471,x29472)+~P31(x29473,x29471,x29474)
% 157.76/157.54 [2948]P31(x29483,x29484,x29482)+~E(x29481,x29482)+~P31(x29483,x29484,x29481)
% 157.76/157.54 [2949]~P81(x29491)+P81(x29492)+~E(x29491,x29492)
% 157.76/157.54 [2950]~P36(x29501)+P36(x29502)+~E(x29501,x29502)
% 157.76/157.54 [2951]P14(x29512,x29513,x29514)+~E(x29511,x29512)+~P14(x29511,x29513,x29514)
% 157.76/157.54 [2952]P14(x29523,x29522,x29524)+~E(x29521,x29522)+~P14(x29523,x29521,x29524)
% 157.76/157.54 [2953]P14(x29533,x29534,x29532)+~E(x29531,x29532)+~P14(x29533,x29534,x29531)
% 157.76/157.54 [2954]~P113(x29541)+P113(x29542)+~E(x29541,x29542)
% 157.76/157.54 [2955]P149(x29552,x29553,x29554)+~E(x29551,x29552)+~P149(x29551,x29553,x29554)
% 157.76/157.54 [2956]P149(x29563,x29562,x29564)+~E(x29561,x29562)+~P149(x29563,x29561,x29564)
% 157.76/157.54 [2957]P149(x29573,x29574,x29572)+~E(x29571,x29572)+~P149(x29573,x29574,x29571)
% 157.76/157.54 [2958]P19(x29582,x29583,x29584,x29585)+~E(x29581,x29582)+~P19(x29581,x29583,x29584,x29585)
% 157.76/157.54 [2959]P19(x29593,x29592,x29594,x29595)+~E(x29591,x29592)+~P19(x29593,x29591,x29594,x29595)
% 157.76/157.54 [2960]P19(x29603,x29604,x29602,x29605)+~E(x29601,x29602)+~P19(x29603,x29604,x29601,x29605)
% 157.76/157.54 [2961]P19(x29613,x29614,x29615,x29612)+~E(x29611,x29612)+~P19(x29613,x29614,x29615,x29611)
% 157.76/157.54 [2962]~P114(x29621)+P114(x29622)+~E(x29621,x29622)
% 157.76/157.54 [2963]~P66(x29631)+P66(x29632)+~E(x29631,x29632)
% 157.76/157.54 [2964]P8(x29642,x29643,x29644)+~E(x29641,x29642)+~P8(x29641,x29643,x29644)
% 157.76/157.54 [2965]P8(x29653,x29652,x29654)+~E(x29651,x29652)+~P8(x29653,x29651,x29654)
% 157.76/157.54 [2966]P8(x29663,x29664,x29662)+~E(x29661,x29662)+~P8(x29663,x29664,x29661)
% 157.76/157.54 [2967]~P129(x29671)+P129(x29672)+~E(x29671,x29672)
% 157.76/157.54 [2968]P34(x29682,x29683,x29684,x29685,x29686)+~E(x29681,x29682)+~P34(x29681,x29683,x29684,x29685,x29686)
% 157.76/157.54 [2969]P34(x29693,x29692,x29694,x29695,x29696)+~E(x29691,x29692)+~P34(x29693,x29691,x29694,x29695,x29696)
% 157.76/157.54 [2970]P34(x29703,x29704,x29702,x29705,x29706)+~E(x29701,x29702)+~P34(x29703,x29704,x29701,x29705,x29706)
% 157.76/157.54 [2971]P34(x29713,x29714,x29715,x29712,x29716)+~E(x29711,x29712)+~P34(x29713,x29714,x29715,x29711,x29716)
% 157.76/157.54 [2972]P34(x29723,x29724,x29725,x29726,x29722)+~E(x29721,x29722)+~P34(x29723,x29724,x29725,x29726,x29721)
% 157.76/157.54 [2973]~P92(x29731)+P92(x29732)+~E(x29731,x29732)
% 157.76/157.54 [2974]~P134(x29741)+P134(x29742)+~E(x29741,x29742)
% 157.76/157.54 [2975]~P97(x29751)+P97(x29752)+~E(x29751,x29752)
% 157.76/157.54 [2976]~P90(x29761)+P90(x29762)+~E(x29761,x29762)
% 157.76/157.54 [2977]P27(x29772,x29773)+~E(x29771,x29772)+~P27(x29771,x29773)
% 157.76/157.54 [2978]P27(x29783,x29782)+~E(x29781,x29782)+~P27(x29783,x29781)
% 157.76/157.54 [2979]~P86(x29791)+P86(x29792)+~E(x29791,x29792)
% 157.76/157.54 [2980]~P72(x29801)+P72(x29802)+~E(x29801,x29802)
% 157.76/157.54 [2981]P43(x29812,x29813)+~E(x29811,x29812)+~P43(x29811,x29813)
% 157.76/157.54 [2982]P43(x29823,x29822)+~E(x29821,x29822)+~P43(x29823,x29821)
% 157.76/157.54 [2983]~P76(x29831)+P76(x29832)+~E(x29831,x29832)
% 157.76/157.54 [2984]~P82(x29841)+P82(x29842)+~E(x29841,x29842)
% 157.76/157.54 [2985]~P132(x29851)+P132(x29852)+~E(x29851,x29852)
% 157.76/157.54 [2986]P11(x29862,x29863,x29864,x29865)+~E(x29861,x29862)+~P11(x29861,x29863,x29864,x29865)
% 157.76/157.54 [2987]P11(x29873,x29872,x29874,x29875)+~E(x29871,x29872)+~P11(x29873,x29871,x29874,x29875)
% 157.76/157.54 [2988]P11(x29883,x29884,x29882,x29885)+~E(x29881,x29882)+~P11(x29883,x29884,x29881,x29885)
% 157.76/157.54 [2989]P11(x29893,x29894,x29895,x29892)+~E(x29891,x29892)+~P11(x29893,x29894,x29895,x29891)
% 157.76/157.54 [2990]~P144(x29901)+P144(x29902)+~E(x29901,x29902)
% 157.76/157.54 [2991]P56(x29912,x29913,x29914)+~E(x29911,x29912)+~P56(x29911,x29913,x29914)
% 157.76/157.54 [2992]P56(x29923,x29922,x29924)+~E(x29921,x29922)+~P56(x29923,x29921,x29924)
% 157.76/157.54 [2993]P56(x29933,x29934,x29932)+~E(x29931,x29932)+~P56(x29933,x29934,x29931)
% 157.76/157.54 [2994]P52(x29942,x29943)+~E(x29941,x29942)+~P52(x29941,x29943)
% 157.76/157.54 [2995]P52(x29953,x29952)+~E(x29951,x29952)+~P52(x29953,x29951)
% 157.76/157.54 [2996]~P91(x29961)+P91(x29962)+~E(x29961,x29962)
% 157.76/157.54 [2997]~P101(x29971)+P101(x29972)+~E(x29971,x29972)
% 157.76/157.54 [2998]~P64(x29981)+P64(x29982)+~E(x29981,x29982)
% 157.76/157.54 [2999]~P70(x29991)+P70(x29992)+~E(x29991,x29992)
% 157.76/157.54 [3000]~P119(x30001)+P119(x30002)+~E(x30001,x30002)
% 157.76/157.54 [3001]~P121(x30011)+P121(x30012)+~E(x30011,x30012)
% 157.76/157.54 [3002]~P73(x30021)+P73(x30022)+~E(x30021,x30022)
% 157.76/157.54 [3003]P38(x30032,x30033)+~E(x30031,x30032)+~P38(x30031,x30033)
% 157.76/157.54 [3004]P38(x30043,x30042)+~E(x30041,x30042)+~P38(x30043,x30041)
% 157.76/157.54 [3005]~P142(x30051)+P142(x30052)+~E(x30051,x30052)
% 157.76/157.54 [3006]~P74(x30061)+P74(x30062)+~E(x30061,x30062)
% 157.76/157.54 [3007]P30(x30072,x30073,x30074)+~E(x30071,x30072)+~P30(x30071,x30073,x30074)
% 157.76/157.54 [3008]P30(x30083,x30082,x30084)+~E(x30081,x30082)+~P30(x30083,x30081,x30084)
% 157.76/157.54 [3009]P30(x30093,x30094,x30092)+~E(x30091,x30092)+~P30(x30093,x30094,x30091)
% 157.76/157.54 [3010]P59(x30102,x30103)+~E(x30101,x30102)+~P59(x30101,x30103)
% 157.76/157.54 [3011]P59(x30113,x30112)+~E(x30111,x30112)+~P59(x30113,x30111)
% 157.76/157.54 [3012]P53(x30122,x30123,x30124)+~E(x30121,x30122)+~P53(x30121,x30123,x30124)
% 157.76/157.54 [3013]P53(x30133,x30132,x30134)+~E(x30131,x30132)+~P53(x30133,x30131,x30134)
% 157.76/157.54 [3014]P53(x30143,x30144,x30142)+~E(x30141,x30142)+~P53(x30143,x30144,x30141)
% 157.76/157.54 [3015]P42(x30152,x30153,x30154,x30155,x30156,x30157)+~E(x30151,x30152)+~P42(x30151,x30153,x30154,x30155,x30156,x30157)
% 157.76/157.54 [3016]P42(x30163,x30162,x30164,x30165,x30166,x30167)+~E(x30161,x30162)+~P42(x30163,x30161,x30164,x30165,x30166,x30167)
% 157.76/157.54 [3017]P42(x30173,x30174,x30172,x30175,x30176,x30177)+~E(x30171,x30172)+~P42(x30173,x30174,x30171,x30175,x30176,x30177)
% 157.76/157.54 [3018]P42(x30183,x30184,x30185,x30182,x30186,x30187)+~E(x30181,x30182)+~P42(x30183,x30184,x30185,x30181,x30186,x30187)
% 157.76/157.54 [3019]P42(x30193,x30194,x30195,x30196,x30192,x30197)+~E(x30191,x30192)+~P42(x30193,x30194,x30195,x30196,x30191,x30197)
% 157.76/157.54 [3020]P42(x30203,x30204,x30205,x30206,x30207,x30202)+~E(x30201,x30202)+~P42(x30203,x30204,x30205,x30206,x30207,x30201)
% 157.76/157.54 [3021]~P145(x30211)+P145(x30212)+~E(x30211,x30212)
% 157.76/157.54 [3022]P15(x30222,x30223)+~E(x30221,x30222)+~P15(x30221,x30223)
% 157.76/157.54 [3023]P15(x30233,x30232)+~E(x30231,x30232)+~P15(x30233,x30231)
% 157.76/157.54 [3024]~P88(x30241)+P88(x30242)+~E(x30241,x30242)
% 157.76/157.54 [3025]~P115(x30251)+P115(x30252)+~E(x30251,x30252)
% 157.76/157.54 [3026]~P77(x30261)+P77(x30262)+~E(x30261,x30262)
% 157.76/157.54 [3027]P33(x30272,x30273,x30274)+~E(x30271,x30272)+~P33(x30271,x30273,x30274)
% 157.76/157.54 [3028]P33(x30283,x30282,x30284)+~E(x30281,x30282)+~P33(x30283,x30281,x30284)
% 157.76/157.54 [3029]P33(x30293,x30294,x30292)+~E(x30291,x30292)+~P33(x30293,x30294,x30291)
% 157.76/157.54 [3030]~P123(x30301)+P123(x30302)+~E(x30301,x30302)
% 157.76/157.54 [3031]~P146(x30311)+P146(x30312)+~E(x30311,x30312)
% 157.76/157.54 [3032]~P143(x30321)+P143(x30322)+~E(x30321,x30322)
% 157.76/157.54 [3033]P35(x30332,x30333,x30334)+~E(x30331,x30332)+~P35(x30331,x30333,x30334)
% 157.76/157.54 [3034]P35(x30343,x30342,x30344)+~E(x30341,x30342)+~P35(x30343,x30341,x30344)
% 157.76/157.54 [3035]P35(x30353,x30354,x30352)+~E(x30351,x30352)+~P35(x30353,x30354,x30351)
% 157.76/157.54 [3036]P50(x30362,x30363)+~E(x30361,x30362)+~P50(x30361,x30363)
% 157.76/157.54 [3037]P50(x30373,x30372)+~E(x30371,x30372)+~P50(x30373,x30371)
% 157.76/157.54 [3038]~P130(x30381)+P130(x30382)+~E(x30381,x30382)
% 157.76/157.54 [3039]P28(x30392,x30393)+~E(x30391,x30392)+~P28(x30391,x30393)
% 157.76/157.54 [3040]P28(x30403,x30402)+~E(x30401,x30402)+~P28(x30403,x30401)
% 157.76/157.54 [3041]~P126(x30411)+P126(x30412)+~E(x30411,x30412)
% 157.76/157.54 [3042]~P104(x30421)+P104(x30422)+~E(x30421,x30422)
% 157.76/157.54 [3043]~P125(x30431)+P125(x30432)+~E(x30431,x30432)
% 157.76/157.54 [3044]P10(x30442,x30443,x30444,x30445,x30446)+~E(x30441,x30442)+~P10(x30441,x30443,x30444,x30445,x30446)
% 157.76/157.54 [3045]P10(x30453,x30452,x30454,x30455,x30456)+~E(x30451,x30452)+~P10(x30453,x30451,x30454,x30455,x30456)
% 157.76/157.54 [3046]P10(x30463,x30464,x30462,x30465,x30466)+~E(x30461,x30462)+~P10(x30463,x30464,x30461,x30465,x30466)
% 157.76/157.54 [3047]P10(x30473,x30474,x30475,x30472,x30476)+~E(x30471,x30472)+~P10(x30473,x30474,x30475,x30471,x30476)
% 157.76/157.54 [3048]P10(x30483,x30484,x30485,x30486,x30482)+~E(x30481,x30482)+~P10(x30483,x30484,x30485,x30486,x30481)
% 157.76/157.54 [3049]P22(x30492,x30493,x30494,x30495,x30496,x30497)+~E(x30491,x30492)+~P22(x30491,x30493,x30494,x30495,x30496,x30497)
% 157.76/157.54 [3050]P22(x30503,x30502,x30504,x30505,x30506,x30507)+~E(x30501,x30502)+~P22(x30503,x30501,x30504,x30505,x30506,x30507)
% 157.76/157.54 [3051]P22(x30513,x30514,x30512,x30515,x30516,x30517)+~E(x30511,x30512)+~P22(x30513,x30514,x30511,x30515,x30516,x30517)
% 157.76/157.54 [3052]P22(x30523,x30524,x30525,x30522,x30526,x30527)+~E(x30521,x30522)+~P22(x30523,x30524,x30525,x30521,x30526,x30527)
% 157.76/157.54 [3053]P22(x30533,x30534,x30535,x30536,x30532,x30537)+~E(x30531,x30532)+~P22(x30533,x30534,x30535,x30536,x30531,x30537)
% 157.76/157.54 [3054]P22(x30543,x30544,x30545,x30546,x30547,x30542)+~E(x30541,x30542)+~P22(x30543,x30544,x30545,x30546,x30547,x30541)
% 157.76/157.54 [3055]P60(x30552,x30553,x30554,x30555)+~E(x30551,x30552)+~P60(x30551,x30553,x30554,x30555)
% 157.76/157.54 [3056]P60(x30563,x30562,x30564,x30565)+~E(x30561,x30562)+~P60(x30563,x30561,x30564,x30565)
% 157.76/157.54 [3057]P60(x30573,x30574,x30572,x30575)+~E(x30571,x30572)+~P60(x30573,x30574,x30571,x30575)
% 157.76/157.54 [3058]P60(x30583,x30584,x30585,x30582)+~E(x30581,x30582)+~P60(x30583,x30584,x30585,x30581)
% 157.76/157.54 [3059]~P99(x30591)+P99(x30592)+~E(x30591,x30592)
% 157.76/157.54 [3060]~P105(x30601)+P105(x30602)+~E(x30601,x30602)
% 157.76/157.54 [3061]~P147(x30611)+P147(x30612)+~E(x30611,x30612)
% 157.76/157.54 [3062]~P136(x30621)+P136(x30622)+~E(x30621,x30622)
% 157.76/157.54 [3063]~P137(x30631)+P137(x30632)+~E(x30631,x30632)
% 157.76/157.54 [3064]~P98(x30641)+P98(x30642)+~E(x30641,x30642)
% 157.76/157.54 [3065]~P131(x30651)+P131(x30652)+~E(x30651,x30652)
% 157.76/157.54 [3066]~P138(x30661)+P138(x30662)+~E(x30661,x30662)
% 157.76/157.54 [3067]~P140(x30671)+P140(x30672)+~E(x30671,x30672)
% 157.76/157.54 [3068]P49(x30682,x30683,x30684,x30685)+~E(x30681,x30682)+~P49(x30681,x30683,x30684,x30685)
% 157.76/157.54 [3069]P49(x30693,x30692,x30694,x30695)+~E(x30691,x30692)+~P49(x30693,x30691,x30694,x30695)
% 157.76/157.54 [3070]P49(x30703,x30704,x30702,x30705)+~E(x30701,x30702)+~P49(x30703,x30704,x30701,x30705)
% 157.76/157.54 [3071]P49(x30713,x30714,x30715,x30712)+~E(x30711,x30712)+~P49(x30713,x30714,x30715,x30711)
% 157.76/157.54 [3072]~P63(x30721)+P63(x30722)+~E(x30721,x30722)
% 157.76/157.54 [3073]~P139(x30731)+P139(x30732)+~E(x30731,x30732)
% 157.76/157.54 [3074]P29(x30742,x30743,x30744)+~E(x30741,x30742)+~P29(x30741,x30743,x30744)
% 157.76/157.54 [3075]P29(x30753,x30752,x30754)+~E(x30751,x30752)+~P29(x30753,x30751,x30754)
% 157.76/157.54 [3076]P29(x30763,x30764,x30762)+~E(x30761,x30762)+~P29(x30763,x30764,x30761)
% 157.76/157.54 [3077]~P118(x30771)+P118(x30772)+~E(x30771,x30772)
% 157.76/157.54 [3078]~P122(x30781)+P122(x30782)+~E(x30781,x30782)
% 157.76/157.54 [3079]P21(x30792,x30793,x30794,x30795,x30796)+~E(x30791,x30792)+~P21(x30791,x30793,x30794,x30795,x30796)
% 157.76/157.54 [3080]P21(x30803,x30802,x30804,x30805,x30806)+~E(x30801,x30802)+~P21(x30803,x30801,x30804,x30805,x30806)
% 157.76/157.54 [3081]P21(x30813,x30814,x30812,x30815,x30816)+~E(x30811,x30812)+~P21(x30813,x30814,x30811,x30815,x30816)
% 157.76/157.54 [3082]P21(x30823,x30824,x30825,x30822,x30826)+~E(x30821,x30822)+~P21(x30823,x30824,x30825,x30821,x30826)
% 157.76/157.54 [3083]P21(x30833,x30834,x30835,x30836,x30832)+~E(x30831,x30832)+~P21(x30833,x30834,x30835,x30836,x30831)
% 157.76/157.54 [3084]~P103(x30841)+P103(x30842)+~E(x30841,x30842)
% 157.76/157.54 [3085]P17(x30852,x30853,x30854)+~E(x30851,x30852)+~P17(x30851,x30853,x30854)
% 157.76/157.54 [3086]P17(x30863,x30862,x30864)+~E(x30861,x30862)+~P17(x30863,x30861,x30864)
% 157.76/157.54 [3087]P17(x30873,x30874,x30872)+~E(x30871,x30872)+~P17(x30873,x30874,x30871)
% 157.76/157.54 [3088]~P75(x30881)+P75(x30882)+~E(x30881,x30882)
% 157.76/157.54 [3089]~P93(x30891)+P93(x30892)+~E(x30891,x30892)
% 157.76/157.54 [3090]~P133(x30901)+P133(x30902)+~E(x30901,x30902)
% 157.76/157.54 [3091]P32(x30912,x30913,x30914,x30915)+~E(x30911,x30912)+~P32(x30911,x30913,x30914,x30915)
% 157.76/157.54 [3092]P32(x30923,x30922,x30924,x30925)+~E(x30921,x30922)+~P32(x30923,x30921,x30924,x30925)
% 157.76/157.54 [3093]P32(x30933,x30934,x30932,x30935)+~E(x30931,x30932)+~P32(x30933,x30934,x30931,x30935)
% 157.76/157.54 [3094]P32(x30943,x30944,x30945,x30942)+~E(x30941,x30942)+~P32(x30943,x30944,x30945,x30941)
% 157.76/157.54 [3095]P54(x30952,x30953)+~E(x30951,x30952)+~P54(x30951,x30953)
% 157.76/157.54 [3096]P54(x30963,x30962)+~E(x30961,x30962)+~P54(x30963,x30961)
% 157.76/157.54 [3097]P51(x30972,x30973)+~E(x30971,x30972)+~P51(x30971,x30973)
% 157.76/157.54 [3098]P51(x30983,x30982)+~E(x30981,x30982)+~P51(x30983,x30981)
% 157.76/157.54 [3099]~P124(x30991)+P124(x30992)+~E(x30991,x30992)
% 157.76/157.54 [3100]P48(x31002,x31003)+~E(x31001,x31002)+~P48(x31001,x31003)
% 157.76/157.54 [3101]P48(x31013,x31012)+~E(x31011,x31012)+~P48(x31013,x31011)
% 157.76/157.54 [3102]~P95(x31021)+P95(x31022)+~E(x31021,x31022)
% 157.76/157.54 [3103]P23(x31032,x31033,x31034,x31035,x31036,x31037)+~E(x31031,x31032)+~P23(x31031,x31033,x31034,x31035,x31036,x31037)
% 157.76/157.54 [3104]P23(x31043,x31042,x31044,x31045,x31046,x31047)+~E(x31041,x31042)+~P23(x31043,x31041,x31044,x31045,x31046,x31047)
% 157.76/157.54 [3105]P23(x31053,x31054,x31052,x31055,x31056,x31057)+~E(x31051,x31052)+~P23(x31053,x31054,x31051,x31055,x31056,x31057)
% 157.76/157.54 [3106]P23(x31063,x31064,x31065,x31062,x31066,x31067)+~E(x31061,x31062)+~P23(x31063,x31064,x31065,x31061,x31066,x31067)
% 157.76/157.54 [3107]P23(x31073,x31074,x31075,x31076,x31072,x31077)+~E(x31071,x31072)+~P23(x31073,x31074,x31075,x31076,x31071,x31077)
% 157.76/157.54 [3108]P23(x31083,x31084,x31085,x31086,x31087,x31082)+~E(x31081,x31082)+~P23(x31083,x31084,x31085,x31086,x31087,x31081)
% 157.76/157.54 [3109]~P116(x31091)+P116(x31092)+~E(x31091,x31092)
% 157.76/157.54 [3110]P47(x31102,x31103,x31104)+~E(x31101,x31102)+~P47(x31101,x31103,x31104)
% 157.76/157.54 [3111]P47(x31113,x31112,x31114)+~E(x31111,x31112)+~P47(x31113,x31111,x31114)
% 157.76/157.54 [3112]P47(x31123,x31124,x31122)+~E(x31121,x31122)+~P47(x31123,x31124,x31121)
% 157.76/157.54 [3113]~P148(x31131)+P148(x31132)+~E(x31131,x31132)
% 157.76/157.54 [3114]P58(x31142,x31143,x31144,x31145,x31146)+~E(x31141,x31142)+~P58(x31141,x31143,x31144,x31145,x31146)
% 157.76/157.54 [3115]P58(x31153,x31152,x31154,x31155,x31156)+~E(x31151,x31152)+~P58(x31153,x31151,x31154,x31155,x31156)
% 157.76/157.54 [3116]P58(x31163,x31164,x31162,x31165,x31166)+~E(x31161,x31162)+~P58(x31163,x31164,x31161,x31165,x31166)
% 157.76/157.54 [3117]P58(x31173,x31174,x31175,x31172,x31176)+~E(x31171,x31172)+~P58(x31173,x31174,x31175,x31171,x31176)
% 157.76/157.54 [3118]P58(x31183,x31184,x31185,x31186,x31182)+~E(x31181,x31182)+~P58(x31183,x31184,x31185,x31186,x31181)
% 157.76/157.54 [3119]~P141(x31191)+P141(x31192)+~E(x31191,x31192)
% 157.76/157.54 [3120]~P106(x31201)+P106(x31202)+~E(x31201,x31202)
% 157.76/157.54 [3121]~P44(x31211)+P44(x31212)+~E(x31211,x31212)
% 157.76/157.54 [3122]P61(x31222,x31223)+~E(x31221,x31222)+~P61(x31221,x31223)
% 157.76/157.54 [3123]P61(x31233,x31232)+~E(x31231,x31232)+~P61(x31233,x31231)
% 157.76/157.54 [3124]~P100(x31241)+P100(x31242)+~E(x31241,x31242)
% 157.76/157.54 [3125]P20(x31252,x31253,x31254,x31255)+~E(x31251,x31252)+~P20(x31251,x31253,x31254,x31255)
% 157.76/157.54 [3126]P20(x31263,x31262,x31264,x31265)+~E(x31261,x31262)+~P20(x31263,x31261,x31264,x31265)
% 157.76/157.54 [3127]P20(x31273,x31274,x31272,x31275)+~E(x31271,x31272)+~P20(x31273,x31274,x31271,x31275)
% 157.76/157.54 [3128]P20(x31283,x31284,x31285,x31282)+~E(x31281,x31282)+~P20(x31283,x31284,x31285,x31281)
% 157.76/157.54 [3129]~P117(x31291)+P117(x31292)+~E(x31291,x31292)
% 157.76/157.54 [3130]~P94(x31301)+P94(x31302)+~E(x31301,x31302)
% 157.76/157.54 [3131]~P78(x31311)+P78(x31312)+~E(x31311,x31312)
% 157.76/157.54 [3132]P9(x31322,x31323,x31324)+~E(x31321,x31322)+~P9(x31321,x31323,x31324)
% 157.76/157.54 [3133]P9(x31333,x31332,x31334)+~E(x31331,x31332)+~P9(x31333,x31331,x31334)
% 157.76/157.54 [3134]P9(x31343,x31344,x31342)+~E(x31341,x31342)+~P9(x31343,x31344,x31341)
% 157.76/157.54 [3135]P46(x31352,x31353,x31354)+~E(x31351,x31352)+~P46(x31351,x31353,x31354)
% 157.76/157.54 [3136]P46(x31363,x31362,x31364)+~E(x31361,x31362)+~P46(x31363,x31361,x31364)
% 157.76/157.54 [3137]P46(x31373,x31374,x31372)+~E(x31371,x31372)+~P46(x31373,x31374,x31371)
% 157.76/157.54 [3138]P41(x31382,x31383,x31384,x31385)+~E(x31381,x31382)+~P41(x31381,x31383,x31384,x31385)
% 157.76/157.54 [3139]P41(x31393,x31392,x31394,x31395)+~E(x31391,x31392)+~P41(x31393,x31391,x31394,x31395)
% 157.76/157.54 [3140]P41(x31403,x31404,x31402,x31405)+~E(x31401,x31402)+~P41(x31403,x31404,x31401,x31405)
% 157.76/157.54 [3141]P41(x31413,x31414,x31415,x31412)+~E(x31411,x31412)+~P41(x31413,x31414,x31415,x31411)
% 157.76/157.54 [3142]P151(x31422,x31423)+~E(x31421,x31422)+~P151(x31421,x31423)
% 157.76/157.54 [3143]P151(x31433,x31432)+~E(x31431,x31432)+~P151(x31433,x31431)
% 157.76/157.54 [3144]P45(x31442,x31443)+~E(x31441,x31442)+~P45(x31441,x31443)
% 157.76/157.54 [3145]P45(x31453,x31452)+~E(x31451,x31452)+~P45(x31453,x31451)
% 157.76/157.54 [3146]~P127(x31461)+P127(x31462)+~E(x31461,x31462)
% 157.76/157.54
% 157.76/157.54 %-------------------------------------------
% 157.76/157.57 cnf(10494,plain,
% 157.76/157.57 (~E(f866(a119,x104941),x104941)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10504,plain,
% 157.76/157.57 (~E(f866(a119,x105041),x105041)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10517,plain,
% 157.76/157.57 (~E(f866(a119,x105171),x105171)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10522,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x105221),f120(x105221)),x105222))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10525,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x105251),f120(x105251)),x105252))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10528,plain,
% 157.76/157.57 (~E(f866(a119,x105281),x105281)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10531,plain,
% 157.76/157.57 (~E(f866(a119,x105311),x105311)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10534,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x105341),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(10537,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x105371),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(10554,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,x105541)),x105541))),
% 157.76/157.57 inference(rename_variables,[],[4787])).
% 157.76/157.57 cnf(10557,plain,
% 157.76/157.57 (~E(f866(f866(f158(x105571),x105572),x105573),x105573)),
% 157.76/157.57 inference(rename_variables,[],[4741])).
% 157.76/157.57 cnf(10563,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x105631),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(10566,plain,
% 157.76/157.57 (E(f866(f292(x105661,x105661),f271(x105661,x105662)),x105662)),
% 157.76/157.57 inference(rename_variables,[],[3515])).
% 157.76/157.57 cnf(10569,plain,
% 157.76/157.57 (E(f866(f292(x105691,x105691),f271(x105691,x105692)),x105692)),
% 157.76/157.57 inference(rename_variables,[],[3515])).
% 157.76/157.57 cnf(10574,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x105741),x105741))),
% 157.76/157.57 inference(rename_variables,[],[4777])).
% 157.76/157.57 cnf(10579,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x105791),x105792)),x105792))),
% 157.76/157.57 inference(rename_variables,[],[4801])).
% 157.76/157.57 cnf(10582,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x105821),x105822)),x105822))),
% 157.76/157.57 inference(rename_variables,[],[4801])).
% 157.76/157.57 cnf(10589,plain,
% 157.76/157.57 (~E(x105891,f866(a119,x105891))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,3341,3515,10566,3385,3451,3382,3412,3393,4741,3622,3539,4781,10534,10537,4778,4736,4786,10522,4777,4787,4376,4784,3532,4770,4803,4801,10579,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420])).
% 157.76/157.57 cnf(10603,plain,
% 157.76/157.57 (~E(f866(a119,x106031),x106031)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10606,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x106061),x106061))),
% 157.76/157.57 inference(rename_variables,[],[4777])).
% 157.76/157.57 cnf(10609,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),f50(a930,x106091,x106092)),x106091))),
% 157.76/157.57 inference(rename_variables,[],[4011])).
% 157.76/157.57 cnf(10630,plain,
% 157.76/157.57 (E(f866(f40(a930),f866(f290(a930),x106301)),x106301)),
% 157.76/157.57 inference(rename_variables,[],[3448])).
% 157.76/157.57 cnf(10638,plain,
% 157.76/157.57 (~E(f866(a119,x106381),x106381)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10641,plain,
% 157.76/157.57 (~E(f866(a119,x106411),x106411)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10644,plain,
% 157.76/157.57 (~E(f866(a119,x106441),x106441)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10649,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x106491),f866(a119,x106491)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10658,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x106581),x106581))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(10665,plain,
% 157.76/157.57 (E(f866(f292(x106651,x106651),f271(x106651,x106652)),x106652)),
% 157.76/157.57 inference(rename_variables,[],[3515])).
% 157.76/157.57 cnf(10668,plain,
% 157.76/157.57 (E(f866(f292(x106681,x106681),f271(x106681,x106682)),x106682)),
% 157.76/157.57 inference(rename_variables,[],[3515])).
% 157.76/157.57 cnf(10685,plain,
% 157.76/157.57 (P107(f866(f866(f243(a1),x106851),x106851))),
% 157.76/157.57 inference(rename_variables,[],[3556])).
% 157.76/157.57 cnf(10690,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x106901),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(10693,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x106931,a925)),x106932),f250(f937(x106931,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(10698,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x106981),f120(x106981)),x106982))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10727,plain,
% 157.76/157.57 (~E(f866(f866(f158(x107271),x107272),x107273),x107273)),
% 157.76/157.57 inference(rename_variables,[],[4741])).
% 157.76/157.57 cnf(10730,plain,
% 157.76/157.57 (~E(f866(a119,x107301),f2(a930))),
% 157.76/157.57 inference(rename_variables,[],[4728])).
% 157.76/157.57 cnf(10741,plain,
% 157.76/157.57 (P107(f866(f866(f243(a1),x107411),x107411))),
% 157.76/157.57 inference(rename_variables,[],[3556])).
% 157.76/157.57 cnf(10746,plain,
% 157.76/157.57 (~E(f866(a119,x107461),x107461)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10749,plain,
% 157.76/157.57 (~P107(f866(f866(f195(f937(x107491,f937(x107492,a925))),x107493),x107494))),
% 157.76/157.57 inference(rename_variables,[],[4804])).
% 157.76/157.57 cnf(10756,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x107561),x107561))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(10769,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x107691),f866(a119,x107691)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10790,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x107901,a925)),x107902),f250(f937(x107901,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(10793,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x107931),f120(x107931)),x107932))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10812,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108121),f120(x108121)),x108122))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10819,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108191),f120(x108191)),x108192))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10830,plain,
% 157.76/157.57 (~E(f866(a119,x108301),f2(a930))),
% 157.76/157.57 inference(rename_variables,[],[4728])).
% 157.76/157.57 cnf(10835,plain,
% 157.76/157.57 (P107(f866(f866(f336(x108351),x108352),f250(f937(x108351,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(10842,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108421),f120(x108421)),x108422))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10847,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x108471),f866(a119,x108471)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10850,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108501),f120(x108501)),x108502))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10853,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108531),f120(x108531)),x108532))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10856,plain,
% 157.76/157.57 (~P107(f866(f67(x108561,x108562,f195(f937(x108561,a925))),x108563))),
% 157.76/157.57 inference(rename_variables,[],[4800])).
% 157.76/157.57 cnf(10859,plain,
% 157.76/157.57 (~P107(f866(f67(x108591,x108592,f195(f937(x108591,a925))),x108593))),
% 157.76/157.57 inference(rename_variables,[],[4800])).
% 157.76/157.57 cnf(10862,plain,
% 157.76/157.57 (~P107(f866(f866(f195(f937(x108621,f937(x108622,a925))),x108623),x108624))),
% 157.76/157.57 inference(rename_variables,[],[4804])).
% 157.76/157.57 cnf(10865,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x108651),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(10870,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x108701),f120(x108701)),x108702))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(10881,plain,
% 157.76/157.57 (~E(f866(a119,x108811),x108811)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(10899,plain,
% 157.76/157.57 (P107(f866(f866(f244(a106),f866(a3,x108991)),f866(a3,f866(a119,x108991))))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,4728,10730,3341,3515,10566,10569,10665,3385,3451,3382,3412,3393,4026,3485,4741,10557,3448,4335,4806,3470,3918,3622,10649,10769,10847,4006,3539,4781,10534,10537,10563,10690,4794,3993,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,4285,3936,10693,3555,10658,10756,3556,10685,4777,10574,10606,3707,3647,4074,4011,10609,4787,10554,4376,4784,4769,3532,3536,4771,4770,4800,10856,4803,4804,10749,4035,4801,10579,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350])).
% 157.76/157.57 cnf(10906,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x109061),x109061))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(10909,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x109091),f866(f866(f87(a930),x109091),x109091)))),
% 157.76/157.57 inference(rename_variables,[],[3818])).
% 157.76/157.57 cnf(10912,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x109121),f866(f866(f87(a930),x109121),x109121)))),
% 157.76/157.57 inference(rename_variables,[],[3818])).
% 157.76/157.57 cnf(10915,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x109151),f866(a119,f866(f866(f86(a930),x109152),x109151))))),
% 157.76/157.57 inference(rename_variables,[],[4004])).
% 157.76/157.57 cnf(10920,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x109201),f866(a119,x109201)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10923,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x109231),f866(a119,x109231)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10926,plain,
% 157.76/157.57 (P107(f866(f866(f336(x109261),x109262),f250(f937(x109261,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(10945,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,x109451)),x109451))),
% 157.76/157.57 inference(rename_variables,[],[4787])).
% 157.76/157.57 cnf(10948,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,x109481)),x109481))),
% 157.76/157.57 inference(rename_variables,[],[4787])).
% 157.76/157.57 cnf(10951,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x109511),x109512)),x109512))),
% 157.76/157.57 inference(rename_variables,[],[4801])).
% 157.76/157.57 cnf(10954,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x109541),x109542)),x109542))),
% 157.76/157.57 inference(rename_variables,[],[4801])).
% 157.76/157.57 cnf(10957,plain,
% 157.76/157.57 (P107(f866(f250(f937(x109571,a925)),x109572))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(10960,plain,
% 157.76/157.57 (E(f866(f40(a930),f866(f290(a930),x109601)),x109601)),
% 157.76/157.57 inference(rename_variables,[],[3448])).
% 157.76/157.57 cnf(10963,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x109631),f866(a119,x109631)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(10970,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x109701),x109701))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(10975,plain,
% 157.76/157.57 (P107(f866(f866(f243(a1),x109751),x109751))),
% 157.76/157.57 inference(rename_variables,[],[3556])).
% 157.76/157.57 cnf(10984,plain,
% 157.76/157.57 (E(f866(f292(x109841,x109841),f271(x109841,x109842)),x109842)),
% 157.76/157.57 inference(rename_variables,[],[3515])).
% 157.76/157.57 cnf(10987,plain,
% 157.76/157.57 (P107(f866(f250(f937(x109871,a925)),x109872))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(10990,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),f2(a930)),x109901))),
% 157.76/157.57 inference(rename_variables,[],[3575])).
% 157.76/157.57 cnf(10993,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x109931,a925)),f195(f937(x109931,a925))),x109932))),
% 157.76/157.57 inference(rename_variables,[],[4003])).
% 157.76/157.57 cnf(10996,plain,
% 157.76/157.57 (P107(f866(f250(f937(x109961,a925)),x109962))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(10999,plain,
% 157.76/157.57 (P107(f866(f250(f937(x109991,a925)),x109992))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(11002,plain,
% 157.76/157.57 (P107(f866(f250(f937(x110021,a925)),x110022))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(11004,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(f866(f87(a930),f866(a119,x110041)),f866(a119,x110041))),x110041))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,4728,10730,3341,3515,10566,10569,10665,10668,3385,3451,3382,3412,3393,4026,3485,4741,10557,3448,10630,4335,4806,3470,3918,3855,3622,10649,10769,10847,10920,10923,4006,3539,4781,10534,10537,10563,10690,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,4285,3936,10693,3555,10658,10756,10906,3556,10685,10741,4777,10574,10606,3707,10835,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,3575,4376,4784,4769,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,4803,4804,10749,4035,4801,10579,10582,10951,4004,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587])).
% 157.76/157.57 cnf(11005,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x110051),f866(f866(f87(a930),x110051),x110051)))),
% 157.76/157.57 inference(rename_variables,[],[3818])).
% 157.76/157.57 cnf(11014,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,f866(a119,f866(f866(f86(a930),x110141),x110142)))),f866(a119,x110142)))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,4728,10730,3341,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3485,4741,10557,3448,10630,4335,4806,3470,3918,3855,3622,10649,10769,10847,10920,10923,10963,4006,3539,4781,10534,10537,10563,10690,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,4285,3936,10693,3555,10658,10756,10906,3556,10685,10741,4777,10574,10606,3707,10835,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,3575,4376,4784,4769,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,4803,4804,10749,4035,4801,10579,10582,10951,4004,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629])).
% 157.76/157.57 cnf(11047,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x110471),x110471))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11058,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x110581),f120(x110581)),x110582))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(11067,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x110671),f866(a119,x110671)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(11069,plain,
% 157.76/157.57 (P107(f866(f866(f244(a1),f866(f866(f23(a1),x110691),f84(a1))),x110691))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,4728,10730,3341,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3485,4741,10557,3448,10630,4335,4194,4806,3470,3918,3855,3622,10649,10769,10847,10920,10923,10963,4006,3539,4781,10534,10537,10563,10690,10865,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,4285,3936,10693,3555,10658,10756,10906,10970,11047,3556,10685,10741,10975,4777,10574,10606,3707,10835,4790,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,4376,4784,4769,4772,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,4803,4804,10749,4035,4801,10579,10582,10951,4004,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897])).
% 157.76/157.57 cnf(11070,plain,
% 157.76/157.57 (P107(f866(f866(f243(a1),x110701),x110701))),
% 157.76/157.57 inference(rename_variables,[],[3556])).
% 157.76/157.57 cnf(11075,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x110751),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(11088,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x110881),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(11091,plain,
% 157.76/157.57 (~P107(f866(f866(f244(f937(x110911,a925)),x110912),f195(f937(x110911,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4798])).
% 157.76/157.57 cnf(11094,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x110941),x110941))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11097,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x110971),x110971))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11112,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x111121),x111121))),
% 157.76/157.57 inference(rename_variables,[],[4777])).
% 157.76/157.57 cnf(11121,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x111211),x111212),f195(f937(x111211,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11128,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x111281),x111281))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11131,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x111311,a925)),f866(f317(x111312,x111311,x111313),f866(f318(x111312,x111311,x111313),x111314))),x111314))),
% 157.76/157.57 inference(rename_variables,[],[4433])).
% 157.76/157.57 cnf(11140,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x111401,a925)),f866(f179(x111401),f866(f143(x111401,x111402),x111403))),f866(f179(x111401),x111403)))),
% 157.76/157.57 inference(rename_variables,[],[4203])).
% 157.76/157.57 cnf(11143,plain,
% 157.76/157.57 (E(f866(f317(x111431,x111431,f5(x111431)),x111432),x111432)),
% 157.76/157.57 inference(rename_variables,[],[3611])).
% 157.76/157.57 cnf(11148,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),f2(a930)),x111481))),
% 157.76/157.57 inference(rename_variables,[],[3575])).
% 157.76/157.57 cnf(11151,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x111511),x111511))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11154,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x111541),x111541))),
% 157.76/157.57 inference(rename_variables,[],[4777])).
% 157.76/157.57 cnf(11163,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x111631),x111631))),
% 157.76/157.57 inference(rename_variables,[],[4777])).
% 157.76/157.57 cnf(11174,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x111741),f866(f866(f87(a930),x111741),x111741)))),
% 157.76/157.57 inference(rename_variables,[],[3818])).
% 157.76/157.57 cnf(11180,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x111801),f866(a119,f866(f866(f86(a930),x111802),x111801))))),
% 157.76/157.57 inference(rename_variables,[],[4004])).
% 157.76/157.57 cnf(11187,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x111871),x111871))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11190,plain,
% 157.76/157.57 (P107(f866(f866(f243(a1),x111901),x111901))),
% 157.76/157.57 inference(rename_variables,[],[3556])).
% 157.76/157.57 cnf(11193,plain,
% 157.76/157.57 (~E(f866(a119,x111931),x111931)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11198,plain,
% 157.76/157.57 (P107(f866(f866(f336(x111981),x111982),f250(f937(x111981,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(11203,plain,
% 157.76/157.57 (~P107(f866(f866(f244(a930),x112031),f2(a930)))),
% 157.76/157.57 inference(rename_variables,[],[4781])).
% 157.76/157.57 cnf(11218,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),f2(a930)),x112181))),
% 157.76/157.57 inference(rename_variables,[],[3575])).
% 157.76/157.57 cnf(11225,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x112251),x112251))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11234,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x112341),x112342),f195(f937(x112341,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11238,plain,
% 157.76/157.57 (E(f866(f866(f108(f937(x112381,a925)),f866(f866(f108(f937(x112381,a925)),x112382),f866(f85(f937(x112381,a925)),x112383))),x112383),f195(f937(x112381,a925)))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,4728,10730,3341,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3611,3485,4741,10557,3448,10630,4335,4194,4806,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,4297,4203,11140,3919,4285,3936,10693,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,4790,11121,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032])).
% 157.76/157.57 cnf(11242,plain,
% 157.76/157.57 (P107(f866(f866(f336(x112421),x112422),f250(f937(x112421,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(11245,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x112451),f931(x112451))),f866(f866(f260(f931(x112451),f931(x112451)),x112452),f120(x112451))),f152(x112451,x112453)))),
% 157.76/157.57 inference(rename_variables,[],[4806])).
% 157.76/157.57 cnf(11251,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(x112511,x112511)),x112512),f271(x112511,f195(f937(x112511,a925)))))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,4728,10730,3341,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3611,3485,4741,10557,3448,10630,4335,4194,4806,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,4297,4203,11140,3919,4285,3936,10693,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,4790,11121,11234,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172])).
% 157.76/157.57 cnf(11252,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x112521),x112522),f195(f937(x112521,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11254,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x112541),x112542),f866(f318(x112541,x112543,x112544),f195(f937(x112543,a925)))))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,4728,10730,3341,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3611,3485,4741,10557,3448,10630,4335,4194,4806,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,4297,4203,11140,3919,4285,3936,10693,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,4790,11121,11234,11252,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,4003,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204])).
% 157.76/157.57 cnf(11255,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x112551),x112552),f195(f937(x112551,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11258,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x112581,a925)),x112582),f866(f866(f316(x112581),x112583),x112582)))),
% 157.76/157.57 inference(rename_variables,[],[4001])).
% 157.76/157.57 cnf(11261,plain,
% 157.76/157.57 (P107(f866(f866(f243(a930),x112611),x112611))),
% 157.76/157.57 inference(rename_variables,[],[3555])).
% 157.76/157.57 cnf(11264,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x112641,a925)),x112642),f866(f866(f316(x112641),x112643),x112642)))),
% 157.76/157.57 inference(rename_variables,[],[4001])).
% 157.76/157.57 cnf(11267,plain,
% 157.76/157.57 (E(f866(f317(x112671,x112671,f5(x112671)),x112672),x112672)),
% 157.76/157.57 inference(rename_variables,[],[3611])).
% 157.76/157.57 cnf(11269,plain,
% 157.76/157.57 (P34(x112691,x112692,x112693,f121(x112691,f120(x112691)),f120(x112692))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,4728,10730,3341,3396,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3611,11143,3485,4741,10557,3448,10630,4335,4194,4806,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,4297,4203,11140,3919,4285,3936,10693,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,4790,11121,11234,11252,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,4001,11258,4003,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310])).
% 157.76/157.57 cnf(11282,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x112821,a925)),x112822),f866(f866(f316(x112821),x112823),x112822)))),
% 157.76/157.57 inference(rename_variables,[],[4001])).
% 157.76/157.57 cnf(11295,plain,
% 157.76/157.57 (~E(f866(a119,x112951),f2(a930))),
% 157.76/157.57 inference(rename_variables,[],[4728])).
% 157.76/157.57 cnf(11298,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x112981),f120(x112981)),x112982))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(11302,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(a930,a930)),f866(f866(f260(a930,a930),f866(a119,x113021)),x113021)),f314(a930,a324)))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,4728,10730,10830,3341,3396,3515,10566,10569,10665,10668,3492,3385,3451,3382,3412,3393,4026,3611,11143,3485,4741,10557,3448,10630,4335,4194,4806,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,3919,4285,3936,10693,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,4790,11121,11234,11252,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,4160,4001,11258,11264,4003,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625])).
% 157.76/157.57 cnf(11311,plain,
% 157.76/157.57 (P107(f866(f866(f244(a930),x113111),f866(a119,x113111)))),
% 157.76/157.57 inference(rename_variables,[],[3622])).
% 157.76/157.57 cnf(11321,plain,
% 157.76/157.57 (~E(f866(f317(x113211,f937(x113211,a925),x113212),x113213),f866(f315(x113211),x113213))),
% 157.76/157.57 inference(rename_variables,[],[4788])).
% 157.76/157.57 cnf(11324,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x113241),x113242),f195(f937(x113241,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11327,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x113271),x113272),f195(f937(x113271,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11330,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(x113301,x113301)),f866(f866(f260(x113301,x113301),x113302),x113303)),f160(x113301,f120(f937(x113301,a930)))))),
% 157.76/157.57 inference(rename_variables,[],[4805])).
% 157.76/157.57 cnf(11333,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(x113331,x113331)),f866(f866(f260(x113331,x113331),x113332),x113333)),f160(x113331,f120(f937(x113331,a930)))))),
% 157.76/157.57 inference(rename_variables,[],[4805])).
% 157.76/157.57 cnf(11338,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x113381),x113382),f195(f937(x113381,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11341,plain,
% 157.76/157.57 (P107(f866(f866(f336(f936(x113411,x113411)),f866(f866(f260(x113411,x113411),x113412),x113412)),f314(x113411,x113413)))),
% 157.76/157.57 inference(rename_variables,[],[4194])).
% 157.76/157.57 cnf(11344,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x113441,a925)),f866(f179(x113441),f183(x113441,x113442,x113443))),f866(f179(x113441),x113442)))),
% 157.76/157.57 inference(rename_variables,[],[4251])).
% 157.76/157.57 cnf(11347,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x113471,a925)),x113472),f250(f937(x113471,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(11363,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x113631,a925)),f195(f937(x113631,a925))),x113632))),
% 157.76/157.57 inference(rename_variables,[],[4003])).
% 157.76/157.57 cnf(11374,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x113741),f931(x113741))),f866(f866(f260(f931(x113741),f931(x113741)),x113742),f120(x113741))),f154(x113741,x113743)))),
% 157.76/157.57 inference(rename_variables,[],[4807])).
% 157.76/157.57 cnf(11385,plain,
% 157.76/157.57 (~E(f866(a119,x113851),x113851)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11388,plain,
% 157.76/157.57 (~E(f866(a119,x113881),x113881)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11392,plain,
% 157.76/157.57 (P107(f866(f866(f336(f936(f931(x113921),f931(x113921))),f866(f866(f260(f931(x113921),f931(x113921)),f120(x113921)),f120(x113921))),f866(f866(f296(f931(x113921),f931(x113921),f931(x113921)),f165(x113921,x113922)),f314(f931(x113921),f165(x113921,x113922)))))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,4728,10730,10830,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,3448,10630,4335,4194,11341,4806,11245,4807,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,4251,3919,4285,3936,10693,10790,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,4790,11121,11234,11252,11255,11324,11327,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,4160,4001,11258,11264,4003,10993,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852])).
% 157.76/157.57 cnf(11395,plain,
% 157.76/157.57 (~E(f866(a119,x113951),f2(a930))),
% 157.76/157.57 inference(rename_variables,[],[4728])).
% 157.76/157.57 cnf(11397,plain,
% 157.76/157.57 (E(f866(x113971,f866(f97(x113972,x113973,f250(f937(x113972,a925)),x113971),f866(x113971,x113974))),f866(x113971,x113974))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,3448,10630,4335,4194,11341,4806,11245,4807,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,4251,3919,4285,3936,10693,10790,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,4790,11121,11234,11252,11255,11324,11327,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,4160,4001,11258,11264,4003,10993,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866])).
% 157.76/157.57 cnf(11400,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x114001,a925)),x114002),x114002))),
% 157.76/157.57 inference(rename_variables,[],[3851])).
% 157.76/157.57 cnf(11407,plain,
% 157.76/157.57 (~E(f866(a119,x114071),x114071)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11410,plain,
% 157.76/157.57 (~E(f866(a119,x114101),x114101)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11412,plain,
% 157.76/157.57 (~P26(x114121,f937(x114121,a925),x114122,x114123,f866(f315(x114121),x114123))),
% 157.76/157.57 inference(scs_inference,[],[4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3448,10630,4335,4194,11341,4806,11245,4807,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,4251,3919,4285,3936,10693,10790,4798,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,4790,11121,11234,11252,11255,11324,11327,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,4160,4001,11258,11264,3851,4003,10993,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905])).
% 157.76/157.57 cnf(11415,plain,
% 157.76/157.57 (P25(x114151,x114151,f5(x114151),x114152)),
% 157.76/157.57 inference(rename_variables,[],[3790])).
% 157.76/157.57 cnf(11420,plain,
% 157.76/157.57 (~E(f866(f317(x114201,f937(x114201,a925),x114202),x114203),f866(f315(x114201),x114203))),
% 157.76/157.57 inference(rename_variables,[],[4788])).
% 157.76/157.57 cnf(11425,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x114251,a925)),x114252),f250(f937(x114251,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(11441,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x114411),x114412),f195(f937(x114411,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11444,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,x114441)),x114441))),
% 157.76/157.57 inference(rename_variables,[],[4787])).
% 157.76/157.57 cnf(11449,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x114491),x114492),f195(f937(x114491,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11460,plain,
% 157.76/157.57 (~P107(f866(f866(f243(a930),f866(a119,x114601)),x114601))),
% 157.76/157.57 inference(rename_variables,[],[4787])).
% 157.76/157.57 cnf(11463,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x114631),x114632),f195(f937(x114631,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11476,plain,
% 157.76/157.57 (P107(f866(f866(f336(f936(x114761,x114761)),f866(f866(f260(x114761,x114761),x114762),x114762)),f314(x114761,x114763)))),
% 157.76/157.57 inference(rename_variables,[],[4194])).
% 157.76/157.57 cnf(11479,plain,
% 157.76/157.57 (P107(f866(f866(f336(x114791),x114792),f250(f937(x114791,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(11482,plain,
% 157.76/157.57 (P107(f866(f866(f336(x114821),x114822),f250(f937(x114821,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(11489,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x114891),f931(x114891))),f866(f866(f260(f931(x114891),f931(x114891)),x114892),f120(x114891))),f152(x114891,x114893)))),
% 157.76/157.57 inference(rename_variables,[],[4806])).
% 157.76/157.57 cnf(11492,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x114921),f931(x114921))),f866(f866(f260(f931(x114921),f931(x114921)),x114922),f120(x114921))),f154(x114921,x114923)))),
% 157.76/157.57 inference(rename_variables,[],[4807])).
% 157.76/157.57 cnf(11495,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x114951),f931(x114951))),f866(f866(f260(f931(x114951),f931(x114951)),x114952),f120(x114951))),f164(x114951,x114953)))),
% 157.76/157.57 inference(rename_variables,[],[4808])).
% 157.76/157.57 cnf(11500,plain,
% 157.76/157.57 (~P107(f866(f866(f244(f937(x115001,a925)),x115002),f195(f937(x115001,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4798])).
% 157.76/157.57 cnf(11502,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x115021),x115022),f866(f317(x115023,x115021,x115024),f195(f937(x115023,a925)))))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3658,3448,10630,4335,4194,11341,4806,11245,11489,4807,11374,4808,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,4798,11091,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,4160,4001,11258,11264,3851,4003,10993,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334])).
% 157.76/157.57 cnf(11503,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x115031),x115032),f195(f937(x115031,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11509,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115091,a925)),x115092),f866(f866(f117(f937(x115091,a925)),x115093),f250(f937(x115091,a925)))))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3658,3448,10630,4335,4194,11341,4806,11245,11489,4807,11374,4808,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,4798,11091,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,4160,4001,11258,11264,3851,4003,10993,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364])).
% 157.76/157.57 cnf(11510,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115101,a925)),x115102),f250(f937(x115101,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(11517,plain,
% 157.76/157.57 (~P107(f866(f866(f179(x115171),f120(x115171)),x115172))),
% 157.76/157.57 inference(rename_variables,[],[4786])).
% 157.76/157.57 cnf(11522,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x115221),x115222),f195(f937(x115221,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11525,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(x115251,x115251)),f866(f866(f260(x115251,x115251),x115252),x115253)),f160(x115251,f120(f937(x115251,a930)))))),
% 157.76/157.57 inference(rename_variables,[],[4805])).
% 157.76/157.57 cnf(11528,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115281,a925)),x115282),x115282))),
% 157.76/157.57 inference(rename_variables,[],[3851])).
% 157.76/157.57 cnf(11531,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x115311),x115312),f195(f937(x115311,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11533,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115331,a925)),f866(f293(x115332,x115331,f195(f937(f936(x115332,x115331),a925))),x115333)),x115334))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3658,3448,10630,4335,4194,11341,4806,11245,11489,4807,11374,4808,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,4798,11091,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,4160,4001,11258,11264,3851,11400,4003,10993,11363,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536])).
% 157.76/157.57 cnf(11534,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115341,a925)),f195(f937(x115341,a925))),x115342))),
% 157.76/157.57 inference(rename_variables,[],[4003])).
% 157.76/157.57 cnf(11537,plain,
% 157.76/157.57 (P107(f866(f866(f336(f936(x115371,x115371)),f866(f866(f260(x115371,x115371),x115372),x115372)),f314(x115371,x115373)))),
% 157.76/157.57 inference(rename_variables,[],[4194])).
% 157.76/157.57 cnf(11539,plain,
% 157.76/157.57 (~P34(x115391,x115392,x115393,f866(f866(f161(x115394,x115391),x115395),f866(a119,f120(x115394))),f120(x115392))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3658,3448,10630,4335,4194,11341,11476,4806,11245,11489,4807,11374,4808,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,4798,11091,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,4160,4001,11258,11264,3851,11400,4003,10993,11363,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544])).
% 157.76/157.57 cnf(11543,plain,
% 157.76/157.57 (P34(x115431,x115432,x115433,f866(f866(f161(x115434,x115431),x115435),f121(x115434,f120(x115434))),f120(x115432))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,4788,11321,3658,3448,10630,4335,4194,11341,11476,4806,11245,11489,4807,11374,4808,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,4798,11091,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,3615,10957,10987,10996,10999,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,4160,4001,11258,11264,3851,11400,4003,10993,11363,3818,10909,10912,11005,11174,4803,4804,10749,4433,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567])).
% 157.76/157.57 cnf(11548,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x115481),f931(x115481))),f866(f866(f260(f931(x115481),f931(x115481)),x115482),f120(x115481))),f164(x115481,x115483)))),
% 157.76/157.57 inference(rename_variables,[],[4808])).
% 157.76/157.57 cnf(11555,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x115551),f931(x115551))),f866(f866(f260(f931(x115551),f931(x115551)),f120(x115551)),x115552)),f152(x115551,x115553)))),
% 157.76/157.57 inference(rename_variables,[],[4809])).
% 157.76/157.57 cnf(11563,plain,
% 157.76/157.57 (P107(f866(f866(f336(x115631),x115632),f250(f937(x115631,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3707])).
% 157.76/157.57 cnf(11568,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115681,a925)),f195(f937(x115681,a925))),x115682))),
% 157.76/157.57 inference(rename_variables,[],[4003])).
% 157.76/157.57 cnf(11571,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x115711),x115712),f195(f937(x115711,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11574,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115741,a925)),x115742),f250(f937(x115741,a925))))),
% 157.76/157.57 inference(rename_variables,[],[3936])).
% 157.76/157.57 cnf(11579,plain,
% 157.76/157.57 (P107(f866(f866(f243(f937(x115791,a925)),f195(f937(x115791,a925))),x115792))),
% 157.76/157.57 inference(rename_variables,[],[4003])).
% 157.76/157.57 cnf(11592,plain,
% 157.76/157.57 (P107(f866(f250(f937(x115921,a925)),x115922))),
% 157.76/157.57 inference(rename_variables,[],[3615])).
% 157.76/157.57 cnf(11600,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x116001),f931(x116001))),f866(f866(f260(f931(x116001),f931(x116001)),x116002),f120(x116001))),f152(x116001,x116003)))),
% 157.76/157.57 inference(rename_variables,[],[4806])).
% 157.76/157.57 cnf(11603,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x116031),f931(x116031))),f866(f866(f260(f931(x116031),f931(x116031)),x116032),f120(x116031))),f154(x116031,x116033)))),
% 157.76/157.57 inference(rename_variables,[],[4807])).
% 157.76/157.57 cnf(11606,plain,
% 157.76/157.57 (~E(f866(f866(f158(x116061),x116062),x116063),x116063)),
% 157.76/157.57 inference(rename_variables,[],[4741])).
% 157.76/157.57 cnf(11609,plain,
% 157.76/157.57 (~E(f866(a119,x116091),x116091)),
% 157.76/157.57 inference(rename_variables,[],[4716])).
% 157.76/157.57 cnf(11611,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x116111),x116112),f866(f293(x116113,x116111,x116114),f195(f937(x116113,a925)))))),
% 157.76/157.57 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,10727,4788,11321,3658,3448,10630,4335,4194,11341,11476,4806,11245,11489,4807,11374,11492,4808,11495,4809,11555,4810,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,11482,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,3615,10957,10987,10996,10999,11002,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,4160,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,4804,10749,4433,4339,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941])).
% 157.76/157.57 cnf(11612,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x116121),x116122),f195(f937(x116121,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11617,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x116171),x116172),f195(f937(x116171,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11620,plain,
% 157.76/157.57 (~P107(f866(f866(f336(x116201),x116202),f195(f937(x116201,a925))))),
% 157.76/157.57 inference(rename_variables,[],[4790])).
% 157.76/157.57 cnf(11623,plain,
% 157.76/157.57 (P107(f866(f866(f336(f936(f931(x116231),f931(x116231))),f866(f866(f260(f931(x116231),f931(x116231)),x116232),x116232)),f165(x116231,f314(x116231,x116233))))),
% 157.76/157.57 inference(rename_variables,[],[4328])).
% 157.76/157.57 cnf(11626,plain,
% 157.76/157.57 (~P107(f866(f866(f336(f936(f931(x116261),f931(x116261))),f866(f866(f260(f931(x116261),f931(x116261)),x116262),f120(x116261))),f152(x116261,x116263)))),
% 157.76/157.57 inference(rename_variables,[],[4806])).
% 157.76/157.57 cnf(11636,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(x116361,x116361)),f866(f866(f260(x116361,x116361),x116362),x116363)),f160(x116361,f120(f937(x116361,a930)))))),
% 157.76/157.58 inference(rename_variables,[],[4805])).
% 157.76/157.58 cnf(11639,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116391),x116392),f195(f937(x116391,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11642,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116421),x116422),f195(f937(x116421,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11645,plain,
% 157.76/157.58 (P107(f866(f866(f336(x116451),x116452),f250(f937(x116451,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3707])).
% 157.76/157.58 cnf(11648,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x116481),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(11653,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(x116531,x116531)),f866(f866(f260(x116531,x116531),x116532),x116533)),f160(x116531,f120(f937(x116531,a930)))))),
% 157.76/157.58 inference(rename_variables,[],[4805])).
% 157.76/157.58 cnf(11656,plain,
% 157.76/157.58 (~E(f866(f317(x116561,f937(x116561,a925),x116562),x116563),f866(f315(x116561),x116563))),
% 157.76/157.58 inference(rename_variables,[],[4788])).
% 157.76/157.58 cnf(11659,plain,
% 157.76/157.58 (~E(f866(f317(x116591,f937(x116591,a925),x116592),x116593),f866(f315(x116591),x116593))),
% 157.76/157.58 inference(rename_variables,[],[4788])).
% 157.76/157.58 cnf(11664,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(f931(x116641),f931(x116641))),f866(f866(f260(f931(x116641),f931(x116641)),x116642),f120(x116641))),f152(x116641,x116643)))),
% 157.76/157.58 inference(rename_variables,[],[4806])).
% 157.76/157.58 cnf(11670,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(f931(x116701),f931(x116701))),f866(f866(f260(f931(x116701),f931(x116701)),x116702),f120(x116701))),f152(x116701,x116703)))),
% 157.76/157.58 inference(rename_variables,[],[4806])).
% 157.76/157.58 cnf(11673,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116731),x116732),f195(f937(x116731,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11675,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x116751,x116752)),f866(f866(f260(x116751,x116752),f866(x116753,x116754)),f866(x116755,x116754))),f866(f317(f936(x116756,x116756),f936(x116751,x116752),f266(x116756,x116751,x116756,x116752,x116753,x116755)),f314(x116756,x116757))))),
% 157.76/157.58 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,10727,4788,11321,11420,11656,3658,3448,10630,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4328,11623,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,11482,11563,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,3615,10957,10987,10996,10999,11002,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,11525,11636,4160,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,4804,10749,4433,4339,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306])).
% 157.76/157.58 cnf(11678,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116781),x116782),f195(f937(x116781,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11681,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116811),x116812),f195(f937(x116811,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11684,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116841),x116842),f195(f937(x116841,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11687,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x116871),x116872),f195(f937(x116871,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11690,plain,
% 157.76/157.58 (P107(f866(f866(f336(x116901),f866(x116902,x116903)),f866(f317(x116904,x116901,x116902),f250(f937(x116904,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(11692,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(x116921,x116922)),x116923),f866(f317(f936(x116924,x116924),f936(x116921,x116922),f266(x116924,x116921,x116924,x116922,x116925,x116926)),f160(x116924,f120(f937(x116924,a930))))))),
% 157.76/157.58 inference(scs_inference,[],[3790,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,4728,10730,10830,11295,3341,3396,3515,10566,10569,10665,10668,3492,4013,3385,3451,3382,3412,3393,4026,3611,11143,3485,4192,4741,10557,10727,4788,11321,11420,11656,3658,3448,10630,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,4006,3539,4781,10534,10537,10563,10690,10865,11075,11088,11203,4794,3993,3759,4142,3581,3583,3557,4778,4736,4328,11623,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,3556,10685,10741,10975,11070,4777,10574,10606,11112,11154,3707,10835,10926,11198,11242,11479,11482,11563,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,3615,10957,10987,10996,10999,11002,3647,4074,4011,10609,4787,10554,10945,10948,11444,3575,10990,11148,4376,4784,4082,4769,4772,3532,3536,4771,4770,4800,10856,4805,11330,11333,11525,11636,11653,4160,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,4804,10749,4433,4339,4035,4801,10579,10582,10951,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478])).
% 157.76/157.58 cnf(11693,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(x116931,x116931)),f866(f866(f260(x116931,x116931),x116932),x116933)),f160(x116931,f120(f937(x116931,a930)))))),
% 157.76/157.58 inference(rename_variables,[],[4805])).
% 157.76/157.58 cnf(11699,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x116991),x116991))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(11700,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x117001,f937(x117002,a925))),x117003),x117004))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(11705,plain,
% 157.76/157.58 (E(f121(x117051,f120(x117051)),f120(x117051))),
% 157.76/157.58 inference(rename_variables,[],[3396])).
% 157.76/157.58 cnf(11708,plain,
% 157.76/157.58 (~E(f866(a119,x117081),x117081)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11715,plain,
% 157.76/157.58 (~E(f866(a119,x117151),x117151)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11720,plain,
% 157.76/157.58 (E(f866(f292(x117201,x117201),f271(x117201,x117202)),x117202)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11723,plain,
% 157.76/157.58 (E(f866(f292(x117231,x117231),f271(x117231,x117232)),x117232)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11729,plain,
% 157.76/157.58 (~E(f866(a119,x117291),x117291)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11734,plain,
% 157.76/157.58 (~E(f866(f866(f86(a1),x117341),x117341),a104)),
% 157.76/157.58 inference(rename_variables,[],[4739])).
% 157.76/157.58 cnf(11741,plain,
% 157.76/157.58 (E(f866(f866(f23(a930),f2(a930)),x117411),f2(a930))),
% 157.76/157.58 inference(rename_variables,[],[3471])).
% 157.76/157.58 cnf(11744,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x117441),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(11751,plain,
% 157.76/157.58 (E(f866(f866(f86(a1),f866(f866(f87(a1),x117511),f866(f866(f41(a1),x117512),x117511))),f50(a1,x117512,x117511)),x117512)),
% 157.76/157.58 inference(rename_variables,[],[4107])).
% 157.76/157.58 cnf(11775,plain,
% 157.76/157.58 (~E(f866(a119,x117751),x117751)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11778,plain,
% 157.76/157.58 (~E(f866(a119,x117781),x117781)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11798,plain,
% 157.76/157.58 (E(f866(f292(x117981,x117981),f271(x117981,x117982)),x117982)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11807,plain,
% 157.76/157.58 (~P107(f866(f866(f179(x118071),f120(x118071)),x118072))),
% 157.76/157.58 inference(rename_variables,[],[4786])).
% 157.76/157.58 cnf(11813,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),f2(a930)),f866(a119,x118131)))),
% 157.76/157.58 inference(rename_variables,[],[3634])).
% 157.76/157.58 cnf(11814,plain,
% 157.76/157.58 (~E(f866(a119,x118141),x118141)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11817,plain,
% 157.76/157.58 (P107(f866(f866(f336(x118171),x118172),f250(f937(x118171,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3707])).
% 157.76/157.58 cnf(11829,plain,
% 157.76/157.58 (~E(f866(a119,x118291),x118291)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11832,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x118321),x118321))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(11839,plain,
% 157.76/157.58 (P107(f866(f71(x118391,x118392,x118393,x118394,f195(f937(x118391,a925))),x118394))),
% 157.76/157.58 inference(rename_variables,[],[4472])).
% 157.76/157.58 cnf(11840,plain,
% 157.76/157.58 (E(f866(f292(x118401,x118401),f271(x118401,x118402)),x118402)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11853,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x118531),x118532)),x118532))),
% 157.76/157.58 inference(rename_variables,[],[4801])).
% 157.76/157.58 cnf(11856,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x118561)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(11879,plain,
% 157.76/157.58 (E(f866(f292(x118791,x118791),f271(x118791,x118792)),x118792)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11884,plain,
% 157.76/157.58 (E(f866(f292(x118841,x118841),f271(x118841,x118842)),x118842)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11887,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x118871)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(11892,plain,
% 157.76/157.58 (~E(f866(a119,x118921),x118921)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11901,plain,
% 157.76/157.58 (~P107(f866(f866(f179(x119011),f120(x119011)),x119012))),
% 157.76/157.58 inference(rename_variables,[],[4786])).
% 157.76/157.58 cnf(11922,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x119221)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(11925,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x119251),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(11926,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x119261),f866(a119,x119261)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(11929,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x119291)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(11932,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x119321),x119322),f195(f937(x119321,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(11933,plain,
% 157.76/157.58 (P107(f866(f866(f336(f937(x119331,a925)),x119332),f866(f315(x119331),x119332)))),
% 157.76/157.58 inference(rename_variables,[],[3919])).
% 157.76/157.58 cnf(11948,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x119481)),x119481))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(11949,plain,
% 157.76/157.58 (~E(f866(a119,x119491),x119491)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11952,plain,
% 157.76/157.58 (E(f866(f292(x119521,x119521),f271(x119521,x119522)),x119522)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11962,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x119621),x119622)),x119621))),
% 157.76/157.58 inference(rename_variables,[],[4802])).
% 157.76/157.58 cnf(11965,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x119651)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(11968,plain,
% 157.76/157.58 (~E(f866(a119,x119681),x119681)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(11981,plain,
% 157.76/157.58 (P107(f866(f866(f336(x119811),x119812),f866(f866(f316(x119811),x119812),x119813)))),
% 157.76/157.58 inference(rename_variables,[],[3867])).
% 157.76/157.58 cnf(11982,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a1),f2(a1)),f866(f85(a1),f866(f107(a1),f866(a119,x119821)))))),
% 157.76/157.58 inference(rename_variables,[],[4803])).
% 157.76/157.58 cnf(11985,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),f866(f866(f23(a930),x119851),x119852)),f866(a119,x119851)))),
% 157.76/157.58 inference(rename_variables,[],[4006])).
% 157.76/157.58 cnf(11988,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f50(a930,x119881,x119882)),x119881))),
% 157.76/157.58 inference(rename_variables,[],[4011])).
% 157.76/157.58 cnf(11994,plain,
% 157.76/157.58 (E(f866(f292(x119941,x119941),f271(x119941,x119942)),x119942)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(11999,plain,
% 157.76/157.58 (E(f866(f866(f141(x119991),f176(x119991,x119992,x119993)),f176(x119991,x119994,x119993)),f866(f866(f141(x119991),f176(x119991,x119994,x119993)),f176(x119991,x119992,x119993)))),
% 157.76/157.58 inference(rename_variables,[],[4121])).
% 157.76/157.58 cnf(12004,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x120041)),x120041))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12013,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x120131),x120131))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12016,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f50(a930,x120161,x120162)),x120161))),
% 157.76/157.58 inference(rename_variables,[],[4011])).
% 157.76/157.58 cnf(12017,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x120171))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(12034,plain,
% 157.76/157.58 (P57(a930,x120341,x120341)),
% 157.76/157.58 inference(rename_variables,[],[3460])).
% 157.76/157.58 cnf(12037,plain,
% 157.76/157.58 (P57(a930,x120371,x120371)),
% 157.76/157.58 inference(rename_variables,[],[3460])).
% 157.76/157.58 cnf(12040,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x120401),x120401))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12043,plain,
% 157.76/157.58 (P107(f866(f866(f336(x120431),f866(x120432,x120433)),f866(f317(x120434,x120431,x120432),f250(f937(x120434,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(12044,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x120441)),x120441))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12047,plain,
% 157.76/157.58 (P107(f866(f866(f336(x120471),f866(x120472,x120473)),f866(f317(x120474,x120471,x120472),f250(f937(x120474,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(12048,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x120481),x120482)),x120482))),
% 157.76/157.58 inference(rename_variables,[],[4801])).
% 157.76/157.58 cnf(12053,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x120531),x120532)),x120531))),
% 157.76/157.58 inference(rename_variables,[],[4802])).
% 157.76/157.58 cnf(12056,plain,
% 157.76/157.58 (~P107(f866(f866(f179(x120561),f120(x120561)),x120562))),
% 157.76/157.58 inference(rename_variables,[],[4786])).
% 157.76/157.58 cnf(12059,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x120591),x120591))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12065,plain,
% 157.76/157.58 (~P35(x120651,x120652,f120(x120651))),
% 157.76/157.58 inference(rename_variables,[],[4752])).
% 157.76/157.58 cnf(12068,plain,
% 157.76/157.58 (P107(f866(f866(f336(x120681),x120682),f250(f937(x120681,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3707])).
% 157.76/157.58 cnf(12069,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x120691)),x120691))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12082,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x120821)),x120821))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12083,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x120831),f866(a119,x120831)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12086,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x120861),x120862),f195(f937(x120861,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12089,plain,
% 157.76/157.58 (E(f866(f866(f16(x120891,x120892),x120893),x120894),x120893)),
% 157.76/157.58 inference(rename_variables,[],[3546])).
% 157.76/157.58 cnf(12092,plain,
% 157.76/157.58 (E(f866(f866(f16(x120921,x120922),x120923),x120924),x120923)),
% 157.76/157.58 inference(rename_variables,[],[3546])).
% 157.76/157.58 cnf(12104,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),f2(a930)),f866(a119,x121041)))),
% 157.76/157.58 inference(rename_variables,[],[3634])).
% 157.76/157.58 cnf(12107,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x121071),x121071))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12110,plain,
% 157.76/157.58 (P107(f866(f66(x121101),f866(f179(x121101),x121102)))),
% 157.76/157.58 inference(rename_variables,[],[3594])).
% 157.76/157.58 cnf(12113,plain,
% 157.76/157.58 (P107(f866(f66(x121131),f866(f179(x121131),x121132)))),
% 157.76/157.58 inference(rename_variables,[],[3594])).
% 157.76/157.58 cnf(12116,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),f866(f85(a1),f866(f107(a1),x121161))),f866(f107(a1),x121162)))),
% 157.76/157.58 inference(rename_variables,[],[4036])).
% 157.76/157.58 cnf(12119,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x121191),x121192),f195(f937(x121191,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12133,plain,
% 157.76/157.58 (~P107(f866(f866(f336(a930),f2(a930)),f866(f311(a930),x121331)))),
% 157.76/157.58 inference(scs_inference,[],[3790,3460,12034,4751,4752,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,3475,4728,10730,10830,11295,3154,3155,3158,3161,3162,3165,3166,3179,3182,3183,3188,3192,3201,3214,3218,3227,3233,3234,3256,3278,3279,3289,3290,3304,3305,3307,3314,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,3492,4013,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3611,11143,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,4608,4609,4739,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,4006,11985,3539,3634,11813,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,4794,11856,11887,11922,11929,3993,3759,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,3556,10685,10741,10975,11070,11190,3630,4777,10574,10606,11112,11154,11163,12013,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,3575,10990,11148,11218,4036,4376,4784,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,4433,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410])).
% 157.76/157.58 cnf(12135,plain,
% 157.76/157.58 (~P107(f866(f866(f336(a930),x121351),f866(f290(a930),f2(a930))))),
% 157.76/157.58 inference(scs_inference,[],[3790,3460,12034,4751,4752,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,3475,4728,10730,10830,11295,3154,3155,3158,3161,3162,3165,3166,3179,3182,3183,3188,3192,3201,3214,3218,3227,3233,3234,3256,3278,3279,3289,3290,3304,3305,3307,3314,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,3492,4013,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3611,11143,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,4608,4609,4739,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,4006,11985,3539,3634,11813,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,4794,11856,11887,11922,11929,3993,3759,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,3556,10685,10741,10975,11070,11190,3630,4777,10574,10606,11112,11154,11163,12013,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,3575,10990,11148,11218,4036,4376,4784,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,4433,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410,6411])).
% 157.76/157.58 cnf(12137,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),f50(a930,x121371,f195(a930))),x121371))),
% 157.76/157.58 inference(scs_inference,[],[3790,3460,12034,4751,4752,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,3475,4728,10730,10830,11295,3154,3155,3158,3161,3162,3165,3166,3179,3182,3183,3188,3192,3201,3214,3218,3227,3233,3234,3256,3278,3279,3289,3290,3304,3305,3307,3314,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,3492,4013,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3611,11143,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,4608,4609,4739,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,4006,11985,3539,3634,11813,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,4794,11856,11887,11922,11929,3993,3759,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,4297,4203,11140,4251,3919,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,3556,10685,10741,10975,11070,11190,11832,3630,4777,10574,10606,11112,11154,11163,12013,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,3575,10990,11148,11218,4036,4376,4784,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,4433,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410,6411,6441])).
% 157.76/157.58 cnf(12138,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x121381),x121381))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12141,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x121411),x121411))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12150,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x121501),x121501))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12153,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x121531),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12158,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x121581),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12167,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x121671))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(12168,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x121681)),x121681))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12171,plain,
% 157.76/157.58 (~P107(f866(f866(f179(x121711),f120(x121711)),x121712))),
% 157.76/157.58 inference(rename_variables,[],[4786])).
% 157.76/157.58 cnf(12174,plain,
% 157.76/157.58 (~P107(f866(f866(f179(x121741),f120(x121741)),x121742))),
% 157.76/157.58 inference(rename_variables,[],[4786])).
% 157.76/157.58 cnf(12177,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x121771),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12178,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x121781),f866(a119,x121781)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12197,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x121971)),x121971))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12200,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x122001)),x122001))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12203,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x122031)),x122031))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12206,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x122061)),x122061))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12209,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x122091),x122091))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12212,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x122121),x122121))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12215,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x122151),x122151))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12218,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x122181),x122181))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12235,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x122351),x122351))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12238,plain,
% 157.76/157.58 (P25(a930,a930,a119,x122381)),
% 157.76/157.58 inference(rename_variables,[],[3758])).
% 157.76/157.58 cnf(12241,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x122411),x122411))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12252,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x122521),x122521))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12255,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(f936(f931(x122551),f931(x122551)),a925)),f165(x122551,x122552)),f314(f931(x122551),f164(x122551,x122552))))),
% 157.76/157.58 inference(rename_variables,[],[4256])).
% 157.76/157.58 cnf(12262,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x122621),f866(a119,x122621)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12265,plain,
% 157.76/157.58 (P107(f866(f866(f336(f937(x122651,a925)),x122652),f866(f315(x122651),x122652)))),
% 157.76/157.58 inference(rename_variables,[],[3919])).
% 157.76/157.58 cnf(12266,plain,
% 157.76/157.58 (~E(f866(a119,x122661),x122661)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12271,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x122711),x122711))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12276,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x122761),x122761))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12283,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x122831,x122832)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(12290,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x122901,a925)),x122902),f866(f866(f316(x122901),x122903),x122902)))),
% 157.76/157.58 inference(rename_variables,[],[4001])).
% 157.76/157.58 cnf(12293,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x122931),x122931))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12294,plain,
% 157.76/157.58 (~E(f866(a119,x122941),x122941)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12305,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123051),x123051))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12306,plain,
% 157.76/157.58 (~E(f866(a119,x123061),x123061)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12309,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x123091),x123091))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12312,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x123121),x123121))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12315,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x123151),x123151))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12318,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x123181),x123181))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12321,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x123211),x123211))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12324,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123241),x123241))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12327,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123271),x123271))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12328,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x123281),f866(a119,x123281)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12335,plain,
% 157.76/157.58 (~E(f866(a119,x123351),x123351)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12340,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123401),x123401))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12341,plain,
% 157.76/157.58 (~E(f866(a119,x123411),x123411)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12344,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x123441),x123441))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12357,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x123571),f866(a119,x123571)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12364,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x123641),x123641))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(12369,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x123691))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(12383,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123831),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12386,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123861),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12389,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x123891),x123892),f195(f937(x123891,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12392,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x123921),x123922),f195(f937(x123921,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12395,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123951),x123951))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12397,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123971),f866(f866(f108(a930),x123971),x123972)))),
% 157.76/157.58 inference(scs_inference,[],[3790,3460,12034,4751,4752,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,3758,3475,4728,10730,10830,11295,3154,3155,3158,3161,3162,3165,3166,3172,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3256,3278,3279,3289,3290,3304,3305,3307,3314,3316,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,3492,3501,4013,4321,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3611,11143,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,4608,4609,4739,3855,4070,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,4006,11985,3539,3634,11813,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,4794,11856,11887,11922,11929,11965,3993,3759,3761,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,4297,4256,4203,11140,4251,3919,11933,4285,3936,10693,10790,11347,11425,11510,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,3575,10990,11148,11218,12017,12167,4036,4376,4784,4048,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,11282,3851,11400,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,4433,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,1030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% 157.76/157.58 cnf(12398,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x123981),x123981))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12401,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x124011),x124011))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12404,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x124041),x124041))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12407,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x124071),f866(a119,x124071)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12414,plain,
% 157.76/157.58 (P107(f866(f866(f336(f937(x124141,a925)),x124142),f866(f315(x124141),x124142)))),
% 157.76/157.58 inference(rename_variables,[],[3919])).
% 157.76/157.58 cnf(12419,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124191,a925)),x124192),f866(f866(f316(x124191),x124193),x124192)))),
% 157.76/157.58 inference(rename_variables,[],[4001])).
% 157.76/157.58 cnf(12426,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x124261),x124262),f195(f937(x124261,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12435,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124351,a925)),x124352),f250(f937(x124351,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12436,plain,
% 157.76/157.58 (~E(f866(a119,x124361),x124361)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12439,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124391,a925)),f866(f179(x124391),f866(f143(x124391,x124392),x124393))),f866(f179(x124391),x124393)))),
% 157.76/157.58 inference(rename_variables,[],[4203])).
% 157.76/157.58 cnf(12445,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x124451),f866(a119,x124451)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12454,plain,
% 157.76/157.58 (E(f866(f292(x124541,x124541),f271(x124541,x124542)),x124542)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12465,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a930),f866(a119,x124651)),x124651))),
% 157.76/157.58 inference(rename_variables,[],[4787])).
% 157.76/157.58 cnf(12466,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x124661),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12469,plain,
% 157.76/157.58 (P107(f866(f66(x124691),f195(f937(x124691,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3630])).
% 157.76/157.58 cnf(12470,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x124701),x124702),f195(f937(x124701,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12477,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124771,a925)),f866(f179(x124771),f183(x124771,x124772,x124773))),f866(f179(x124771),x124772)))),
% 157.76/157.58 inference(rename_variables,[],[4251])).
% 157.76/157.58 cnf(12480,plain,
% 157.76/157.58 (P25(x124801,x124801,f5(x124801),x124802)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12485,plain,
% 157.76/157.58 (P107(f866(f866(f336(f937(x124851,a925)),x124852),f866(f315(x124851),x124852)))),
% 157.76/157.58 inference(rename_variables,[],[3919])).
% 157.76/157.58 cnf(12492,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x124921),x124921))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12495,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x124951),x124952),f195(f937(x124951,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12498,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124981,a925)),x124982),f866(f866(f316(x124981),x124983),x124982)))),
% 157.76/157.58 inference(rename_variables,[],[4001])).
% 157.76/157.58 cnf(12499,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x124991,a925)),x124992),f250(f937(x124991,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12506,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x125061),x125061))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12509,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x125091),x125091))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12512,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x125121),x125121))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12515,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x125151),x125151))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12518,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x125181),f866(a119,x125181)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12521,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x125211),f866(a119,x125211)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12524,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x125241,a925)),x125242),x125242))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12526,plain,
% 157.76/157.58 (~P107(f866(f866(f243(a1),f866(f866(f23(a1),a89),a104)),f2(a1)))),
% 157.76/157.58 inference(scs_inference,[],[3790,11415,3460,12034,4751,4752,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,3758,3475,4728,10730,10830,11295,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3256,3278,3279,3289,3290,3304,3305,3307,3314,3316,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,3492,3501,4013,4321,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3611,11143,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,3918,4608,4609,4739,3855,4070,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,4794,11856,11887,11922,11929,11965,3993,3759,3761,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,12113,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,4297,4256,4203,11140,4251,11344,3919,11933,12265,12414,4285,3936,10693,10790,11347,11425,11510,11574,12435,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,12469,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,3575,10990,11148,11218,12017,12167,4036,4376,4784,4048,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,11282,12290,12419,3851,11400,11528,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,4433,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410,6411,6441,6458,6510,6547,6549,6570,6571,6578,6583,6584,6588,6602,6617,6638,6639,6644,6647,6656,6671,6694,6700,6702,6717,6718,6721,6722,6724,6726,6727,6728,6730,6732,6734,6740,6741,6743,6744,6750,6752,6797,6802,6818,6820,6821,6822,6855,6860,6862,6867,6868,6876,6880,6892,6915,6916,6918,6919,6930,6934,6937,6956,6959,6977,7006,7007,7008,7014,7028,7047,7049,7051,7053,7058,7064,7067,7081,7086,7087,7122,7123,7124,7139,7140,7142,7143,7144,7162,7164,7179,7205,7227,7238,7240,7242,7244,7245,7276,7277,7281,7282,7289,7290,7292,7294,7316,7325,7326,7337,7347,7387,7397,7401,7408,7419,7424,7426,7433,7441,7454,7471,7492,7494,7513,7568,7569,7570,7572,7574,7578,7583,7645,7674,7689,7705,7736,7739,7761,7784,7802,7805,7806,7816,7836,7838,7840,7842,7843,7844,7869,7895])).
% 157.76/157.58 cnf(12531,plain,
% 157.76/157.58 (P107(f866(f866(f336(f937(x125311,a925)),x125312),f866(f315(x125311),x125312)))),
% 157.76/157.58 inference(rename_variables,[],[3919])).
% 157.76/157.58 cnf(12540,plain,
% 157.76/157.58 (~E(f866(a119,x125401),x125401)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12541,plain,
% 157.76/157.58 (E(f866(f317(x125411,x125411,f5(x125411)),x125412),x125412)),
% 157.76/157.58 inference(rename_variables,[],[3611])).
% 157.76/157.58 cnf(12544,plain,
% 157.76/157.58 (P32(x125441,x125442,f120(x125441),f120(x125441))),
% 157.76/157.58 inference(rename_variables,[],[3799])).
% 157.76/157.58 cnf(12547,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x125471,a925)),f866(f179(x125471),f183(x125471,x125472,x125473))),f866(f179(x125471),x125472)))),
% 157.76/157.58 inference(rename_variables,[],[4251])).
% 157.76/157.58 cnf(12548,plain,
% 157.76/157.58 (P107(f866(f66(x125481),f866(f179(x125481),x125482)))),
% 157.76/157.58 inference(rename_variables,[],[3594])).
% 157.76/157.58 cnf(12559,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x125591),x125591))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12562,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x125621),x125621))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12567,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x125671))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(12574,plain,
% 157.76/157.58 (P13(a930,f866(f175(a930),f866(f866(f161(f931(x125741),a930),f196(f931(x125741))),f186(x125741,x125742))))),
% 157.76/157.58 inference(rename_variables,[],[4117])).
% 157.76/157.58 cnf(12577,plain,
% 157.76/157.58 (P25(x125771,x125771,f5(x125771),x125772)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12580,plain,
% 157.76/157.58 (P25(x125801,x125801,f5(x125801),x125802)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12583,plain,
% 157.76/157.58 (P107(f866(f866(f336(f931(x125831)),f120(x125831)),f168(x125831,x125832)))),
% 157.76/157.58 inference(rename_variables,[],[3750])).
% 157.76/157.58 cnf(12586,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x125861,f937(x125862,a925))),x125863),x125864))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(12591,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x125911),x125911))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12592,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x125921))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(12595,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x125951,f937(x125952,a925))),x125953),x125954))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(12598,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(f936(f931(x125981),f931(x125981)),a925)),f165(x125981,x125982)),f314(f931(x125981),f164(x125981,x125982))))),
% 157.76/157.58 inference(rename_variables,[],[4256])).
% 157.76/157.58 cnf(12604,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126041,a925)),f866(f317(x126042,x126041,x126043),f866(f318(x126042,x126041,x126043),x126044))),x126044))),
% 157.76/157.58 inference(rename_variables,[],[4433])).
% 157.76/157.58 cnf(12607,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126071,a925)),f866(f179(x126071),f183(x126071,x126072,x126073))),f866(f179(x126071),x126072)))),
% 157.76/157.58 inference(rename_variables,[],[4251])).
% 157.76/157.58 cnf(12608,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126081,a925)),f866(f179(x126081),f866(f143(x126081,x126082),x126083))),f866(f179(x126081),x126083)))),
% 157.76/157.58 inference(rename_variables,[],[4203])).
% 157.76/157.58 cnf(12611,plain,
% 157.76/157.58 (~P107(f866(f866(f244(f937(x126111,a925)),x126112),f195(f937(x126111,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4798])).
% 157.76/157.58 cnf(12619,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126191,a925)),f866(f317(x126192,x126191,x126193),f866(f318(x126192,x126191,x126193),x126194))),x126194))),
% 157.76/157.58 inference(rename_variables,[],[4433])).
% 157.76/157.58 cnf(12624,plain,
% 157.76/157.58 (P107(f866(f866(f336(f931(x126241)),f120(x126241)),f168(x126241,x126242)))),
% 157.76/157.58 inference(rename_variables,[],[3750])).
% 157.76/157.58 cnf(12627,plain,
% 157.76/157.58 (~P107(f866(f866(f336(f936(f931(x126271),f931(x126271))),f866(f866(f260(f931(x126271),f931(x126271)),x126272),f120(x126271))),f152(x126271,x126273)))),
% 157.76/157.58 inference(rename_variables,[],[4806])).
% 157.76/157.58 cnf(12630,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x126301),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12632,plain,
% 157.76/157.58 (~P107(f866(f66(x126321),f250(f937(x126321,a925))))),
% 157.76/157.58 inference(scs_inference,[],[3790,11415,12480,12577,3799,3807,3460,12034,3525,4751,4752,3422,3425,4750,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,3758,3475,4728,10730,10830,11295,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3247,3256,3278,3279,3289,3290,3304,3305,3307,3314,3316,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,3492,3501,4013,4321,3385,3752,4107,11751,3451,3382,3412,3407,3393,3394,4026,3432,3611,11143,11267,3485,4192,4741,10557,10727,3546,12089,4788,11321,11420,11656,11659,3658,3448,10630,10960,3449,3711,3363,3471,11741,4335,4194,11341,11476,11537,4806,11245,11489,11600,11626,11664,11670,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,3918,4608,4609,4739,3855,4070,4117,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,4794,11856,11887,11922,11929,11965,3993,3759,3761,4142,3581,3583,3557,4778,4736,3743,4795,4328,11623,3877,3594,12110,12113,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,4297,4256,12255,12598,4203,11140,12439,4251,11344,12477,12547,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,12469,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,4036,4376,4784,4048,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,4160,11690,12043,4001,11258,11264,11282,12290,12419,3851,11400,11528,12524,4003,10993,11363,11534,11568,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,11700,12586,4433,11131,12604,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,918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% 157.76/157.58 cnf(12633,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126331,a925)),x126332),x126332))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12636,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x126361),x126362),f195(f937(x126361,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12639,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x126391,f937(x126392,a925))),x126393),x126394))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(12642,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126421,a925)),f866(f317(x126422,x126421,x126423),f866(f318(x126422,x126421,x126423),x126424))),x126424))),
% 157.76/157.58 inference(rename_variables,[],[4433])).
% 157.76/157.58 cnf(12643,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126431,a925)),x126432),x126432))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12648,plain,
% 157.76/157.58 (E(f866(f292(x126481,x126481),f271(x126481,x126482)),x126482)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12651,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x126511,a925)),f866(f179(x126511),f183(x126511,x126512,x126513))),f866(f179(x126511),x126512)))),
% 157.76/157.58 inference(rename_variables,[],[4251])).
% 157.76/157.58 cnf(12652,plain,
% 157.76/157.58 (P107(f866(f66(x126521),f866(f179(x126521),x126522)))),
% 157.76/157.58 inference(rename_variables,[],[3594])).
% 157.76/157.58 cnf(12655,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x126551),x126551))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12658,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x126581),x126581))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12661,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x126611),x126611))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12672,plain,
% 157.76/157.58 (P25(x126721,x126721,f5(x126721),x126722)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12680,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x126801),x126802),f195(f937(x126801,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12683,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x126831,x126831)),f866(f866(f260(x126831,x126831),x126832),x126832)),f314(x126831,x126833)))),
% 157.76/157.58 inference(rename_variables,[],[4194])).
% 157.76/157.58 cnf(12686,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x126861),x126862),f195(f937(x126861,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12689,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x126891,x126891)),f866(f866(f260(x126891,x126891),x126892),x126892)),f314(x126891,x126893)))),
% 157.76/157.58 inference(rename_variables,[],[4194])).
% 157.76/157.58 cnf(12699,plain,
% 157.76/157.58 (~E(f866(f866(f158(x126991),x126992),x126993),x126993)),
% 157.76/157.58 inference(rename_variables,[],[4741])).
% 157.76/157.58 cnf(12706,plain,
% 157.76/157.58 (P107(f866(f866(f336(x127061),x127062),f250(f937(x127061,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3707])).
% 157.76/157.58 cnf(12707,plain,
% 157.76/157.58 (~E(f866(a119,x127071),x127071)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12710,plain,
% 157.76/157.58 (P107(f866(f866(f336(f931(x127101)),f120(x127101)),f168(x127101,x127102)))),
% 157.76/157.58 inference(rename_variables,[],[3750])).
% 157.76/157.58 cnf(12711,plain,
% 157.76/157.58 (~E(f866(f866(f158(x127111),x127112),x127113),f120(x127111))),
% 157.76/157.58 inference(rename_variables,[],[4748])).
% 157.76/157.58 cnf(12714,plain,
% 157.76/157.58 (P25(x127141,x127141,f5(x127141),x127142)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12717,plain,
% 157.76/157.58 (P107(f866(f866(f336(x127171),f866(x127172,x127173)),f866(f317(x127174,x127171,x127172),f250(f937(x127174,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(12718,plain,
% 157.76/157.58 (P25(x127181,x127181,f5(x127181),x127182)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12721,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127211,a925)),f195(f937(x127211,a925))),x127212))),
% 157.76/157.58 inference(rename_variables,[],[4003])).
% 157.76/157.58 cnf(12722,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127221,a925)),x127222),x127222))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12725,plain,
% 157.76/157.58 (P107(f866(f866(f336(x127251),f866(x127252,x127253)),f866(f317(x127254,x127251,x127252),f250(f937(x127254,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(12726,plain,
% 157.76/157.58 (P25(x127261,x127261,f5(x127261),x127262)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12729,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(f931(x127291),f931(x127291))),f866(f866(f260(f931(x127291),f931(x127291)),f120(x127291)),f120(x127291))),f165(x127291,x127292)))),
% 157.76/157.58 inference(rename_variables,[],[4335])).
% 157.76/157.58 cnf(12733,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x127331),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(12739,plain,
% 157.76/157.58 (E(f866(f866(f141(x127391),x127392),f120(x127391)),x127392)),
% 157.76/157.58 inference(rename_variables,[],[3486])).
% 157.76/157.58 cnf(12740,plain,
% 157.76/157.58 (~E(f866(f866(f158(x127401),x127402),x127403),x127403)),
% 157.76/157.58 inference(rename_variables,[],[4741])).
% 157.76/157.58 cnf(12743,plain,
% 157.76/157.58 (E(f866(f866(f141(x127431),x127432),f120(x127431)),x127432)),
% 157.76/157.58 inference(rename_variables,[],[3486])).
% 157.76/157.58 cnf(12744,plain,
% 157.76/157.58 (~E(f866(f866(f158(x127441),x127442),x127443),x127443)),
% 157.76/157.58 inference(rename_variables,[],[4741])).
% 157.76/157.58 cnf(12747,plain,
% 157.76/157.58 (E(f866(f866(f141(x127471),x127472),f120(x127471)),x127472)),
% 157.76/157.58 inference(rename_variables,[],[3486])).
% 157.76/157.58 cnf(12754,plain,
% 157.76/157.58 (P52(x127541,f271(x127541,x127542))),
% 157.76/157.58 inference(rename_variables,[],[3426])).
% 157.76/157.58 cnf(12757,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127571,a925)),f866(f179(x127571),f866(f143(x127571,x127572),x127573))),f866(f179(x127571),x127573)))),
% 157.76/157.58 inference(rename_variables,[],[4203])).
% 157.76/157.58 cnf(12758,plain,
% 157.76/157.58 (E(f866(f317(x127581,x127581,f5(x127581)),x127582),x127582)),
% 157.76/157.58 inference(rename_variables,[],[3611])).
% 157.76/157.58 cnf(12763,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127631,a925)),x127632),f250(f937(x127631,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12767,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x127671),x127671))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12768,plain,
% 157.76/157.58 (~E(f866(a119,x127681),x127681)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12771,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127711,a925)),f195(f937(x127711,a925))),x127712))),
% 157.76/157.58 inference(rename_variables,[],[4003])).
% 157.76/157.58 cnf(12774,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x127741),x127741))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12777,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127771,a925)),x127772),x127772))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12782,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127821,a925)),x127822),f866(f866(f316(x127821),x127823),x127822)))),
% 157.76/157.58 inference(rename_variables,[],[4001])).
% 157.76/157.58 cnf(12785,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x127851,a925)),x127852),x127852))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12786,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x127861),x127862),f195(f937(x127861,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12789,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x127891),x127892),f195(f937(x127891,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12797,plain,
% 157.76/157.58 (~P107(f866(f866(f243(f937(f936(x127971,x127971),a925)),f866(f317(f936(x127971,x127971),f936(x127971,x127971),f5(f936(x127971,x127971))),f250(f937(f936(x127971,x127971),a925)))),f866(f317(f936(x127971,x127971),f936(x127971,x127971),f5(f936(x127971,x127971))),f195(f937(f936(x127971,x127971),a925)))))),
% 157.76/157.58 inference(scs_inference,[],[3790,11415,12480,12577,12580,12672,12714,12718,12726,3799,3807,3460,12034,3525,4751,4752,3422,3425,3426,4750,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,3610,3758,12238,3475,4728,10730,10830,11295,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3247,3256,3257,3278,3279,3289,3290,3304,3305,3307,3314,3316,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,3486,12739,12743,3492,3501,4013,4321,3385,3752,4107,11751,3451,3382,3412,3872,3407,3393,3394,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,4748,12711,3546,12089,4788,11321,11420,11656,11659,3658,4766,3448,10630,10960,3449,3711,3363,3471,11741,4335,12729,4194,11341,11476,11537,12683,12689,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,4739,11734,3855,4070,4117,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,4794,11856,11887,11922,11929,11965,3993,3759,3761,4142,3581,3583,3557,4778,4736,3944,3743,4795,4328,11623,3877,3594,12110,12113,12548,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,12469,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,3615,10957,10987,10996,10999,11002,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,4036,4376,4784,4048,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,4001,11258,11264,11282,12290,12419,12498,3851,11400,11528,12524,12633,12643,12722,12777,4003,10993,11363,11534,11568,11579,12721,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,11700,12586,12595,4433,11131,12604,12619,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,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% 157.76/157.58 cnf(12798,plain,
% 157.76/157.58 (P25(x127981,x127981,f5(x127981),x127982)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12801,plain,
% 157.76/157.58 (E(f866(f196(f931(x128011)),f176(x128011,x128012,x128013)),x128012)),
% 157.76/157.58 inference(rename_variables,[],[3621])).
% 157.76/157.58 cnf(12804,plain,
% 157.76/157.58 (P26(x128041,x128041,f32(x128041),x128042,x128042)),
% 157.76/157.58 inference(rename_variables,[],[4218])).
% 157.76/157.58 cnf(12807,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x128071),x128071))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12808,plain,
% 157.76/157.58 (P107(f866(f250(f937(x128081,a925)),x128082))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(12811,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x128111),x128112),f195(f937(x128111,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12814,plain,
% 157.76/157.58 (P107(f866(f866(f336(x128141),f866(x128142,x128143)),f866(f317(x128144,x128141,x128142),f250(f937(x128144,a925)))))),
% 157.76/157.58 inference(rename_variables,[],[4160])).
% 157.76/157.58 cnf(12815,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x128151,x128151)),f866(f866(f260(x128151,x128151),x128152),x128152)),f314(x128151,x128153)))),
% 157.76/157.58 inference(rename_variables,[],[4194])).
% 157.76/157.58 cnf(12818,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x128181,x128181)),f866(f866(f260(x128181,x128181),x128182),x128182)),f314(x128181,x128183)))),
% 157.76/157.58 inference(rename_variables,[],[4194])).
% 157.76/157.58 cnf(12821,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x128211),x128211))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(12822,plain,
% 157.76/157.58 (P107(f866(f250(f937(x128221,a925)),x128222))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(12825,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x128251,a925)),x128252),f250(f937(x128251,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12826,plain,
% 157.76/157.58 (P26(x128261,x128261,f32(x128261),x128262,x128262)),
% 157.76/157.58 inference(rename_variables,[],[4218])).
% 157.76/157.58 cnf(12829,plain,
% 157.76/157.58 (P107(f866(f66(x128291),f866(f179(x128291),x128292)))),
% 157.76/157.58 inference(rename_variables,[],[3594])).
% 157.76/157.58 cnf(12834,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(f931(x128341),f931(x128341))),f866(f866(f260(f931(x128341),f931(x128341)),f120(x128341)),f120(x128341))),f866(f866(f296(f931(x128341),f931(x128341),f931(x128341)),f165(x128341,x128342)),f165(x128341,x128342))))),
% 157.76/157.58 inference(scs_inference,[],[4218,12804,3790,11415,12480,12577,12580,12672,12714,12718,12726,3799,3807,3460,12034,3525,4751,4752,3422,3425,3426,4750,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,3610,3758,12238,3475,4728,10730,10830,11295,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3247,3256,3257,3278,3279,3289,3290,3304,3305,3307,3314,3316,3324,3337,3341,4712,4121,11999,3396,11705,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,3486,12739,12743,12747,3492,3501,4013,4321,3621,3385,3752,4107,11751,3451,3382,3412,3872,3407,3393,3394,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,4748,12711,3546,12089,4788,11321,11420,11656,11659,3658,4766,3448,10630,10960,3449,3711,3363,3471,11741,4335,12729,4194,11341,11476,11537,12683,12689,12815,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,4739,11734,3855,4070,4117,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,4794,11856,11887,11922,11929,11965,3993,3759,3761,4142,3581,3583,3557,4778,4736,3944,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,12469,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,3615,10957,10987,10996,10999,11002,11592,12808,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,4036,4376,4784,4048,4082,4769,4772,3532,3536,4771,4770,3867,4472,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,4001,11258,11264,11282,12290,12419,12498,3851,11400,11528,12524,12633,12643,12722,12777,4003,10993,11363,11534,11568,11579,12721,3818,10909,10912,11005,11174,4803,11982,4804,10749,10862,11700,12586,12595,4433,11131,12604,12619,4339,4035,3979,4801,10579,10582,10951,10954,11853,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311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% 157.76/157.58 cnf(12839,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x128391,f937(x128392,a925))),x128393),x128394))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(12842,plain,
% 157.76/157.58 (~P107(f866(f866(f195(f937(x128421,f937(x128422,a925))),x128423),x128424))),
% 157.76/157.58 inference(rename_variables,[],[4804])).
% 157.76/157.58 cnf(12845,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x128451,a925)),x128452),f250(f937(x128451,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12848,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(x128481,x128481)),f866(f866(f260(x128481,x128481),x128482),x128482)),f314(x128481,x128483)))),
% 157.76/157.58 inference(rename_variables,[],[4194])).
% 157.76/157.58 cnf(12851,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),f866(f866(f86(a930),x128511),x128512)),x128512))),
% 157.76/157.58 inference(rename_variables,[],[4801])).
% 157.76/157.58 cnf(12852,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x128521),f866(a119,x128521)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(12855,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x128551,a925)),x128552),f250(f937(x128551,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3936])).
% 157.76/157.58 cnf(12858,plain,
% 157.76/157.58 (E(f866(f292(x128581,x128581),f271(x128581,x128582)),x128582)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12869,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x128691),x128692),f195(f937(x128691,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12870,plain,
% 157.76/157.58 (P107(f866(f866(f336(f936(f931(x128701),f931(x128701))),f866(f866(f260(f931(x128701),f931(x128701)),f120(x128701)),f120(x128701))),f165(x128701,x128702)))),
% 157.76/157.58 inference(rename_variables,[],[4335])).
% 157.76/157.58 cnf(12875,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x128751),x128752),f195(f937(x128751,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12880,plain,
% 157.76/157.58 (P31(x128801,x128802,f120(x128801))),
% 157.76/157.58 inference(rename_variables,[],[3491])).
% 157.76/157.58 cnf(12883,plain,
% 157.76/157.58 (E(f866(f196(f931(x128831)),f176(x128831,x128832,x128833)),x128832)),
% 157.76/157.58 inference(rename_variables,[],[3621])).
% 157.76/157.58 cnf(12886,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x128861),x128862),f195(f937(x128861,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12892,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x128921),x128921))),
% 157.76/157.58 inference(rename_variables,[],[4777])).
% 157.76/157.58 cnf(12895,plain,
% 157.76/157.58 (P107(f866(f866(f336(x128951),x128952),f250(f937(x128951,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3707])).
% 157.76/157.58 cnf(12902,plain,
% 157.76/157.58 (P107(f866(f866(f243(f937(x129021,a925)),x129022),x129022))),
% 157.76/157.58 inference(rename_variables,[],[3851])).
% 157.76/157.58 cnf(12905,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x129051),x129052),f195(f937(x129051,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(12908,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),f2(a1)),f866(f866(f252(a1),f866(f81(a1),x129081)),x129082)))),
% 157.76/157.58 inference(rename_variables,[],[4035])).
% 157.76/157.58 cnf(12913,plain,
% 157.76/157.58 (~E(f866(a119,x129131),x129131)),
% 157.76/157.58 inference(rename_variables,[],[4716])).
% 157.76/157.58 cnf(12915,plain,
% 157.76/157.58 (E(f866(f292(x129151,x129151),f271(x129151,x129152)),x129152)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12919,plain,
% 157.76/157.58 (E(f195(f937(f936(x129191,x129191),a925)),f271(x129191,f195(f937(x129191,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3625])).
% 157.76/157.58 cnf(12921,plain,
% 157.76/157.58 (E(f195(f937(f936(x129211,x129211),a925)),f271(x129211,f195(f937(x129211,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3625])).
% 157.76/157.58 cnf(12934,plain,
% 157.76/157.58 (P37(x129341,f160(x129341,x129342))),
% 157.76/157.58 inference(rename_variables,[],[3422])).
% 157.76/157.58 cnf(12938,plain,
% 157.76/157.58 (E(f866(f292(x129381,x129381),f271(x129381,x129382)),x129382)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12942,plain,
% 157.76/157.58 (E(f866(f292(x129421,x129421),f271(x129421,x129422)),x129422)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12948,plain,
% 157.76/157.58 (E(f866(f292(x129481,x129481),f271(x129481,x129482)),x129482)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12950,plain,
% 157.76/157.58 (E(f866(f292(x129501,x129501),f271(x129501,x129502)),x129502)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12952,plain,
% 157.76/157.58 (E(f866(f292(x129521,x129521),f271(x129521,x129522)),x129522)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12954,plain,
% 157.76/157.58 (P25(x129541,x129541,f5(x129541),x129542)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12956,plain,
% 157.76/157.58 (P25(x129561,x129561,f5(x129561),x129562)),
% 157.76/157.58 inference(rename_variables,[],[3790])).
% 157.76/157.58 cnf(12963,plain,
% 157.76/157.58 (P55(x129631,x129631,f271(x129631,x129632))),
% 157.76/157.58 inference(rename_variables,[],[3525])).
% 157.76/157.58 cnf(12969,plain,
% 157.76/157.58 (P26(x129691,x129691,f32(x129691),x129692,x129692)),
% 157.76/157.58 inference(rename_variables,[],[4218])).
% 157.76/157.58 cnf(12971,plain,
% 157.76/157.58 (P26(x129711,x129711,f32(x129711),x129712,x129712)),
% 157.76/157.58 inference(rename_variables,[],[4218])).
% 157.76/157.58 cnf(12973,plain,
% 157.76/157.58 (P26(x129731,x129731,f32(x129731),x129732,x129732)),
% 157.76/157.58 inference(rename_variables,[],[4218])).
% 157.76/157.58 cnf(12978,plain,
% 157.76/157.58 (E(f866(f292(x129781,x129781),f271(x129781,x129782)),x129782)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12980,plain,
% 157.76/157.58 (E(f866(f292(x129801,x129801),f271(x129801,x129802)),x129802)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12984,plain,
% 157.76/157.58 (E(f866(f292(x129841,x129841),f271(x129841,x129842)),x129842)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(12990,plain,
% 157.76/157.58 (P14(x129901,f937(x129901,a925),f316(x129901))),
% 157.76/157.58 inference(rename_variables,[],[3529])).
% 157.76/157.58 cnf(12999,plain,
% 157.76/157.58 (E(f195(f937(f936(x129991,x129991),a925)),f271(x129991,f195(f937(x129991,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3625])).
% 157.76/157.58 cnf(13007,plain,
% 157.76/157.58 (P56(x130071,f195(f937(x130071,a925)),x130072)),
% 157.76/157.58 inference(rename_variables,[],[3573])).
% 157.76/157.58 cnf(13011,plain,
% 157.76/157.58 (P52(x130111,f271(x130111,x130112))),
% 157.76/157.58 inference(rename_variables,[],[3426])).
% 157.76/157.58 cnf(13016,plain,
% 157.76/157.58 (P38(x130161,f271(x130161,x130162))),
% 157.76/157.58 inference(rename_variables,[],[3423])).
% 157.76/157.58 cnf(13020,plain,
% 157.76/157.58 (P53(x130201,x130202,f271(x130201,x130202))),
% 157.76/157.58 inference(rename_variables,[],[3524])).
% 157.76/157.58 cnf(13022,plain,
% 157.76/157.58 (P53(x130221,x130222,f271(x130221,x130222))),
% 157.76/157.58 inference(rename_variables,[],[3524])).
% 157.76/157.58 cnf(13024,plain,
% 157.76/157.58 (P53(x130241,x130242,f271(x130241,x130242))),
% 157.76/157.58 inference(rename_variables,[],[3524])).
% 157.76/157.58 cnf(13026,plain,
% 157.76/157.58 (P42(x130261,x130262,x130263,x130264,f195(f937(x130261,a925)),x130264)),
% 157.76/157.58 inference(rename_variables,[],[4494])).
% 157.76/157.58 cnf(13033,plain,
% 157.76/157.58 (E(f866(f292(x130331,x130331),f271(x130331,x130332)),x130332)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(13042,plain,
% 157.76/157.58 (P32(x130421,x130422,f120(x130421),f120(x130421))),
% 157.76/157.58 inference(rename_variables,[],[3799])).
% 157.76/157.58 cnf(13044,plain,
% 157.76/157.58 (P32(x130441,x130442,f120(x130441),f120(x130441))),
% 157.76/157.58 inference(rename_variables,[],[3799])).
% 157.76/157.58 cnf(13056,plain,
% 157.76/157.58 (E(f866(f292(x130561,x130561),f271(x130561,x130562)),x130562)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(13057,plain,
% 157.76/157.58 (~E(f866(a119,x130571),f2(a930))),
% 157.76/157.58 inference(rename_variables,[],[4728])).
% 157.76/157.58 cnf(13060,plain,
% 157.76/157.58 (E(f866(f292(x130601,x130601),f271(x130601,x130602)),x130602)),
% 157.76/157.58 inference(rename_variables,[],[3515])).
% 157.76/157.58 cnf(13061,plain,
% 157.76/157.58 (~E(f866(a119,x130611),f2(a930))),
% 157.76/157.58 inference(rename_variables,[],[4728])).
% 157.76/157.58 cnf(13073,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x130731),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(13082,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x130821)),f866(f85(a1),f866(f107(a1),x130822))))),
% 157.76/157.58 inference(rename_variables,[],[4799])).
% 157.76/157.58 cnf(13092,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x130921),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(13095,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x130951),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(13098,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x130981,x130982)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13101,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x131011,x131012)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13104,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x131041,x131042)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13107,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x131071,x131072)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13114,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),f866(f85(a1),f866(f107(a1),x131141))),f866(f107(a1),x131142)))),
% 157.76/157.58 inference(rename_variables,[],[4036])).
% 157.76/157.58 cnf(13116,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),f2(a1)),f866(f110(a1),f2(a1))))),
% 157.76/157.58 inference(scs_inference,[],[4218,12804,12826,12969,12971,3790,11415,12480,12577,12580,12672,12714,12718,12726,12798,12954,3799,12544,13042,13044,3807,3460,12034,3524,13020,13022,13024,3525,12963,3491,12880,4751,4752,12065,4494,13026,3529,12990,3360,3422,12934,3423,13016,3424,3425,3426,12754,13011,4750,3853,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,12768,3610,3573,13007,3758,12238,3475,4728,10730,10830,11295,11395,13057,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3173,3179,3182,3183,3188,3192,3198,3201,3214,3218,3227,3233,3234,3247,3256,3257,3278,3279,3289,3290,3304,3305,3307,3314,3315,3316,3324,3337,4711,3341,3421,4712,3891,4121,11999,3396,11705,3537,3512,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,12648,12858,12915,12938,12942,12948,12950,12952,12978,12980,12984,13033,13056,3486,12739,12743,12747,3492,3501,4013,4321,3621,12801,12883,3385,3752,4107,11751,3609,3451,3382,3412,3872,3407,3607,4227,4115,3934,4674,3393,3394,3366,3372,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,12744,4748,12711,3546,12089,4150,4788,11321,11420,11656,11659,3953,3658,3878,4766,3625,12919,12921,12999,3448,10630,10960,3449,3711,3440,3363,3471,11741,4335,12729,12870,4194,11341,11476,11537,12683,12689,12815,12818,12848,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,3771,4739,11734,3895,3855,4070,4117,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,12733,13073,13092,4794,11856,11887,11922,11929,11965,3993,3759,3761,12283,13098,13101,13104,4142,3581,3583,3557,4778,4736,3944,4257,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,12825,12845,12855,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,3630,12469,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,12807,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,12706,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,12811,12869,12875,12886,3615,10957,10987,10996,10999,11002,11592,12808,3654,3647,4074,4011,10609,11988,12016,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,4036,12116,4376,4784,4048,4082,4769,4772,4773,3532,3536,4771,4770,4501,3867,4472,11839,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,4001,11258,11264,11282,12290,12419,12498,3851,11400,11528,12524,12633,12643,12722,12777,12785,4333,4003,10993,11363,11534,11568,11579,12721,3818,10909,10912,11005,11174,3820,4803,11982,4799,13082,4804,10749,10862,11700,12586,12595,12639,12839,12842,4433,11131,12604,12619,4339,4035,3979,3980,4801,10579,10582,10951,10954,11853,12048,4802,11962,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545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% 157.76/157.58 cnf(13119,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x131191),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(13120,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x131201),x131201))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(13127,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x131271),f866(a119,x131271)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(13134,plain,
% 157.76/157.58 (P107(f866(f866(f243(a1),x131341),x131341))),
% 157.76/157.58 inference(rename_variables,[],[3556])).
% 157.76/157.58 cnf(13137,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x131371,x131372)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13140,plain,
% 157.76/157.58 (P107(f866(f66(a930),f312(a930,x131401,x131402)))),
% 157.76/157.58 inference(rename_variables,[],[3761])).
% 157.76/157.58 cnf(13143,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x131431),x131431))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(13144,plain,
% 157.76/157.58 (~E(f866(a119,x131441),f2(a930))),
% 157.76/157.58 inference(rename_variables,[],[4728])).
% 157.76/157.58 cnf(13161,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f50(a930,x131611,x131612)),x131611))),
% 157.76/157.58 inference(rename_variables,[],[4011])).
% 157.76/157.58 cnf(13166,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x131661),f866(a119,x131661)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(13169,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x131691),f866(a119,x131691)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(13170,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a930),x131701),f2(a930)))),
% 157.76/157.58 inference(rename_variables,[],[4781])).
% 157.76/157.58 cnf(13179,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x131791)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(13180,plain,
% 157.76/157.58 (P107(f866(f250(f937(x131801,a925)),x131802))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(13183,plain,
% 157.76/157.58 (~P107(f866(f866(f244(a1),f866(f107(a1),x131831)),f2(a1)))),
% 157.76/157.58 inference(rename_variables,[],[4794])).
% 157.76/157.58 cnf(13184,plain,
% 157.76/157.58 (P107(f866(f250(f937(x131841,a925)),x131842))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(13187,plain,
% 157.76/157.58 (P107(f866(f250(f937(x131871,a925)),x131872))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(13190,plain,
% 157.76/157.58 (P107(f866(f250(f937(x131901,a925)),x131902))),
% 157.76/157.58 inference(rename_variables,[],[3615])).
% 157.76/157.58 cnf(13193,plain,
% 157.76/157.58 (P57(a930,x131931,x131931)),
% 157.76/157.58 inference(rename_variables,[],[3460])).
% 157.76/157.58 cnf(13201,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x132011),x132012),f195(f937(x132011,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(13202,plain,
% 157.76/157.58 (P107(f866(f66(x132021),f195(f937(x132021,a925))))),
% 157.76/157.58 inference(rename_variables,[],[3630])).
% 157.76/157.58 cnf(13205,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x132051),x132051))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(13214,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),f2(a930)),x132141))),
% 157.76/157.58 inference(rename_variables,[],[3575])).
% 157.76/157.58 cnf(13217,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x132171),x132172),f195(f937(x132171,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(13220,plain,
% 157.76/157.58 (~P107(f866(f866(f336(x132201),x132202),f195(f937(x132201,a925))))),
% 157.76/157.58 inference(rename_variables,[],[4790])).
% 157.76/157.58 cnf(13223,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x132231),x132231))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(13231,plain,
% 157.76/157.58 (P107(f866(f866(f244(a930),x132311),f866(a119,x132311)))),
% 157.76/157.58 inference(rename_variables,[],[3622])).
% 157.76/157.58 cnf(13234,plain,
% 157.76/157.58 (P107(f866(f866(f243(a930),x132341),x132341))),
% 157.76/157.58 inference(rename_variables,[],[3555])).
% 157.76/157.58 cnf(13239,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x132391),x132391))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13242,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x132421),x132421))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13245,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x132451),x132451))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13248,plain,
% 157.85/157.58 (E(f866(f866(f23(f937(x132481,a925)),f195(f937(x132481,a925))),x132482),f195(f937(x132481,a925)))),
% 157.85/157.58 inference(rename_variables,[],[3822])).
% 157.85/157.58 cnf(13249,plain,
% 157.85/157.58 (P107(f866(f66(x132491),f195(f937(x132491,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13252,plain,
% 157.85/157.58 (E(f866(f866(f23(f937(x132521,a925)),f195(f937(x132521,a925))),x132522),f195(f937(x132521,a925)))),
% 157.85/157.58 inference(rename_variables,[],[3822])).
% 157.85/157.58 cnf(13253,plain,
% 157.85/157.58 (P107(f866(f66(x132531),f195(f937(x132531,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13256,plain,
% 157.85/157.58 (E(f866(f866(f23(f937(x132561,a925)),f195(f937(x132561,a925))),x132562),f195(f937(x132561,a925)))),
% 157.85/157.58 inference(rename_variables,[],[3822])).
% 157.85/157.58 cnf(13257,plain,
% 157.85/157.58 (P107(f866(f66(x132571),f195(f937(x132571,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13260,plain,
% 157.85/157.58 (E(f866(f866(f23(f937(x132601,a925)),f195(f937(x132601,a925))),x132602),f195(f937(x132601,a925)))),
% 157.85/157.58 inference(rename_variables,[],[3822])).
% 157.85/157.58 cnf(13261,plain,
% 157.85/157.58 (P107(f866(f66(x132611),f195(f937(x132611,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13265,plain,
% 157.85/157.58 (E(f866(f292(x132651,x132651),f271(x132651,x132652)),x132652)),
% 157.85/157.58 inference(rename_variables,[],[3515])).
% 157.85/157.58 cnf(13270,plain,
% 157.85/157.58 (E(f866(f866(f23(f937(x132701,a925)),f195(f937(x132701,a925))),x132702),f195(f937(x132701,a925)))),
% 157.85/157.58 inference(rename_variables,[],[3822])).
% 157.85/157.58 cnf(13271,plain,
% 157.85/157.58 (P107(f866(f66(x132711),f195(f937(x132711,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13275,plain,
% 157.85/157.58 (P107(f866(f66(x132751),f195(f937(x132751,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3630])).
% 157.85/157.58 cnf(13278,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x132781),x132781))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13282,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x132821),x132821))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13289,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x132891),x132891))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13302,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x133021),x133021))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13305,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x133051),x133051))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13315,plain,
% 157.85/157.58 (~P107(f866(f866(f336(x133151),x133152),f195(f937(x133151,a925))))),
% 157.85/157.58 inference(rename_variables,[],[4790])).
% 157.85/157.58 cnf(13326,plain,
% 157.85/157.58 (P107(f866(f866(f336(x133261),x133262),f250(f937(x133261,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3707])).
% 157.85/157.58 cnf(13327,plain,
% 157.85/157.58 (E(f866(f199(x133271,x133272),x133273),f128(x133271,x133272))),
% 157.85/157.58 inference(rename_variables,[],[3469])).
% 157.85/157.58 cnf(13330,plain,
% 157.85/157.58 (P107(f866(f866(f336(x133301),f866(x133302,x133303)),f866(f317(x133304,x133301,x133302),f250(f937(x133304,a925)))))),
% 157.85/157.58 inference(rename_variables,[],[4160])).
% 157.85/157.58 cnf(13334,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x133341,a925)),x133342),f250(f937(x133341,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3936])).
% 157.85/157.58 cnf(13337,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x133371,a925)),x133372),x133372))),
% 157.85/157.58 inference(rename_variables,[],[3851])).
% 157.85/157.58 cnf(13343,plain,
% 157.85/157.58 (~P107(f866(f866(f244(a930),x133431),f2(a930)))),
% 157.85/157.58 inference(rename_variables,[],[4781])).
% 157.85/157.58 cnf(13344,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x133441),x133441))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13348,plain,
% 157.85/157.58 (~P107(f866(f866(f244(a930),x133481),f2(a930)))),
% 157.85/157.58 inference(rename_variables,[],[4781])).
% 157.85/157.58 cnf(13349,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x133491),x133491))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13354,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x133541),x133541))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13361,plain,
% 157.85/157.58 (E(f866(f866(f16(x133611,x133612),x133613),x133614),x133613)),
% 157.85/157.58 inference(rename_variables,[],[3546])).
% 157.85/157.58 cnf(13364,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x133641,a925)),f866(f179(x133641),f183(x133641,x133642,x133643))),f866(f179(x133641),x133642)))),
% 157.85/157.58 inference(rename_variables,[],[4251])).
% 157.85/157.58 cnf(13368,plain,
% 157.85/157.58 (~P107(f866(f866(f244(a930),x133681),f2(a930)))),
% 157.85/157.58 inference(rename_variables,[],[4781])).
% 157.85/157.58 cnf(13369,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x133691),x133691))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13373,plain,
% 157.85/157.58 (~P107(f866(f866(f244(a930),x133731),f2(a930)))),
% 157.85/157.58 inference(rename_variables,[],[4781])).
% 157.85/157.58 cnf(13374,plain,
% 157.85/157.58 (P107(f866(f866(f243(a1),x133741),x133741))),
% 157.85/157.58 inference(rename_variables,[],[3556])).
% 157.85/157.58 cnf(13378,plain,
% 157.85/157.58 (~P107(f866(f866(f243(f937(a930,a925)),f310(a930,f866(a119,x133781),f866(a119,x133781))),f310(a930,x133782,x133781)))),
% 157.85/157.58 inference(scs_inference,[],[4218,12804,12826,12969,12971,3790,11415,12480,12577,12580,12672,12714,12718,12726,12798,12954,3799,12544,13042,13044,3807,3460,12034,12037,3524,13020,13022,13024,3525,12963,3491,12880,4751,4752,12065,4494,13026,3529,12990,3360,3422,12934,3423,13016,3424,3425,3426,12754,13011,4750,3853,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,12768,3610,3573,13007,3758,12238,3475,4728,10730,10830,11295,11395,13057,13061,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3173,3174,3178,3179,3182,3183,3188,3192,3198,3201,3211,3214,3218,3227,3233,3234,3241,3247,3253,3256,3257,3258,3259,3272,3278,3279,3285,3289,3290,3304,3305,3307,3308,3314,3315,3316,3317,3324,3337,4711,3341,3421,4712,3891,4121,11999,3396,11705,3537,3512,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,12648,12858,12915,12938,12942,12948,12950,12952,12978,12980,12984,13033,13056,13060,3486,12739,12743,12747,3492,3501,4013,4321,3469,13327,3621,12801,12883,3385,3752,4107,11751,3609,3451,3382,3412,3872,3407,3607,4227,4115,3934,4674,3393,3394,3366,3372,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,12744,4748,12711,3546,12089,12092,4150,4788,11321,11420,11656,11659,3953,3658,3878,4766,3625,12919,12921,12999,3448,10630,10960,3449,3711,3440,3363,3471,11741,4335,12729,12870,4194,11341,11476,11537,12683,12689,12815,12818,12848,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,3771,4739,11734,3895,3855,3897,4070,3822,13248,13252,13256,13260,13270,4117,12574,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,12852,13127,13166,13169,13231,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,12733,13073,13092,13095,13119,13170,13343,13348,13368,4794,11856,11887,11922,11929,11965,13179,13183,3993,3759,3761,12283,13098,13101,13104,13107,13137,4142,3581,3583,3557,4778,3447,4736,3944,4257,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,12829,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,12825,12845,12855,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,12821,13120,13143,13205,13223,13234,13239,13242,13245,13278,13289,13302,13354,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,12364,13134,13282,13305,13344,13349,13369,3630,12469,13202,13249,13253,13257,13261,13271,13275,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,12807,12892,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,12706,12895,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,12811,12869,12875,12886,12905,13201,13217,13220,3615,10957,10987,10996,10999,11002,11592,12808,12822,13180,13184,13187,13190,3654,3647,4074,4011,10609,11988,12016,13161,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,12592,4036,12116,13114,4376,3765,4784,4048,4082,4769,4772,4773,3532,3536,4771,4770,4501,3867,4472,11839,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,12814,4001,11258,11264,11282,12290,12419,12498,3851,11400,11528,12524,12633,12643,12722,12777,12785,12902,4333,4003,10993,11363,11534,11568,11579,12721,3818,10909,10912,11005,11174,3820,4803,11982,4799,13082,4804,10749,10862,11700,12586,12595,12639,12839,12842,4433,11131,12604,12619,4339,4035,12908,3979,3980,4801,10579,10582,10951,10954,11853,12048,12851,4802,11962,12053,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410,6411,6441,6458,6510,6547,6549,6570,6571,6578,6583,6584,6588,6602,6617,6638,6639,6644,6647,6656,6671,6694,6700,6702,6717,6718,6721,6722,6724,6726,6727,6728,6730,6732,6734,6740,6741,6743,6744,6750,6752,6797,6802,6818,6820,6821,6822,6855,6860,6862,6867,6868,6876,6880,6892,6915,6916,6918,6919,6930,6934,6937,6956,6959,6977,7006,7007,7008,7014,7028,7047,7049,7051,7053,7058,7064,7067,7081,7086,7087,7122,7123,7124,7139,7140,7142,7143,7144,7162,7164,7179,7205,7227,7238,7240,7242,7244,7245,7276,7277,7281,7282,7289,7290,7292,7294,7316,7325,7326,7337,7347,7387,7397,7401,7408,7419,7424,7426,7433,7441,7454,7471,7492,7494,7513,7568,7569,7570,7572,7574,7578,7583,7645,7674,7689,7705,7736,7739,7761,7784,7802,7805,7806,7816,7836,7838,7840,7842,7843,7844,7869,7895,7896,7927,7929,7930,7931,7936,7957,7975,7980,7987,7989,7997,8009,8010,8012,8033,8039,8060,8126,8127,8128,8175,8181,8182,8206,8207,8224,8225,8226,8283,8284,8313,8342,8351,8362,8374,8403,8407,8413,8425,8443,8448,8470,8515,8545,8559,8578,8581,8607,8633,8690,8691,8694,8695,8765,8799,8800,8801,8802,8829,8861,8890,8898,8899,8940,8961,9006,9022,9068,9071,9086,9093,9137,9180,9181,9199,9200,9214,9331,9337,9341,9361,9372,9395,9397,9400,9406,9408,9409,9419,9420,9439,9445,9455,9462,9505,9524,9579,9580,9586,9625,9648,9653,9692,9702,9705,9706,9708,9709,9721,9744,9759,9768,9769,9771,9773,9802,9923,9924,9974,9975,10015,10050,10161,10219,10285,10368,10386,10391,10411,3,2875,2876,2877,2879,2880,2886,2887,2889,2890,2891,2892,2893,2894,2896,2897,2898,2906,2909,2910,2911,2912,2913,2917,2918,2919,2920,2921,2927,2928,2929,2930,2931,2932,2933,2934,2936,2939,2942,2943,2946,2947,2948,2951,2953,2955,2956,2957,2964,2965,2966,2968,2969,2971,2972,2986,2988,2991,2992,2994,2995,3003,3004,3012,3013,3014,3015,3018,3019,3020,3026,3033,3034,3035,3040,3070,3071,3091,3093,3094,3095,3096,3116,3117,3122,3144,5397,5400,5531,5570,5716,5717,5718,5802,5904,5936,5970,5986,5988,5994,6056,6057,6058,6059,6067,6104,6236,6276,6286,6308,6342,6379,6526,6531,6568,6569,6593,6595,6597,6604,6605,6606,6607,6608,6609,6610,6611,6695,6764,6765,6854,6887,6888,6927,6928,6947,7066,7080,7134,7152,7153,7159,7180,7211,7213,7259,7279,7280,7298,7299,7336,7381,7382,7478,7549,7550,7551,7552,7567,7599,7650,7651,7660,7665,7666,7677,7708,7709,7710,7711,7850,7851,7853,7855,7861,7862,7970,8068,8074,8075,8085,8123,8124,8202,8242,8296,8318,8319,8389,8483,8555,8556,8560,8593,8654,8655,8722,8741])).
% 157.85/157.58 cnf(13379,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x133791),x133791))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13381,plain,
% 157.85/157.58 (~P107(f866(f866(f244(f937(a930,a925)),f310(a930,f866(a119,x133811),f866(a119,x133811))),f310(a930,x133812,x133811)))),
% 157.85/157.58 inference(scs_inference,[],[4218,12804,12826,12969,12971,3790,11415,12480,12577,12580,12672,12714,12718,12726,12798,12954,3799,12544,13042,13044,3807,3460,12034,12037,3524,13020,13022,13024,3525,12963,3491,12880,4751,4752,12065,4494,13026,3529,12990,3360,3422,12934,3423,13016,3424,3425,3426,12754,13011,4750,3853,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,12768,3610,3573,13007,3758,12238,3475,4728,10730,10830,11295,11395,13057,13061,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3173,3174,3178,3179,3182,3183,3188,3192,3198,3201,3211,3214,3218,3227,3233,3234,3241,3247,3253,3256,3257,3258,3259,3272,3278,3279,3285,3289,3290,3304,3305,3307,3308,3314,3315,3316,3317,3324,3337,4711,3341,3421,4712,3891,4121,11999,3396,11705,3537,3512,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,12648,12858,12915,12938,12942,12948,12950,12952,12978,12980,12984,13033,13056,13060,3486,12739,12743,12747,3492,3501,4013,4321,3469,13327,3621,12801,12883,3385,3752,4107,11751,3609,3451,3382,3412,3872,3407,3607,4227,4115,3934,4674,3393,3394,3366,3372,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,12744,4748,12711,3546,12089,12092,4150,4788,11321,11420,11656,11659,3953,3658,3878,4766,3625,12919,12921,12999,3448,10630,10960,3449,3711,3440,3363,3471,11741,4335,12729,12870,4194,11341,11476,11537,12683,12689,12815,12818,12848,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,3771,4739,11734,3895,3855,3897,4070,3822,13248,13252,13256,13260,13270,4117,12574,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,12852,13127,13166,13169,13231,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,12733,13073,13092,13095,13119,13170,13343,13348,13368,4794,11856,11887,11922,11929,11965,13179,13183,3993,3759,3761,12283,13098,13101,13104,13107,13137,4142,3581,3583,3557,4778,3447,4736,3944,4257,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,12829,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,12825,12845,12855,4798,11091,11500,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,12821,13120,13143,13205,13223,13234,13239,13242,13245,13278,13289,13302,13354,13379,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,12364,13134,13282,13305,13344,13349,13369,3630,12469,13202,13249,13253,13257,13261,13271,13275,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,12807,12892,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,12706,12895,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,12811,12869,12875,12886,12905,13201,13217,13220,3615,10957,10987,10996,10999,11002,11592,12808,12822,13180,13184,13187,13190,3654,3647,4074,4011,10609,11988,12016,13161,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,3575,10990,11148,11218,12017,12167,12369,12567,12592,4036,12116,13114,4376,3765,4784,4048,4082,4769,4772,4773,3532,3536,4771,4770,4501,3867,4472,11839,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,12814,4001,11258,11264,11282,12290,12419,12498,3851,11400,11528,12524,12633,12643,12722,12777,12785,12902,4333,4003,10993,11363,11534,11568,11579,12721,3818,10909,10912,11005,11174,3820,4803,11982,4799,13082,4804,10749,10862,11700,12586,12595,12639,12839,12842,4433,11131,12604,12619,4339,4035,12908,3979,3980,4801,10579,10582,10951,10954,11853,12048,12851,4802,11962,12053,4004,10915,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,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,7211,7213,7259,7279,7280,7298,7299,7336,7381,7382,7478,7549,7550,7551,7552,7567,7599,7650,7651,7660,7665,7666,7677,7708,7709,7710,7711,7850,7851,7853,7855,7861,7862,7970,8068,8074,8075,8085,8123,8124,8202,8242,8296,8318,8319,8389,8483,8555,8556,8560,8593,8654,8655,8722,8741,8742])).
% 157.85/157.58 cnf(13382,plain,
% 157.85/157.58 (P107(f866(f866(f243(a930),x133821),x133821))),
% 157.85/157.58 inference(rename_variables,[],[3555])).
% 157.85/157.58 cnf(13385,plain,
% 157.85/157.58 (~P107(f866(f866(f243(a930),f866(a119,x133851)),x133851))),
% 157.85/157.58 inference(rename_variables,[],[4787])).
% 157.85/157.58 cnf(13391,plain,
% 157.85/157.58 (P107(f866(f866(f336(x133911),f866(x133912,x133913)),f866(f317(x133914,x133911,x133912),f250(f937(x133914,a925)))))),
% 157.85/157.58 inference(rename_variables,[],[4160])).
% 157.85/157.58 cnf(13392,plain,
% 157.85/157.58 (P25(x133921,x133921,f5(x133921),x133922)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13397,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x133971,a925)),x133972),f250(f937(x133971,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3936])).
% 157.85/157.58 cnf(13398,plain,
% 157.85/157.58 (P25(x133981,x133981,f5(x133981),x133982)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13402,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x134021,a925)),x134022),f250(f937(x134021,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3936])).
% 157.85/157.58 cnf(13403,plain,
% 157.85/157.58 (P25(x134031,x134031,f5(x134031),x134032)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13407,plain,
% 157.85/157.58 (P25(x134071,x134071,f5(x134071),x134072)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13410,plain,
% 157.85/157.58 (~P107(f866(f866(f244(f937(x134101,a925)),x134102),f195(f937(x134101,a925))))),
% 157.85/157.58 inference(rename_variables,[],[4798])).
% 157.85/157.58 cnf(13413,plain,
% 157.85/157.58 (P25(x134131,x134131,f5(x134131),x134132)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13416,plain,
% 157.85/157.58 (P25(x134161,x134161,f5(x134161),x134162)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13422,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x134221,a925)),x134222),f250(f937(x134221,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3936])).
% 157.85/157.58 cnf(13427,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x134271,a925)),f195(f937(x134271,a925))),x134272))),
% 157.85/157.58 inference(rename_variables,[],[4003])).
% 157.85/157.58 cnf(13431,plain,
% 157.85/157.58 (E(f866(f292(x134311,x134311),f271(x134311,x134312)),x134312)),
% 157.85/157.58 inference(rename_variables,[],[3515])).
% 157.85/157.58 cnf(13435,plain,
% 157.85/157.58 (~P107(f866(f866(f336(x134351),x134352),f195(f937(x134351,a925))))),
% 157.85/157.58 inference(rename_variables,[],[4790])).
% 157.85/157.58 cnf(13440,plain,
% 157.85/157.58 (P25(x134401,x134401,f5(x134401),x134402)),
% 157.85/157.58 inference(rename_variables,[],[3790])).
% 157.85/157.58 cnf(13443,plain,
% 157.85/157.58 (P107(f866(f866(f243(f937(x134431,a925)),x134432),f250(f937(x134431,a925))))),
% 157.85/157.58 inference(rename_variables,[],[3936])).
% 157.85/157.58 cnf(13451,plain,
% 157.85/157.58 (E(f866(f866(f16(x134511,x134512),x134513),x134514),x134513)),
% 157.85/157.58 inference(rename_variables,[],[3546])).
% 157.85/157.58 cnf(13454,plain,
% 157.85/157.58 (~P107(f866(f866(f336(x134541),x134542),f195(f937(x134541,a925))))),
% 157.85/157.58 inference(rename_variables,[],[4790])).
% 157.85/157.58 cnf(13457,plain,
% 157.85/157.58 (~P107(f866(f866(f336(x134571),x134572),f195(f937(x134571,a925))))),
% 157.85/157.58 inference(rename_variables,[],[4790])).
% 157.85/157.58 cnf(13460,plain,
% 157.85/157.58 (P107(f866(f866(f244(a930),x134601),f866(a119,x134601)))),
% 157.85/157.58 inference(rename_variables,[],[3622])).
% 157.85/157.58 cnf(13461,plain,
% 157.85/157.58 (~E(f866(a119,x134611),x134611)),
% 157.85/157.58 inference(rename_variables,[],[4716])).
% 157.85/157.58 cnf(13464,plain,
% 157.85/157.58 (P107(f866(f866(f244(a930),x134641),f866(a119,f866(f866(f86(a930),x134642),x134641))))),
% 157.85/157.58 inference(rename_variables,[],[4004])).
% 157.85/157.58 cnf(13465,plain,
% 157.85/157.58 (P107(f866(f866(f244(a930),x134651),f866(a119,x134651)))),
% 157.85/157.58 inference(rename_variables,[],[3622])).
% 157.85/157.58 cnf(13467,plain,
% 157.85/157.58 (~E(f866(f866(f87(a930),f866(a119,f2(a930))),f126(x134671)),f866(f866(f87(a930),f866(a119,f2(a930))),f133(x134671,x134672,x134673)))),
% 157.85/157.58 inference(scs_inference,[],[4218,12804,12826,12969,12971,12973,3790,11415,12480,12577,12580,12672,12714,12718,12726,12798,12954,12956,13392,13398,13403,13407,13413,13416,3799,12544,13042,13044,3807,3460,12034,12037,3524,13020,13022,13024,3525,12963,3491,12880,4751,4752,12065,4494,13026,3529,12990,3360,3422,12934,3423,13016,3424,3425,3426,12754,13011,4750,3853,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,12768,12913,13461,3610,3573,13007,3758,12238,3475,4728,10730,10830,11295,11395,13057,13061,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3173,3174,3178,3179,3182,3183,3188,3192,3198,3201,3211,3214,3218,3227,3233,3234,3241,3247,3253,3256,3257,3258,3259,3272,3278,3279,3285,3289,3290,3304,3305,3307,3308,3314,3315,3316,3317,3324,3337,4711,3341,3421,4712,3891,4121,11999,3396,11705,3537,3512,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,12648,12858,12915,12938,12942,12948,12950,12952,12978,12980,12984,13033,13056,13060,13265,3486,12739,12743,12747,3492,3501,4013,4321,3469,13327,3621,12801,12883,3385,3386,3752,4107,11751,3609,3451,3382,3412,3872,3407,3607,4227,4115,3934,4674,3393,3394,3366,3372,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,12744,4748,12711,3546,12089,12092,13361,4150,4788,11321,11420,11656,11659,3953,3543,3658,3878,4766,3625,12919,12921,12999,3448,10630,10960,3449,4775,3711,3440,3363,3471,11741,4335,12729,12870,4194,11341,11476,11537,12683,12689,12815,12818,12848,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,11548,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,3771,4739,11734,3895,3855,3897,4070,3822,13248,13252,13256,13260,13270,4117,12574,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,12852,13127,13166,13169,13231,13460,4006,11985,3539,3634,11813,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,12733,13073,13092,13095,13119,13170,13343,13348,13368,4794,11856,11887,11922,11929,11965,13179,13183,3993,3759,3761,12283,13098,13101,13104,13107,13137,4142,3581,3583,3557,4778,3447,4736,3944,4257,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,12829,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,4251,11344,12477,12547,12607,12651,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,12825,12845,12855,13334,13397,13402,13422,4798,11091,11500,12611,13410,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,12821,13120,13143,13205,13223,13234,13239,13242,13245,13278,13289,13302,13354,13379,13382,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,12364,13134,13282,13305,13344,13349,13369,3630,12469,13202,13249,13253,13257,13261,13271,13275,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,12807,12892,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,12706,12895,13326,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,12811,12869,12875,12886,12905,13201,13217,13220,13315,13435,13454,3615,10957,10987,10996,10999,11002,11592,12808,12822,13180,13184,13187,13190,3654,3647,4074,4011,10609,11988,12016,13161,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,13385,3575,10990,11148,11218,12017,12167,12369,12567,12592,4036,12116,13114,4376,3765,4784,4048,4082,4769,4772,4773,3532,3536,4771,4770,4501,3867,11981,4472,11839,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,12814,13330,13391,4001,11258,11264,11282,12290,12419,12498,12782,3851,11400,11528,12524,12633,12643,12722,12777,12785,12902,4333,4003,10993,11363,11534,11568,11579,12721,12771,3818,10909,10912,11005,11174,3820,4803,11982,4799,13082,4804,10749,10862,11700,12586,12595,12639,12839,12842,4433,11131,12604,12619,12642,4339,4035,12908,3979,3980,4801,10579,10582,10951,10954,11853,12048,12851,4802,11962,12053,4004,10915,11180,4271,4819,4845,4900,4904,4934,4949,4956,4958,4994,4999,5029,5035,5121,5147,5148,5163,5185,5213,5214,5236,5237,5251,5254,5279,5285,5301,5304,5305,5306,5311,5312,5335,5359,5361,5362,5373,5378,5384,5420,5421,5429,5437,5441,5443,5446,5458,5460,5466,5473,5474,5487,5493,5496,5497,5501,5534,5548,5557,5559,5560,5563,5564,5565,5575,5577,5583,5584,5585,5591,5595,5596,5597,5605,5609,5610,5615,5628,5636,5648,5650,5658,5660,5661,5664,5668,5694,5708,5709,5724,5736,5758,5764,5786,5787,5791,5813,5821,5822,5827,5828,5838,5841,5855,5859,5868,5869,5871,5872,5888,5893,5902,5903,5914,5921,5937,5941,5944,5950,5951,5952,5955,5960,5996,5997,6000,6002,6004,6006,6007,6008,6010,6012,6014,6019,6026,6041,6055,6061,6062,6065,6076,6077,6084,6088,6090,6095,6105,6142,6155,6164,6167,6176,6180,6181,6182,6183,6184,6188,6193,6203,6209,6227,6230,6240,6271,6285,6309,6326,6327,6330,6344,6346,6348,6350,6365,6366,6369,6371,6374,6375,6389,6397,6398,6399,6401,6403,6438,6439,6444,6447,6453,6457,6491,6493,6495,6497,6507,6509,6511,6517,6519,6524,6527,6535,6543,6545,6546,6552,6573,6574,6575,6576,6577,6580,6587,6592,6625,6626,6629,6630,6631,6633,6634,6635,6636,6646,6678,6679,6680,6689,6712,6713,6733,6735,6747,6748,6754,6785,6787,6803,6807,6842,6844,6845,6897,6920,6964,6983,6992,6993,6994,6995,7012,7013,7020,7032,7035,7037,7039,7040,7041,7043,7057,7069,7070,7071,7084,7137,7149,7151,7172,7173,7207,7214,7219,7249,7278,7334,7363,7418,7439,7447,7450,7510,7523,7582,7584,7598,7607,7608,7609,7625,7629,7631,7678,7688,7691,7706,7753,7755,7758,7800,7801,7819,7887,7905,7928,7951,7963,7978,7990,8001,8002,8028,8030,8032,8041,8077,8088,8113,8172,8204,8237,8276,8292,8294,8310,8311,8371,8382,8447,8471,8490,8517,8518,8557,8558,8575,8614,8616,8618,8625,8639,8643,8658,8679,8687,8689,8699,8704,8708,8709,8710,8711,8712,8713,8732,8748,8749,8767,8768,8773,8774,8775,8776,8777,8795,8796,8797,8807,8820,8823,8834,8839,8841,8843,8844,8845,8852,8858,8866,8869,8886,8887,8896,8897,8905,8924,8937,8941,8962,8984,8985,8988,8989,8995,9004,9005,9028,9039,9049,9050,9051,9054,9077,9078,9089,9140,9146,9152,9154,9170,9173,9184,9185,9186,9197,9261,9292,9293,9294,9309,9326,9334,9335,9363,9364,9432,9463,9469,9479,9480,9481,9491,9520,9536,9540,9544,9566,9567,9594,9656,9661,9664,9696,9697,9698,9722,9723,9739,9760,9766,9778,9803,9824,9833,9834,9835,9836,9851,9853,9858,9888,9889,9895,9896,9941,9942,9953,9954,9979,9998,10000,10001,10009,10014,10021,10045,10079,10081,10085,10136,10176,10177,10179,10189,10190,10210,10215,10306,10394,10395,10396,10397,10460,10478,2,8,9,9507,4832,4833,4851,4893,4895,4896,4919,4927,4928,4938,4983,4985,5034,5164,5165,5178,5202,5257,5258,5264,5265,5267,5269,5278,5281,5282,5290,5302,5303,5309,5330,5331,5348,5353,5354,5355,5356,5360,5368,5371,5372,5379,5434,5439,5440,5445,5452,5484,5494,5499,5515,5532,5533,5540,5541,5542,5553,5571,5573,5574,5581,5588,5589,5601,5602,5603,5604,5606,5607,5611,5612,5613,5614,5644,5645,5646,5654,5655,5656,5657,5700,5705,5707,5743,5745,5746,5748,5749,5751,5752,5754,5763,5768,5769,5770,5772,5774,5775,5776,5777,5778,5779,5788,5789,5801,5804,5816,5832,5833,5836,5849,5851,5852,5853,5880,5890,5905,5906,5915,5916,5918,5920,5925,5962,5967,5969,6028,6063,6064,6069,6075,6078,6079,6080,6081,6096,6097,6102,6106,6107,6116,6139,6168,6187,6191,6192,6194,6217,6221,6224,6225,6226,6238,6242,6252,6253,6287,6288,6292,6311,6314,6317,6338,6339,6367,6370,6378,6388,6396,6400,6408,6409,6410,6411,6441,6458,6510,6547,6549,6570,6571,6578,6583,6584,6588,6602,6617,6638,6639,6644,6647,6656,6671,6694,6700,6702,6717,6718,6721,6722,6724,6726,6727,6728,6730,6732,6734,6740,6741,6743,6744,6750,6752,6797,6802,6818,6820,6821,6822,6855,6860,6862,6867,6868,6876,6880,6892,6915,6916,6918,6919,6930,6934,6937,6956,6959,6977,7006,7007,7008,7014,7028,7047,7049,7051,7053,7058,7064,7067,7081,7086,7087,7122,7123,7124,7139,7140,7142,7143,7144,7162,7164,7179,7205,7227,7238,7240,7242,7244,7245,7276,7277,7281,7282,7289,7290,7292,7294,7316,7325,7326,7337,7347,7387,7397,7401,7408,7419,7424,7426,7433,7441,7454,7471,7492,7494,7513,7568,7569,7570,7572,7574,7578,7583,7645,7674,7689,7705,7736,7739,7761,7784,7802,7805,7806,7816,7836,7838,7840,7842,7843,7844,7869,7895,7896,7927,7929,7930,7931,7936,7957,7975,7980,7987,7989,7997,8009,8010,8012,8033,8039,8060,8126,8127,8128,8175,8181,8182,8206,8207,8224,8225,8226,8283,8284,8313,8342,8351,8362,8374,8403,8407,8413,8425,8443,8448,8470,8515,8545,8559,8578,8581,8607,8633,8690,8691,8694,8695,8765,8799,8800,8801,8802,8829,8861,8890,8898,8899,8940,8961,9006,9022,9068,9071,9086,9093,9137,9180,9181,9199,9200,9214,9331,9337,9341,9361,9372,9395,9397,9400,9406,9408,9409,9419,9420,9439,9445,9455,9462,9505,9524,9579,9580,9586,9625,9648,9653,9692,9702,9705,9706,9708,9709,9721,9744,9759,9768,9769,9771,9773,9802,9923,9924,9974,9975,10015,10050,10161,10219,10285,10368,10386,10391,10411,3,2875,2876,2877,2879,2880,2886,2887,2889,2890,2891,2892,2893,2894,2896,2897,2898,2906,2909,2910,2911,2912,2913,2917,2918,2919,2920,2921,2927,2928,2929,2930,2931,2932,2933,2934,2936,2939,2942,2943,2946,2947,2948,2951,2953,2955,2956,2957,2964,2965,2966,2968,2969,2971,2972,2986,2988,2991,2992,2994,2995,3003,3004,3012,3013,3014,3015,3018,3019,3020,3026,3033,3034,3035,3040,3070,3071,3091,3093,3094,3095,3096,3116,3117,3122,3144,5397,5400,5531,5570,5716,5717,5718,5802,5904,5936,5970,5986,5988,5994,6056,6057,6058,6059,6067,6104,6236,6276,6286,6308,6342,6379,6526,6531,6568,6569,6593,6595,6597,6604,6605,6606,6607,6608,6609,6610,6611,6695,6764,6765,6854,6887,6888,6927,6928,6947,7066,7080,7134,7152,7153,7159,7180,7211,7213,7259,7279,7280,7298,7299,7336,7381,7382,7478,7549,7550,7551,7552,7567,7599,7650,7651,7660,7665,7666,7677,7708,7709,7710,7711,7850,7851,7853,7855,7861,7862,7970,8068,8074,8075,8085,8123,8124,8202,8242,8296,8318,8319,8389,8483,8555,8556,8560,8593,8654,8655,8722,8741,8742,8743,8744,8894,9156,9157,9228,9242,9295,9296,9416,9448,9474,9508,9549,9742,9865,10010,10188,10244,10246,6676,6677,6767])).
% 157.85/157.59 cnf(13469,plain,
% 157.85/157.59 (~E(f866(a119,x134691),x134691)),
% 157.85/157.59 inference(rename_variables,[],[4716])).
% 157.85/157.59 cnf(13474,plain,
% 157.85/157.59 (P107(f866(f866(f243(a1),f2(a1)),f866(f107(a1),x134741)))),
% 157.85/157.59 inference(rename_variables,[],[3654])).
% 157.85/157.59 cnf(13477,plain,
% 157.85/157.59 (P107(f866(f866(f243(a930),f2(a930)),x134771))),
% 157.85/157.59 inference(rename_variables,[],[3575])).
% 157.85/157.59 cnf(13481,plain,
% 157.85/157.59 (~E(f866(a119,x134811),f2(a930))),
% 157.85/157.59 inference(rename_variables,[],[4728])).
% 157.85/157.59 cnf(13486,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x134861),x134862),f195(f937(x134861,a925))))),
% 157.85/157.59 inference(rename_variables,[],[4790])).
% 157.85/157.59 cnf(13489,plain,
% 157.85/157.59 (P107(f866(f66(a930),f312(a930,x134891,x134892)))),
% 157.85/157.59 inference(rename_variables,[],[3761])).
% 157.85/157.59 cnf(13490,plain,
% 157.85/157.59 (E(f866(f866(f242(a930),f866(a119,x134901)),f866(a119,x134902)),f866(a119,f866(f866(f242(a930),x134901),x134902)))),
% 157.85/157.59 inference(rename_variables,[],[3725])).
% 157.85/157.59 cnf(13493,plain,
% 157.85/157.59 (P107(f866(f66(a930),f312(a930,x134931,x134932)))),
% 157.85/157.59 inference(rename_variables,[],[3761])).
% 157.85/157.59 cnf(13494,plain,
% 157.85/157.59 (E(f866(f866(f241(a930),f866(a119,x134941)),f866(a119,x134942)),f866(a119,f866(f866(f241(a930),x134941),x134942)))),
% 157.85/157.59 inference(rename_variables,[],[3724])).
% 157.85/157.59 cnf(13497,plain,
% 157.85/157.59 (P107(f866(f66(a930),f312(a930,x134971,x134972)))),
% 157.85/157.59 inference(rename_variables,[],[3761])).
% 157.85/157.59 cnf(13506,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x135061),x135062),f195(f937(x135061,a925))))),
% 157.85/157.59 inference(rename_variables,[],[4790])).
% 157.85/157.59 cnf(13507,plain,
% 157.85/157.59 (E(f866(f866(f16(x135071,x135072),x135073),x135074),x135073)),
% 157.85/157.59 inference(rename_variables,[],[3546])).
% 157.85/157.59 cnf(13510,plain,
% 157.85/157.59 (P107(f866(f866(f243(f937(x135101,a925)),f866(f179(x135101),f866(f143(x135101,x135102),x135103))),f866(f179(x135101),x135103)))),
% 157.85/157.59 inference(rename_variables,[],[4203])).
% 157.85/157.59 cnf(13511,plain,
% 157.85/157.59 (E(f866(f866(f16(x135111,x135112),x135113),x135114),x135113)),
% 157.85/157.59 inference(rename_variables,[],[3546])).
% 157.85/157.59 cnf(13514,plain,
% 157.85/157.59 (P107(f866(f866(f243(f937(x135141,a925)),f866(f179(x135141),f866(f866(f182(x135141),x135142),x135143))),f866(f179(x135141),x135143)))),
% 157.85/157.59 inference(rename_variables,[],[4246])).
% 157.85/157.59 cnf(13515,plain,
% 157.85/157.59 (E(f866(f866(f16(x135151,x135152),x135153),x135154),x135153)),
% 157.85/157.59 inference(rename_variables,[],[3546])).
% 157.85/157.59 cnf(13519,plain,
% 157.85/157.59 (E(f866(f866(f16(x135191,x135192),x135193),x135194),x135193)),
% 157.85/157.59 inference(rename_variables,[],[3546])).
% 157.85/157.59 cnf(13532,plain,
% 157.85/157.59 (P107(f866(f866(f243(a1),f2(a1)),f866(f107(a1),x135321)))),
% 157.85/157.59 inference(rename_variables,[],[3654])).
% 157.85/157.59 cnf(13537,plain,
% 157.85/157.59 (P25(x135371,x135371,f5(x135371),x135372)),
% 157.85/157.59 inference(rename_variables,[],[3790])).
% 157.85/157.59 cnf(13540,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x135401),x135402),f195(f937(x135401,a925))))),
% 157.85/157.59 inference(rename_variables,[],[4790])).
% 157.85/157.59 cnf(13541,plain,
% 157.85/157.59 (E(f866(f292(x135411,x135411),f271(x135411,x135412)),x135412)),
% 157.85/157.59 inference(rename_variables,[],[3515])).
% 157.85/157.59 cnf(13542,plain,
% 157.85/157.59 (P25(x135421,x135421,f5(x135421),x135422)),
% 157.85/157.59 inference(rename_variables,[],[3790])).
% 157.85/157.59 cnf(13546,plain,
% 157.85/157.59 (E(f866(f292(x135461,x135461),f271(x135461,x135462)),x135462)),
% 157.85/157.59 inference(rename_variables,[],[3515])).
% 157.85/157.59 cnf(13560,plain,
% 157.85/157.59 (P107(f866(f866(f243(a930),f2(a930)),x135601))),
% 157.85/157.59 inference(rename_variables,[],[3575])).
% 157.85/157.59 cnf(13561,plain,
% 157.85/157.59 (P107(f866(f866(f244(a930),f2(a930)),f866(a119,x135611)))),
% 157.85/157.59 inference(rename_variables,[],[3634])).
% 157.85/157.59 cnf(13562,plain,
% 157.85/157.59 (E(f866(f292(x135621,x135621),f271(x135621,x135622)),x135622)),
% 157.85/157.59 inference(rename_variables,[],[3515])).
% 157.85/157.59 cnf(13646,plain,
% 157.85/157.59 (P107(f866(f866(f244(a1),f2(a1)),f866(f81(a1),f84(a1))))),
% 157.85/157.59 inference(scs_inference,[],[4218,12804,12826,12969,12971,12973,3790,11415,12480,12577,12580,12672,12714,12718,12726,12798,12954,12956,13392,13398,13403,13407,13413,13416,13440,13537,13542,3799,12544,13042,13044,3807,3460,12034,12037,13193,3524,13020,13022,13024,3525,12963,3491,12880,4751,4752,12065,4494,13026,3529,12990,3360,3422,12934,3423,13016,3424,3425,3426,12754,13011,4750,3853,4716,10494,10504,10517,10528,10531,10603,10638,10641,10644,10746,10881,11193,11385,11388,11407,11410,11609,11708,11715,11729,11775,11778,11814,11829,11892,11949,11968,12266,12294,12306,12335,12341,12436,12540,12707,12768,12913,13461,13469,3610,3573,13007,3758,12238,3475,4728,10730,10830,11295,11395,13057,13061,13144,13481,3154,3155,3157,3158,3161,3162,3164,3165,3166,3172,3173,3174,3178,3179,3182,3183,3188,3192,3198,3201,3208,3211,3212,3214,3218,3219,3227,3233,3234,3241,3247,3251,3253,3256,3257,3258,3259,3272,3278,3279,3285,3289,3290,3297,3304,3305,3307,3308,3314,3315,3316,3317,3324,3337,4711,3341,3421,4712,3891,4121,11999,3396,11705,3537,3512,3515,10566,10569,10665,10668,10984,11720,11723,11798,11840,11879,11884,11952,11994,12454,12648,12858,12915,12938,12942,12948,12950,12952,12978,12980,12984,13033,13056,13060,13265,13431,13541,13546,13562,3486,12739,12743,12747,3492,3501,4013,4321,3469,13327,3621,12801,12883,3385,3386,3526,3752,4107,11751,3609,3451,3382,3412,3872,3407,3607,4227,4115,3934,4674,3393,3394,3366,3372,4026,3432,3611,11143,11267,12541,12758,3485,4192,4741,10557,10727,11606,12699,12740,12744,4748,12711,3546,12089,12092,13361,13451,13507,13511,13515,13519,4150,4788,11321,11420,11656,11659,3520,3953,3543,3658,3878,3650,4766,3625,12919,12921,12999,3448,10630,10960,3449,4775,3711,3440,3363,3471,11741,4335,12729,12870,4194,11341,11476,11537,12683,12689,12815,12818,12848,4806,11245,11489,11600,11626,11664,11670,12627,4807,11374,11492,11603,4808,11495,11548,4809,11555,4810,3470,3750,12583,12624,12710,3918,3700,4608,4609,3734,3771,4739,11734,3895,3855,3897,4070,3822,13248,13252,13256,13260,13270,4117,12574,3736,3996,3622,10649,10769,10847,10920,10923,10963,11067,11311,11926,12083,12178,12262,12328,12357,12407,12445,12518,12521,12852,13127,13166,13169,13231,13460,13465,4006,11985,3539,3634,11813,12104,13561,3817,4781,10534,10537,10563,10690,10865,11075,11088,11203,11648,11744,11925,12153,12158,12177,12383,12386,12466,12630,12733,13073,13092,13095,13119,13170,13343,13348,13368,13373,4794,11856,11887,11922,11929,11965,13179,13183,3993,3759,3761,12283,13098,13101,13104,13107,13137,13140,13489,13493,13497,4142,3724,13494,3725,13490,3581,3583,3557,4778,3447,4736,3944,4257,3743,4795,4328,11623,3877,3594,12110,12113,12548,12652,12829,4786,10522,10525,10698,10793,10812,10819,10842,10850,10853,10870,11058,11298,11517,11807,11901,12056,12171,12174,4297,4256,12255,12598,4203,11140,12439,12608,12757,13510,4246,13514,4251,11344,12477,12547,12607,12651,13364,4252,3919,11933,12265,12414,12485,12531,4285,3936,10693,10790,11347,11425,11510,11574,12435,12499,12763,12825,12845,12855,13334,13397,13402,13422,13443,4798,11091,11500,12611,13410,3555,10658,10756,10906,10970,11047,11094,11097,11128,11151,11187,11225,11261,11699,12059,12107,12235,12293,12309,12312,12315,12318,12492,12506,12509,12512,12515,12591,12655,12774,12821,13120,13143,13205,13223,13234,13239,13242,13245,13278,13289,13302,13354,13379,13382,3556,10685,10741,10975,11070,11190,11832,12138,12141,12150,12241,12252,12271,12276,12321,12344,12364,13134,13282,13305,13344,13349,13369,13374,3630,12469,13202,13249,13253,13257,13261,13271,13275,4777,10574,10606,11112,11154,11163,12013,12040,12209,12212,12215,12218,12305,12324,12327,12340,12395,12398,12401,12404,12559,12562,12658,12661,12767,12807,12892,3707,10835,10926,11198,11242,11479,11482,11563,11645,11817,12068,12706,12895,13326,4790,11121,11234,11252,11255,11324,11327,11338,11441,11449,11463,11503,11522,11531,11571,11612,11617,11620,11639,11642,11673,11678,11681,11684,11687,11932,12086,12119,12389,12392,12426,12470,12495,12636,12680,12686,12786,12789,12811,12869,12875,12886,12905,13201,13217,13220,13315,13435,13454,13457,13486,13506,13540,3615,10957,10987,10996,10999,11002,11592,12808,12822,13180,13184,13187,13190,3654,13474,13532,3647,4074,4011,10609,11988,12016,13161,4787,10554,10945,10948,11444,11460,11948,12004,12044,12069,12082,12168,12197,12200,12203,12206,12465,13385,3575,10990,11148,11218,12017,12167,12369,12567,12592,13214,13477,13560,4036,12116,13114,4376,3765,4784,4048,4082,4769,4772,4773,3532,3536,4771,4770,4501,4545,3867,11981,4472,11839,4800,10856,10859,4805,11330,11333,11525,11636,11653,11693,4160,11690,12043,12047,12717,12725,12814,13330,13391,4001,11258,11264,11282,12290,12419,12498,12782,3851,11400,11528,12524,12633,12643,12722,12777,12785,12902,13337,4333,4003,10993,11363,11534,11568,11579,12721,12771,13427,3818,10909,10912,11005,11174,3820,4803,11982,4799,13082,4804,10749,10862,11700,12586,12595,12639,12839,12842,4433,11131,12604,12619,12642,4339,4035,12908,3979,3980,4801,10579,10582,10951,10954,11853,12048,12851,480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% 157.85/157.59 cnf(13858,plain,
% 157.85/157.59 (~E(f866(f866(f158(x138581),x138582),x138583),x138583)),
% 157.85/157.59 inference(rename_variables,[],[4741])).
% 157.85/157.59 cnf(13861,plain,
% 157.85/157.59 (P107(f866(f866(f243(a930),f2(a930)),x138611))),
% 157.85/157.59 inference(rename_variables,[],[3575])).
% 157.85/157.59 cnf(13872,plain,
% 157.85/157.59 (~E(f866(f866(f158(x138721),x138722),x138723),f120(x138721))),
% 157.85/157.59 inference(rename_variables,[],[4748])).
% 157.85/157.59 cnf(13877,plain,
% 157.85/157.59 (~E(f866(f866(f158(x138771),x138772),x138773),x138773)),
% 157.85/157.59 inference(rename_variables,[],[4741])).
% 157.85/157.59 cnf(13880,plain,
% 157.85/157.59 (P107(f866(f866(f336(x138801),f866(x138802,x138803)),f866(f317(x138804,x138801,x138802),f250(f937(x138804,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[4160])).
% 157.85/157.59 cnf(13897,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x138971),x138972),f195(f937(x138971,a925))))),
% 157.85/157.59 inference(rename_variables,[],[4790])).
% 157.85/157.59 cnf(13907,plain,
% 157.85/157.59 (~P107(f866(f866(f336(f936(x139071,x139071)),x139072),f271(x139071,f195(f937(x139071,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11251])).
% 157.85/157.59 cnf(13929,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x139291),x139292),f866(f317(x139293,x139291,x139294),f195(f937(x139293,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11502])).
% 157.85/157.59 cnf(13941,plain,
% 157.85/157.59 (~P107(f866(f866(f336(f936(x139411,x139411)),x139412),f271(x139411,f195(f937(x139411,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11251])).
% 157.85/157.59 cnf(13944,plain,
% 157.85/157.59 (P107(f866(f866(f243(a930),x139441),f866(f866(f86(a930),x139441),x139442)))),
% 157.85/157.59 inference(rename_variables,[],[3820])).
% 157.85/157.59 cnf(13957,plain,
% 157.85/157.59 (P107(f866(f866(f244(a1),f866(f866(f23(a1),x139571),f84(a1))),x139571))),
% 157.85/157.59 inference(rename_variables,[],[11069])).
% 157.85/157.59 cnf(13960,plain,
% 157.85/157.59 (~E(f866(f866(f316(x139601),x139602),x139603),f195(f937(x139601,a925)))),
% 157.85/157.59 inference(rename_variables,[],[4766])).
% 157.85/157.59 cnf(13963,plain,
% 157.85/157.59 (~P107(f866(f866(f195(f937(x139631,f937(x139632,a925))),x139633),x139634))),
% 157.85/157.59 inference(rename_variables,[],[4804])).
% 157.85/157.59 cnf(13975,plain,
% 157.85/157.59 (~P107(f866(f866(f336(f936(x139751,x139751)),x139752),f271(x139751,f195(f937(x139751,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11251])).
% 157.85/157.59 cnf(13980,plain,
% 157.85/157.59 (P107(f866(f866(f243(f937(x139801,a925)),f866(f179(x139801),f183(x139801,x139802,x139803))),f866(f179(x139801),x139802)))),
% 157.85/157.59 inference(rename_variables,[],[4251])).
% 157.85/157.59 cnf(13997,plain,
% 157.85/157.59 (~P107(f866(f866(f336(f936(x139971,x139971)),x139972),f271(x139971,f195(f937(x139971,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11251])).
% 157.85/157.59 cnf(14000,plain,
% 157.85/157.59 (P107(f866(f866(f243(f937(x140001,a925)),f866(f179(x140001),f183(x140001,x140002,x140003))),f866(f179(x140001),x140002)))),
% 157.85/157.59 inference(rename_variables,[],[4251])).
% 157.85/157.59 cnf(14010,plain,
% 157.85/157.59 (~P107(f866(f866(f336(f936(x140101,x140101)),x140102),f271(x140101,f195(f937(x140101,a925)))))),
% 157.85/157.59 inference(rename_variables,[],[11251])).
% 157.85/157.59 cnf(14046,plain,
% 157.85/157.59 (~P107(f866(f866(f336(x140461),x140462),f195(f937(x140461,a925))))),
% 157.85/157.59 inference(rename_variables,[],[4790])).
% 157.85/157.59 cnf(14049,plain,
% 157.85/157.59 (~P107(f866(f866(f244(a930),x140491),x140491))),
% 157.85/157.59 inference(rename_variables,[],[4777])).
% 157.85/157.59 cnf(14072,plain,
% 157.85/157.59 (P107(f866(f866(f243(a930),f2(a930)),x140721))),
% 157.85/157.59 inference(rename_variables,[],[3575])).
% 157.85/157.59 cnf(14099,plain,
% 157.85/157.59 (P107(f866(f866(f243(f937(x140991,a925)),f866(f179(x140991),f183(x140991,x140992,x140993))),f866(f179(x140991),x140992)))),
% 157.85/157.59 inference(rename_variables,[],[4251])).
% 157.85/157.59 cnf(14135,plain,
% 157.85/157.59 (~P107(f866(f866(f195(f937(x141351,f937(x141352,a925))),x141353),x141354))),
% 157.85/157.59 inference(rename_variables,[],[4804])).
% 157.85/157.59 cnf(14179,plain,
% 157.85/157.59 ($false),
% 157.85/157.59 inference(scs_inference,[],[3993,3583,4297,4335,3341,4803,3557,4769,4778,4194,3630,4806,3647,4006,4160,13880,4790,13897,14046,4251,13980,14000,14099,3654,4741,13858,13877,4748,13872,4766,13960,3556,4011,3575,13861,14072,4001,3851,3818,3820,13944,4004,3510,4807,4810,4777,14049,4787,4799,4804,13963,14135,4801,3758,10589,13467,12834,11675,13646,13116,10899,11392,11509,11069,13957,12137,11533,11397,11238,11302,13378,13381,11014,12526,12632,12133,12135,11251,13907,13941,13975,13997,14010,11254,11502,13929,11611,11004,12397,11692,12797,11539,11269,11543,11412,3185,9,5446,6580,7598,6592,9858,5709,6090,9309,4845,7706,8140,5420,5564,5952,9049,7013,6022,5236,7800,10397,9463,10306,9481,8924,5487,8237,9089,9480,5557,6992,8711,6155,10396,7607,6062,6453,6680,6735,8797,6689,5304,6182,6120,6447,10085,10460,5808,6439,7219,6374,6920,7071,6629,8773,6897,10021,8658,9853,5959,7652,9479,9895,10179,5902,9326,7151,8557,9363,9834,6033,5429,7758,8292,6747,7905,10190,6164,6519,7715,7753,7887,9889,5585,5029,6084,6633,9851,5821,7629,5474,8866,5809,8001,10478,5822,6077,8858,8618,9520,6733,7510,7634,7963,9567,9364,7584,5668,5955,6002,6061,6444,6527,7012,9028,2,6803,6995,8712,7207,7278,6285,9544,8823,6577,5591,6646,6844,9154,8575,8905,8774,4934]),
% 157.85/157.59 ['proof']).
% 157.85/157.59 % SZS output end Proof
% 157.85/157.59 % Total time :143.320000s
%------------------------------------------------------------------------------